DOCUMENT RESUME

ED 476 226 HE 035 845

AUTHOR Haignere, Lois

TITLE Paychecks: A Guide to Conducting Salary-Equity Studies forHigher Education Faculty. Second Edition.

INSTITUTION American Association of Univ. Professors, Washington, DC.;United Univ. Professions, Albany, NY.

ISBN ISBN-0-9649548-2-6PUB DATE 2002-00-00NOTE 110p.; Also produced by Haignere, Inc.AVAILABLE FROM American Association of University Professors, 1012

Fourteenth Street, NW, Suite 500, Washington, DC 20005(members, $18; nonmembers, $28). Tel: 202-737-5900; Web site:http://www.aaup.org.

PUB TYPE Guides Non-Classroom (055)EDRS PRICE EDRS Price MF01/PC05 Plus Postage.DESCRIPTORS *College Faculty; Contract Salaries; Databases; *Equal

Opportunities (Jobs); Evaluation Methods; Higher Education;*Research Methodology; Sex Discrimination; *Teacher Salaries

ABSTRACT

This guidebook is designed as a resource for those in thehigher education community who want to conduct analyses of bias in facultysalaries or to understand and interpret the results of studies presented tothem. This edition will help readers detect gender and face bias in currentrank, select a salary-equity consultant, understand different perspectives onhow bias occurs and ways to remedy it, and accomplish many other tasksrelated to ensuring equity in faculty salaries. The chapters are: (1)

"Introduction to Equal Pay for Equal Work" (Lois Haignere); (2)

"Considerations before Launching a Salary Study" (Lois Haignere and DonnaEuben); (3) "Database Decisions and Development" (Lois Haignere and YangjingLin); (4) "Gender and Race Bias in Current Rank" (Lois Haignere and BonnieEisenberg); (5) "Gender and Race Bias in Salaries" (Lois Haignere); (6)

"Small Errors with Big Consequences" (Lois Haignere); and (7) "DiagnosisDynamics and Treatment Turmoil" (Lois Haignere). Nine appendixes containsupplemental information in essays on specific topics, such as studymethodology, contract language, discrimination law, and statisticaltechniques. (Contains 10 tables, 9 figures, and 154 references.) (SLD)

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Paychecks

3

Paychecks

A Guide to Conducting Salary-Equity Studiesfor Higher Education Faculty

Principal author: Lois Haignere

Second Edition

American Association of University Professors

Washington, D.C.

4

© 2002 American Association of University Professors, Lois Haignere, Inc., UnitedUniversity Professions. All rights reserved. Reproductions of excerpts for nonprofit useis hereby granted to educators, scholars, students, nonprofit educational institutions,and government. Any reproduction for commercial use without written permission isstrictly prohibited.

American Association of University Professors1012 Fourteenth St., NW, Suite 500Washington, DC 20005

Lois Haignere, Inc.40 Parkwood EastAlbany, NY 12203-3629

United University Professions159 Wolf RoadAlbany, NY 12205

First published 1996 by United University ProfessionsSecond edition 2002ISBN 0-9649548-2-6

Contents

Contributors ix

Figures and Tables xi

Preface xiiiAcknowledgments xv

1. Introduction to Equal Pay for Equal Work 1

Lois Haignere

Cost of Salary Inequity 1

Unconscious Ideology 1

Objectives of This Book 2Neglected Groups 3White Males 3SUNY Studies 3Limits on Coverage 3

Demographics 4Regression Analysis 4Quality of Regression Results 6Curiosity, Not Conviction 6

2. Considerations Before Launching a Salary Study 9

Lois Haignere and Donna Euben

Politics of Technical Decisions 9Basic Requirements 10Salary-Equity Consultants 12Happy Endings 13

3. Database Decisions and Development 17Lois Haignere and Yangjing Lin

Policy-Making Committee 17Study Population 18Data Collection 18Variables and Possible Substitutes 19Variables for Verification of Data 23Cleaning of Data 24

4. Gender and Race Bias in Current Rank 27Lois Haignere and Bonnie Eisenberg

Details and Options 27Frequency Tables 28Categorical Modeling 28Limitations of Categorical Modeling 31Event History Analysis 31Next Steps 34

5. Gender and Race Bias in Salaries 37Lois Haignere

Re-engineered Variables 37Redesigned Categorical Variables: Dummies 39Suggested Categorical Variables 39Three Multiple-Regression Approaches 41Recommendations 43Two Additional Checks 45

6. Small Errors with Big Consequences 49Lois Haignere

Standardization of the Coefficients 49Exclusion of Certain Categories 49Dropping of Outliers 51Tainted Variables 51The Significance of Significance 53Divide and Hide 55Stepwise Abuse 55Dropping of Gender and Race 56Summary 57

7. Diagnosis Dynamics and Treatment Turmoil 59Lois Haignere

Diagnosis Dynamics 59Pockets of Bias 60Case Study 61Institutional-Systemic Remedy 61Longevity 63Flagging and Other Remedies 63Toward a More Permanent Solution 66

Appendices

A. Multiple Regression and Gender- andRace-Equity in Salaries 69Lois Haignere

Dummy Variables 71Validity of Regression Equation 72Interpretation of Results 72

B. The Twelve SONY Data Sets 75Lois Haignere

C. Salary-Equity Contract Language 77Donna Euben

Joint Faculty-Administration Committees 77Money 78

vi7

Minimum-Salary Scales 78

Grievance Procedures 79

D. U.S. Laws on Gender-Based Wage Discrimination 81

Donna Euben

Equal Pay Act 81Title VII of Civil Rights Act 81

Title IX 82Executive Orders 82

E. Activist Strategies When All Else Fails 83

Malta Levine

F. Categorical Modeling 85Lois Haignere and Bonnie Eisenberg

Data 85

Overall Model Statistic 86

G. Redundancy Problems 87Lois Haignere and Bonnie Eisenberg

H. Promotion and Salary Inequities BetweenMen and Women Faculty 89Robert Johnson and Dorothy Kovacevich

Academic Rank As a Measure of Productivity 89Academic Rank As a Reflection of Status 89Conceptual and Statistical Models 90Data . 91Findings 91Conclusion 93

I. Locating Outliers 95

Lois Haignere and Yangjing Lin

Studentized Residual 95Hat Matrix Diagonal Element 95Cook's Distance 95Comparison of the Three Outlier Measures 96

Glossary 97

Bibliography 101

VII

Contributors

Lois Haignere, principalauthor of Paychecks, ispresident and sole ownerof Haignere, Inc., locatedin Albany, New York<www.payequityresearch.corn>. She is a recognizedexpert on salary equity atinstitutions of highereducation, and she con-sults internationally onpay equity and equal pay.In her more than fifteenyears of research andconsulting, she has con-ducted hundreds of stud-ies of salary disparities inuniversities, governmentagencies, and unions.Through her publications,she has made the statisti-cal results of these stud-ies understandable to awide audience. Haignere,who holds a Ph.D. insociology, formerlyserved as director ofresearch for the Centerfor Women inGovernment at the StateUniversity of New Yorkat Albany and director ofresearch for UnitedUniversity Professions.

Bonnie Eisenberg, a statis-tical programmer, has tenyears of experience in con-ducting studies of salaryequity at institutions ofhigher education. Shereceived an M.A. in publichealth from YaleUniversity's School ofMedicine in 1996 and hasserved as a research assis-tant for United UniversityProfessions and Haignere,Inc.

Donna Euben, counsel atthe American Associationof University Professors,staffs the Association'sCommittee on the Status ofWomen in the AcademicProfession. She is a gradu-ate of Oberlin College andBrooklyn Law School(magna cum laude), whereshe served as editor-in-chief of Brooklyn LawReview. She clerked withJustice Handler of the NewJersey Supreme Court.

Robert Johnson, professorof sociology at Kent StateUniversity, specializes in

medical sociology, lifecourse and aging studies,and the social psychologyof the self. His researchinterests include the socialand psychological corre-lates of physical and men-tal health. Johnson's recentpublications haveappeared in the Journal ofHealth and Social Behavior,the Gerontologist, and theJournal of Aging and Health.

Dorothy Kovacevich, pro-fessor emerita of specialeducation at Kent StateUniversity, was a leader ofher campus AAUP chap-ter's Committee on theStatus of Women in theAcademic Profession andan activist for equal payand status for women fac-ulty at her university. Shewas also the plaintiff inKovacevich v. Kent StateUniversity, 224 F.3d 806(6th Cir. 2000).

Maita Levine, professoremerita of mathematics atthe University ofCincinnati, joined the fac-

ix 9

ulty at Cincinnati in 1963and received her Ph.D.from Ohio StateUniversity in 1970. She is amember of Phi Beta Kappaand Sigma Xi and a recipi-ent of a National ScienceFoundation ScienceFaculty Fellowship. Shehas also served as firstvice president of theAmerican Association ofUniversity Professors,chair of the Association'sOhio conference, and pres-ident of the Association'sUniversity of Cincinnatichapter.

Yangjing Lin, senior pro-gram analyst at AutomaticData Processing, receiveda Ph.D. in educationaladministration and policystudies from the StateUniversity of New York atAlbany in 1993. He for-merly served as a researchassociate for UnitedUniversity Professions,where he studied salarydisparities based on gen-der and race among highereducation faculty.

Figures and Tables

Figures1.1 Growth in the Percentage of Women Among Full-Time Faculty in the United

States, Selected Years, 1974-2000

1.2 Women's Salaries As a Percentage of Men's Salaries Among Full-Time Faculty inthe United States, Selected Years, 1976-2000

5.1 Accelerating Curve

5.2 Decelerating Curve

6.1 Salaries for a Two-Year College, State University of New York

7.1 Salaries Before Remedy

7.2 Salaries After Remedy

7.3 Below-the-Line Remedy

7.4 Below-the-Line Remedy Extended to All

A.1 Salary by Years of Service

A.2 Salary by Years of Service

Tables4.1 Frequency Distribution for Hypothetical Institution

4.2 Categorical Modeling: A Pairwise Comparison for Gender Bias

4.3 Example of Categorical-Modeling Analysis of Rank

4.4 Analysis of Promotion-Probability Table: Transition from Associateto Full Professor

4.5 Event History of Promotion Results

A.1 Predicted Salaries of Male and Female Faculty in Three Disciplines

A.2 Sample Computer Output for Proxy College: Regression Analysisof Faculty Salaries

B.1 Faculty Composition by Race and Gender at Twelve State Universityof New York Institutions

H.1 Hazard Rate and Cumulative Proportion Not Promoted to AssociateProfessor, by Sex and Year Since Highest Degree

H.2 Hazard Rate and Cumulative Proportion Not Promoted to Full Professor,by Sex and Year Since Highest Degree

xi 0

Preface

'n 1993 United University Professions (UUP) released a study of gender- and race-based salary disparities among faculty and professional staff at the State University ofNew York (SUNY). Lois Haignere, one of the nation's leading experts on pay equity

and equal pay, conducted the study on the twenty-nine SUNY campuses on which theUUP acts as a collective bargaining agent. The findings resulted in $2.2 million in wageadjustments for some 5,700 women and minority faculty and professional staff.

Although the immediate outcome of the study was gratifying, no one tried to pretendthat the wage adjustments would make salary disparities in higher education a thing ofthe past. Recognizing that low pay for women and minorities inevitably undercuts allsalaries, UUP president William Scheuerman approached the American Federation ofTeachers for funding and support to pursue the issue. The result was the first edition ofthis book, Pay Checks: A Guide to Achieving Salary Equity in Higher Education, published in1996.

Since that time, the UUP's research department has maintained an ongoing interest instudying equal pay. Each year, it publishes a report titled Discounted Salaries and DismalPromotions: A UUP Research Report on Issues of Gender Equity at the State University of NewYork. The current edition of Pay Checks, now called Paychecks: A Guide to ConductingSalary-Equity Studies for Higher Education Faculty, is further evidence of the UUP'sinvolvement in the subject. The book results from a collaboration among the UUP, theAmerican Association of University Professors (AAUP), and Haignere, Inc.

The SUNY-UUP research, like that of hundreds of other colleges and universities, wasbuilt on techniques applied by the AAUP to identify and remedy salary inequalities. TheAAUP pioneered the movement to correct salary inequities between female and male pro-fessors in the academy through its Committee on the Status of Women in the AcademicProfession. The first project of the newly created committee in 1917 was a "preliminarystudy" of 176 institutions of higher education. It found that 47 percent of the coeduca-tional colleges and 27 percent of the women's colleges studied "frankly admitted thatwomen are given less salary and lower rank than men for the same work."

Over the decades, the AAUP has continued to help faculty members andadministrators promote gender equity in compensation. In 1977 the AAUP developed theHigher Education Salary Evaluation Kit, which hundreds of administrators and facultymembers have used to examine salary structures for gender inequities and ways tocorrect them. In addition, members of the AAUP's women's committee have offered theacademic community detailed strategies for documenting and rectifying gender-basedsalary inequities.

Each year, the AAUP publishes a salary survey that provides comparative salarydata by gender. From time to time, the Association also issues special research reportsthat examine women's salaries in the academy. In 1998 the AAUP published Disparities inthe Salaries and Appointments of Academic Women and Men: An Update of a 1988 Report ofCommittee Won the Status of Women in the Academic Profession. The report found thatsubstantial disparities in salary, rank, and tenure status between male and female facultymembers persist despite the increasing proportion of women in the academic profession.

On the local level, AAUP chapters at colleges and universities across the countryhave helped establish policies to correct salary disparities. These policies are oftenincluded in faculty handbooks or collective bargaining agreements. In addition, the

11

AAUP supports litigation to promote salary equity on college and university campusesand offers technical advice to faculty members and administrators who want to conductsalary and promotion studies. Hundreds of colleges and universities have used the tech-niques pioneered by the AAUP to identify and rectify salary inequities.

Lois Haignere began her research on salaries at SUNY's Center for Women andGovernment, where she directed projects investigating pay equity.' In 1988 she becamedirector of research at the WP. Over the next twelve years, she analyzed data sets fromSUNY campuses ranging from two-year technical schools to research universities. Thediversity of the SUNY system allowed her to observe the effects of different statisticalapproaches on different types and sizes of institutions.

Subsequent to her work with SUNY, Haignere conducted equal pay research at otherU.S. and Canadian colleges and universities. In 1998 she launched her own firm,Haignere, Inc., and has since carried out equal pay and pay equity projects for manyunions and institutions of higher education, including the University of Maine HigherEducation System, as well as the Canadian Human Rights Commission, the City ofToronto, and Toronto Public Libraries. For details, see <www.payequityresearch.com>.

To inform the writing of Paychecks, twelve SUNY institutions were selected on which totest the methods discussed. Selections were made with an eye toward including data setsranging widely in size and content within three institutional types. Four two-year col-leges, four four-year colleges, and four research universities werechosen. (For more detailed information about these twelve institutions, see appendix B.)

The contributors to this book have used their combined experience across thedecades to help readers appreciate the importance of faculty salary analyses, learn how toconduct them, and understand the analyses that have been done by others.

Note1. Pay equity, also called comparable worth, refers to the issue of paying those with traditionallyfemale job titles, such as nurse, secretary, or teacher's aide, what men with jobs requiring compara-ble levels of skills and responsibilities would be paid. It is an area of gender bias not covered inthis guide.

12Iry

Acknowledgments

Mary W. Gray, professor of mathematics at American University, was instrumental inproviding direction for this edition of Paychecks. The contributors are grateful to herfor her thorough review of the manuscript and the numerous insights and sugges-

tions she offered. The enthusiasm of Maita Levine, professor emerita of mathematics at theUniversity of Cincinnati, helped initiate the collaboration that resulted in this second edition,and her commitment to the project is reflected in many ways in the final product. Members ofthe AAUP's Committee on the Status of Women in the Academic Profession also participatedin bringing this project to fruition. The AAUP's editorial staff deserves recognition for coordi-nating the editing and production of the guide.

Special thanks to those who reviewed the final draft of the manuscript, including Mary W.Gray, Marica L. Bellas of the University of Cincinnati, Myra Marx Ferree of the University ofWisconsin, Thomas Kriger of United University Professions, and Herbert I. Brown of the StateUniversity of New York at Albany. Their comments were extremely helpful.

Sincere thanks also to the research assistants who worked on the project: Michelle L.Johnson, Sharon Baker, and John McCarthy.

xv 10

The best interests of labor require the admission of women to full citizenship as a matter ofjustice to them and as a necessary step towards insuring and raising the scale of wages for all.

American Federation of Labor ResolutionAmerican Federationist

April 1919

ONE

Introduction to Equal Pay for Equal WorkBy Lois Haignere

Institutions of higher education have played animportant role in establishing the fundamental prin-ciple that discrimination based on race or sex is

unfair to individuals and counterproductive for society.Yet many of the same features that give vitality to high-er education leave it vulnerable to salary discrimination,however inadvertent. Academic departments, for exam-ple, enjoy great autonomy in appointing faculty mem-bers and setting their salaries. Professors believe this lat-itude, which is grounded in historic respect for academ-ic freedom, market forces, and peer review, helps raisethe quality of their departments and institutions.

Unlike universities, most large employers have cen-tralized personnel procedures that lead to relatively uni-form policies for hiring and salary setting, including jobclassification and job evaluation, across different depart-ments and units. These uniform procedures help guardagainst gender and race bias in salaries.

Costs of Salary InequityEven relatively small differences in initial salary growover time. If annual across-the-board salary incrementsaverage 3.5 percent, a woman or minority male whoearns $1,000 less than a colleague at the outset wouldaccumulate $84,550 less over a forty-year career. If$1,000 a year were invested or saved in an account at 5percent interest, at the end of forty years the accountwould hold $210,684. For a salary difference of $2,000,this figure would more than double, owing to com-pounding. After forty years, the highest salary of a facul-ty member starting $1,000 behind her colleague wouldlag by $3,825, affecting her calculated pension. Pensionsderived from "percent of salary" contributions to annu-ity plans are similarly reduced. So, too, are maximumcontributions to supplemental retirement plans and anyemployee contributions to such plans. Add to this anybias that may occur in the allocation of discretionary ormerit awards and promotions, and it is clear that sys-temic bias is potentially very costly to the individual.

Fairness alone justifies a review of parity in facultysalaries. But benefits also accrue to the institution and toall faculty members, men and women alike, and theirfamilies. These benefits include a sense of inclusivenessamong faculty, improved academic morale, better over-all salaries, lower staff turnover, and an enhanced pub-lic image.

Unconscious IdeologySystemic discrimination seeps into salary decisions byway of unconscious ideology, which is prevalent in oursociety and affects everyone: men and women, mem-bers of minority groups, and those from nonminoritypopulations.

One determinant of starting pay is what a new hirerequests. It is commonly believed that some women andminority candidates ask for less than their white-malecounterparts. To the extent that this is so, it may stem, inpart, from their immediate experience with market bias,as evidenced by their previous salaries. We all haveinternalized biases that are expressed even when, intel-lectually, we know better.

In many contexts, the mere fact of identifying work ashaving been done by a woman results in its receiving alower evaluation and a lesser reward than when thesame work is attributed to a man. Research shows thatboth men and women judge artwork, literature,resumes, and scholarly articles attributed to womenmore harshly than these same items attributed to men(Goldberg 1968; Pheterson, Kiesler, and Goldberg 1971;Paludi and Bauer 1983). Moreover, for women, unlikemen, a favorable performance evaluation tends not tolead to promotion and advancement. And research indi-cates a strong inclination among managers to discrimi-nate against women when reviewing applications fortechnical-managerial jobs and making recommenda-tions for promotion or training (Rosen and Jerdee 1974;Ruble and Ruble 1982; Gerdes and Garber 1983; Valian1998).

14

Lois Haignere

Studies specific to higher education reveal thatdepartment chairs, deans, and members of facultysearch committees prefer curricula vitae attached tomale names over the same vitae attached to femalenames (Fide 11 1970; Top 1991; Steinpreis, Anders, andRitzke 1999; Davidson and Burke 2000). When searchcommittees in one study offered positions to hypotheti-cal candidates, female names were more likely toreceive non-tenure-track, lower-rank positions; onlymale names were offered full professorships (Fidel!1970).

The combined impact of the internalized biases ofcandidates themselves, of those providing references forcandidates, and of those involved in the hiring processcan mean that equally qualified women and minoritiesare hired to do the same work as their white-male coun-terparts at lower salaries. Promotion and discretionaryraises can also be affected.

Lest we fool ourselves that these phenomena havedisappeared with time or feminist enlightenment, it hasbeen shown that sex stereotypes persist, in spite of thewomen's movement, legal protections, and the profes-sional advancement of some women (Ruble and Ruble1982; Valian 1998; Top 1991; Toren 2000).

Over the past two decades, hundreds of institutionsin the United States and Canada have conducted statis-tical studies looking for possible salary bias (Gray 1993).The studies have been initiated variously by bargainingunits, women's groups, faculty members, and adminis-trators. The growing numbers of women and minorityfaculty members and the increasing availability of com-puterized human-resources data make it likely thatmore requests for statistical reviews of salaries will arisein coming years.

Objectives of This BookFrom a perspective of faculty employment and laborpolicy, what does it mean to review salaries statistical-ly? What are the political and legal implications? Whatinformation is gained and how useful is it? Can somestatistical methods actually hide or fail to make visiblegender and race bias? Will all faculty members under-stand the results of such reviews? The contributors tothis guidebook provide practical answers to these ques-tions based on our access to a wealth of data and ourexperience conducting analyses of salary bias.

The guidebook is designed to be a "full service"resource for those who want to conduct salary bias analy-ses or to understand and interpret results presented tothem. The objective of the contributors is twofold: to pre-sent information in a way that is not too technical for

2

nonstatistician faculty leaders and other policy makers tograsp, and to provide the technical information neededby statistical researchers to conduct multiple-regressionsalary reviews.

This dual purpose has led us to include a glossary andan appendix describing multiple regression as it is usedto study equity in salaries (appendix A). Recognizingthat our audience has a wide range of mathematicalexpertise, we have attempted to make this appendixunderstandable to anyone who can add, subtract, andmultiply. It walks readers through regression modelingand provides a basic guide to the computer output ofregression results. Those already familiar with multipleregression may find this appendix helpful in under-standing the relative strengths and weaknesses of thedifferent types of regression models we discuss (chapter5), why we suggest that certain approaches be avoided(chapter 6), and the recommendations we offer for mak-ing salary adjustments to remove bias (chapter 7).

This introductory chapter and chapters 2, 6, and 7give an overview of research methods and related reme-dies and discuss their political implications. Chapter 2describes what a multiple-regression salary study canreveal; the expertise, computer resources, and timeneeded to conduct such a study; the process for select-ing a consultant; and the value judgments and decisionsinvolved in conducting the study. Chapter 6 analyzesthe eight pitfalls that can mask gender and race bias.Too often, research decisions are touted as strictlymethodological, and their subjective nature and poten-tial political impact are ignored. Chapter 7 explores thepolitical dynamics of diagnosing and treating salaryinequities. In particular, it discusses two common viewsof how bias becomes embedded in salaries, the politicsassociated with these views, and the impact of some ofthe remedies that have been undertaken to eliminatesalary bias. In addition, the chapter describes themethodological limits of responding to political pres-sures for further analyses, the remedy that was appliedat the State University of New York and why it was cho-sen, some of the ramifications of certain remedies, andproactive steps to keep salary inequities from occurring.

Chapters 3, 4, and 5 are intended primarily for thosewho are directly involved in designing and implement-ing salary reviews, but we have tried to keep even thesemore technical chapters accessible by confining some ofthe technical information to notes and appendices. Thechapters provide details on what variables are neededand how to collect and clean the data (chapter 3), meth-ods for examining bias in rank assignment and promo-tion (chapter 4), and ways to conduct multiple-regression salary reviews (chapter 5).

15

Introduction to Equal Pay for Equal Work

Neglected GroupsAnother goal of this guidebook is to encourage analyseswhere they have been neglected. Most of the reportedmultiple-regression salary reviews in higher educationhave been done at universities, with fewer such analy-ses having been conducted at four-year colleges andeven fewer at two-year community and technical col-leges. The scarcity of studies at two-year institutionsmay result in part from the fact that many of these col-leges have salary schedules or grids that are presumedto preclude gender or race bias.' The relative lack ofstudies at two-year colleges is, however, notable in lightof the large number of women and minority faculty atthese institutions.

Two-year colleges are not the only neglected catego-ry. Racial minorities have also been left out of mostanalyses. Throughout this guidebook, we stress theimportance of looking at both race and gender. In somecases, we cite studies or reports that consider only gen-der and we therefore do not mention race when refer-ring to those studies. (In many salary studies, the num-ber of racial minorities is too small to assess racial biasvalidly.) But the SUNY-UUP analyses consistently tookrace as well as gender into account whenever data onrace were available. (See the preface and appendix B fordetails on the SUNY-UUP studies.) Chapters 3, 4, and 5give recommendations concerning how best to combineor disaggregate race categories for specific analyses.

White MalesTesting for race and gender bias requires comparisons,and the appropriate comparison is with the race andgender category that predominates at almost all U.S.institutions of higher education: white males. Thus"white male" is mentioned often, particularly inmethodological chapters explaining how to test for biasin rank assignment (chapter 4) and salary (chapter 5).We mean to assign no blameand certainly not to kin-dle animosityby these frequent references. We aresimply acknowledging the fact that white males definethe necessary standardthe reference categoryagainst which other groups are measured. Rectifyingsalary inequities is about raising the pay of gender andrace groups when the analyses indicate bias. It is neverabout lowering the pay of those in the standard or refer-ence category.

SUNY StudiesThe collective bargaining agreement negotiated by theUUP and SUNY in 1985 resulted in multiple-regressionanalyses of faculty salaries at twenty-nine SUNY cam-puses. The university system's Central Administration

Office of Employee Relations and Personnel Operationscoordinated the collection of data from the employeerelations or personnel offices on each of the twenty-ninecampuses. Because of time and staffing constraints,SUNY's Central Institutional Research Office chosemerely to replicate and validate the findings, leavingthe UUP's research department to take the lead in clean-ing the data and conducting the analyses. Initial analy-ses often revealed the need to carry out clarifying analy-ses with redesigned variables or corrected data. It wasnot unusual for a dozen or more analyses to be run ateach institution. As noted in the preface, these studiesresulted in $2.2 million in wage adjustments for 5,700women and minority academics.

In addition, analyses were conducted specifically toinform the writing of this book. Twelve SUNY campus-es were selected on which to test the methods discussedhere. Selections were made to obtain data sets withmaximum variations of size and content within threeinstitutional types. Four two-year colleges, four four-year colleges, and four research universities were cho-sen, with faculty populations ranging from 99 to 811.Specific reanalyses of salaries and rank data were con-ducted. The statistical methods for determining bias inrank discussed in chapter 4, and the three types ofmultiple-regression analyses of salaries described inchapter 5 were tested using different variables on thesetwelve different SUNY populations. (For more detailsabout the institutions, see appendix B.)

Limits on CoverageAlthough, as was just noted, we have conducted manyanalyses of faculty salaries, in general this guidebookdoes not report specific institutional-level findings. Oneexception is the Kent State University case study, whichis reported in appendix H.

Also not included is information about the common-ly used qualitative approach called "paired compar-isons" or "counterparting." This technique involvesmatching white-male and female or minority facultymembers on the basis of similar qualifications. At best,such case-by-case methods are cumbersome, particular-ly at larger institutions; when there are female orminority faculty with no peers, they are impossible.Moreover, the process of selecting appropriate counter-parts generates animosity (K. Moore and Amey 1993).There are further problems when the counterparts areselected by the same administrators responsible for cre-ating any existing inequities (Muffo, Braskamp, andLangston 1979). The paired comparisons methodignores the concept of systemic bias, which affects allwomen and minorities, in favor of the concept that only

Lots Haignere

a few women and minority faculty members have beenaffected (see chapter 7). Multiple-regression analyses,on the other hand, statistically make every conceivablepaired comparison.

DemographicsOver the past two decades, the percentage of womenamong full-time faculty in the United States has grownsteadily from only 22.5 percent in 1974 to more than 35percent in 1999 (see figure 1.1). The continuing increasein the proportion of doctoral degrees granted to womensuggests that this trend will continue (Magner 1999).

Many people in academia expected that as morewomen became faculty members, the gap between theaverage salary for faculty women and the averagesalary for faculty men would decrease. In fact, however,data from the AAUP's Annual Report on the EconomicStatus of the Profession, published each spring in theAssociation's magazine, Academe, indicate that just the

opposite has occurred. Figure 1.2 shows that between1976 and 1995 women's salaries declined relative tomen's at the ranks of assistant, associate, and full pro-fessor. Moreover, between 1981 and 1984, the averagesalary for female faculty declined sharply relative tothat for male faculty.

Since 1984, the ratios have remained remarkably stablefor associate and full professors. Women assistant profes-sors, however, continued to lose ground until 1987, whenthe gap between their salaries and those of their male col-leagues began to close somewhat. In 1999 the gapwidened again and remained roughly the same in 2000. Itis too early to tell if this downturn signals the beginningof a downward trend or is just a temporary fluctuation.At best, salary differences seem to be entrenched, recur-ring at the same magnitude year after year.

Often, upon hearing this information, people will say,"Yes, but women are paid less because they tend to (a)have less education, (b) have fewer years of experience,

(c) be in lower-paid disciplines, (d) be inlower ranks, or (e) publish less often." Thestatistical techniques in this guidebook aredesigned to test the validity of these "yes,buts." As is noted later on, it is hard to testthe "publish less" factor directly because ofthe difficulty of collecting the necessarydata and of assessing quality versus quanti-ty. If the data are available, however,regression analyses can test the validity ofthis explanation as well as others. Becausethe data on average salaries do not suggestthat gender-based salary differences aregoing to go away, it is important to look atwhether or not these differences can beexplained by career attributes.

Figure 1.1

Growth in the Percentage of WomenAmong Full-Time Faculty in theUnited States, Selected Years, 1974-2000

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20 1 I I I

1974 1980

I I 1 1 1 I 1 1 1 1 1 I 1

1990 1995

Year

Note: The AAUP's Annual Report on the Economic Status of the Profession,the source of data for this figure, did not provide data on the percentage ofwomen among full-time faculty in the United States for 1978-79,1981-82,or 1983-86.Source: AAUP, Annual Report on the Economic Status of the Profession,1974-2000

2000

4

17

Regression AnalysisThe studies this guidebook will help youconduct can be seen as tools for approxi-mating what the salaries of women andminority faculty on campus would be in acompletely gender- and race-blind society.We can ask statistically whether faculty inthe category female would be paid more onaverage, given their career profiles, if theywere in the category male. And we can askstatistically whether the salaries of those inthe category male would on average earnless if they were female.

Regression analyses answer these ques-tions by creating a line that "best fits" thedata points scattered above and below it.

Introduction to Equal Pay for Equal Work

a).c

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Figure 1.2

Women's Salaries As a Percentage of Men's Salaries Among Full-Time Faculty inthe United States, Selected Years, 1976-2000

Associate Professor

Assistant Professor

Full Professor

1990 2000

Year

Note: The AAUP's Annual Report on the Economic Status of the Profession, the source of data for this figure, did not provide comparable figures foraverage salaries for all institutional types in 1979-80 or 1985-86.Source: AAUP, Annual Report on the Economic Status of the Profession, 1976-2000

Points below the line represent individuals whose actu-al salaries are lower than the salaries predicted by thevariables in the regression analysis. These people arebeing paid less than colleagues at the same institutionwith comparable career attributes.

In all likelihood, some points representing men will fallbelow the line, and some points representing women willfall above it. If, however, you add all the positive and neg-ative distances from the line of the faculty women's scat-ter points and find a lower total than for faculty men,regression analysis provides a negative number (coeffi-cient) for the variable female. That negative coefficientindicates the average amount that women's salarieswould need to be increased for them to be distributed likemen's salaries. In other words, this one summary numberrepresents how much, on average, it costs a faculty mem-ber to be a woman at the institution under study.

The beauty of the answer provided by multipleregression is that it takes care of most of the "yes, buts."Conceptually, multiple regression lets us compare peo-ple with the same level of education, the same years ofexperience, and in the same discipline and rank, who

vary only in their gender or race. Multiple-regressionanalyses account for variations in salaries by using a setof control or predictor variables, such as years of experi-ence, highest degree attained, rank, and discipline. Theinformation concerning these variables is mathematical-ly held constant while we examine the impact of genderand race on salaries.

Publishing records are not held constant in most .

salary analyses. Publishing, research, service, and quali-ty of teaching are widely recognized as measures of per-formance or productivity. Although it would be desir-able to include performance information in multiple-regression salary reviews, the time and difficultyinvolved in collecting and appropriately valuing the rel-evant information is usually deemed prohibitive. Inmeasuring publications, for example, do we look atquantity alone or also quality? Does the value of a jour-nal article relative to a book depend on the discipline ofthe faculty member? Do the decisions of journal refereesand grant-review committees incorporate gender bias?

Studies that have included performance variableshave found that bias in salaries persists; rarely do these

a5

Lois Haignere

variables have a significant effect on results (Weiner 1990;Dwyer, Flynn, and Inman 1991; Persell 1993; Toutkoushian1994b; Kolpin and Singell 1996; Nettles, Perna, andBradburn 2000). One explanation for this finding is thatthe characteristics of faculty members at institutionsemphasizing research and publication are relatively uni-form. People who have "made it" are remarkably alike(Gray 1990). At such institutions, rank and tenure mayact as proxies for research and publication.

Most community and technical colleges do notemphasize research and publication, and the argumentthat women tend to teach less or less well has rarelybeen suggested to explain salary disparities at theseinstitutions. As a result, noninclusion of performancevariables may be less debated at these institutions thanat research-oriented universities.

In considering the relative importance of performanceor productivity measures, remember that regression anal-yses focus on variations in salaries between classes orgroups, not between individuals. The factors that make asignificant difference in individual salaries may not beimportant when the focus is on group differences. Toshow, for example, that some women are less qualified orproductive than some men would not refute findingsconcerning group differences. Instead, it would be neces-sary to demonstrate that females, as a group, are lessqualified or productive than males, as a group. Findingsby Bellas and Toutkoushian (1999) suggest that differ-ences in research productivity by gender are small aftercontrolling for other factors, such as institutional type.

Quality of Regression ResultsAll multiple-regression salary analyses are not createdequal. It is important to know how to judge the validi-ty of different regression equations. An analysisshould be based on appropriate predictor variables. Ifinstead of the variable "years of experience," we used"years at current residence," or if we used "highestmonthly credit card debt" instead of "highest degree,"the result would be a fancy equation that would nottell us much.

Multiple regression gives an estimate of how well theset of control or predictor variablesyears of experience,discipline, and the likeaccount for the variation in thedependent variable, salary. This measure is called theadjusted R (R-square). The adjusted R takes into accountthe number of predictor variables relative to the numberof cases (faculty members) in the data set. An adjusted Rof 0.75 indicates that 75 percent of the variation in salaryis accounted for by the predictor variables in the equa-tion; an adjusted R of 0.55 indicates that 55 percent ofthe variation is accounted for by the variables.

6

Assuming that the predictor variables include thosemost commonly used (see chapter 3), most analyses offaculty salaries have adjusted R values greater than0.50, and values above 0.70 are common. Thus the vari-ables included in most faculty salary analyses do a goodjob of explaining the differences between salaries. Formore information on adjusted R , see appendix A.

Having a high adjusted R does not, however, ensurethe validity of your findings. In particular, care must betaken that the predictor variables used do not mask gen-der bias. A variable that does so is commonly referredto as a "confounding variable" in the statistical litera-ture and a "tainted variable" in the literature on genderbias in salaries. If, for example, height were included ina salary disparity analysis, the shortness of women facul-ty relative to men could mask gender differences insalaries. It is highly unlikely, of course, that heightwould be included in an analysis of faculty salaries. Butif administrative or twelve-month positions, tenure, orrank are disproportionately awarded to men at yourinstitution, and variables for these criteria are includedin the salary analysis, they may mask bias. Tainted vari-ables are discussed at greater length in chapters 4 and 6.

Curiosity, Not ConvictionSalary equity is a politically charged issue. Many indi-viduals think they already know what the outcome of asalary-equity study will be. Some, including administra-tors charged with managing the salary-setting process,may believe strongly that there is no pay bias. Others,such as women and minority professors, may be just asconvinced that a great deal of bias exists.

In a substantial minority of cases, study results showthat gender and race have played little, if any, role insalary setting. Among the twenty-nine separate assess-ments of salaries carried out at SUNY campuses, forexample, roughly one-third indicated no tangible gen-der or race bias. (See the preface for details about theSUNY study.) That some institutions are free of salarybias demonstrates that gender- and race-neutral salary-setting is possible. Yet most analyses that are properlydesigned to avoid methods that tend to mask bias, findevidence of gender inequity in salaries. Try to be curi-ous about the outcome of your study without second-guessing the results in either direction.

Notes1. Studies have been conducted at American University,Concordia University, Florida State University, Iowa StateUniversity, Kansas State University, Memorial University ofNewfoundland, Monroe Community College, New MexicoState University, Oregon State University, Seton Hall

19

Introduction to Equal Pay for Equal Work

University, Simon Fraser University, Queens University, theUniversity of Cincinnati, the University of Connecticut, theUniversity of Hawaii at Manoa, the University of Illinois atUrbana-Champaign, the University of Maine System, theBaltimore College of Dental Surgery of the University ofMaryland, the University of Maryland at College Park, theUniversity of Nebraska at Omaha, the University of RhodeIsland, the University of Western Ontario, the University ofWisconsin at Madison, and elsewhere. Some of these studieshave uncovered bias, others have not. For details about themand the methods used to conduct them, see Allen 1984;Finkler, Van Dyke, and Klawsky 1989; Geetter 1988; Gray1993, 1990; Gray and Scott 1980; Hauser and Mason 1993;Ikeda 1995; Hurley et al. 1981; Johnson, Riggs, and Downey1987; McLaughlin, Zirkes, and Mahan 1983; Muffo, Braskamp,and Langston 1979; Brittingham et al. 1979; Ramsay 1979;Schau and Heyward 1987; Schrank 1988, 1985, 1977; and Scott1977.

2. Although the author of this chapter has conducted no analy-ses of two-year colleges with salary grids, she has carried outmultiple-regression salary analyses at a Canadian universitythat had a salary schedule with specified minimums, incre-ments, and maximums in place for more than twenty years.Evidence of gender bias was found, and salary adjustmentswere made.

3. The 1980-81 edition of the AAUP's Annual Report on theEconomic Status of the Profession suggests that the slippage insalary among faculty women compared with that among fac-ulty mendespite the increasing numbers of women facultyoverallcould result from two nondiscriminatory phenome-na. First, as women move up in rank, they are paid less thanmen in the same rank because more women are at the bottomrungs of each rank's salary ladder. Second, the report notesthat "women faculty may be concentrated in lower-paid disci-plines even though their salaries are the same as those of menwith(in) each rank in these disciplines."

The first explanation is implausible given the continuingdecline of women's salaries relative to men's despite theirincreasing years in rank and the fact that the decline existseven at the lowest ranks, those of lecturer, instructor, andassistant professor. Indeed, the 1995-96 AAUP salary reportnotes, based on research controlling for age, that salarydifferences are not the result of women's later arrival in rank.

The second explanation regarding the concentration ofwomen in lower-paid disciplines was undercut in 1988 bycomparisons reported by the AAUP's Committee on theStatus of Women in the Academic Profession showing thataverage salaries for women were below those of men withindiscipline and rank (Gray 1988). The committee assessedthe equally plausible demographic explanation that thesalaries of women faculty lagged behind those of menbecause women were being hired disproportionately atlower-status institutions. The committee found the erosionof women's salaries relative to men's within every institu-tional type.

Women in academe are disproportionately in lower-paiddisciplines (Bellas and Reskin 1994), but there is no evidencethat the sharp decline in women's salaries relative to men'sfrom 1981 to 1984 came about because more women enteredlower- rather than higher-paid disciplines during this period.Given the increasing number of women studying nontradi-tional fields as a result of the heightened feminist awareness ofthe 1970s, it is doubtful that the new faculty women of theearly 1980s opted for the lower-paid disciplines in greater pro-portions than their predecessors.

Another suggested explanation is that before 1980, equallyqualified women with new Ph.D.'s were hired at lesser ranksthan their male counterparts, perhaps as instructors or lectur-ers rather than as assistant professors. After 1980, morewomen may have been hired at equal ranks, but salary differ-entials increased.

In any case, the multiple-regression statistical methodsillustrated in this guidebook can control directly for disciplineas well as rank, years in rank, and other career attributes. Mostsalary-regression studies show that lower salaries for womenpersist even after controlling for these career attributes.

4. Bellas (1992) shows that the wives of faculty men seem toprovide a "(house)wife bonus," which contributes to the pro-ductivity of male faculty members. For research indicatinghow faculty time allocations toward research, teaching, andservice differ by race, gender, and family status, see Be llas andToutkoushian (1999).

5. If the salaries under study have been adjusted to a nine- orten-month base and all administrative supplements have beenremoved, there is no need to include these potentially biasedvariables.

7

Persuading administrators and some faculty members that statistically identified disparitiesrepresent a systemic bias and not just a few cases of possible underpayment of women is thehardest part of a salary review.

Mary W. GrayProfessor of Mathematics

American University

TWO

Considerations Before Launching a Salary StudyBy Lois Haignere and Donna Euben

Deciding whether to assess faculty salaries statisti-cally for gender or race bias (or both) involvestechnical and political considerations. This

chapter offers an overview of some technical and policydecisions you will have to make to carry out a multiple-regression salary review. (Appendix D addresses thelaws that apply to salary-equity issues.) The chapter alsocovers the resources you will need and the process forselecting a consultant. It concludes with a summary ofseven salary studies that led to pay adjustments.

Politics of Technical DecisionsSome people mistakenly believe that applying statisticsto a political issue such as salary bias eliminates subjec-tivity and human judgment. But it does not. Althoughusing statistical methods may hide from public view thearena in which value judgments are made, it does noteliminate them (N. Moore 1993). Nor, we would add,does it remove their political impact.

Conducting research on bias in salaries often meansinvolvement in administration-faculty politics. To helpensure a cooperative relationship, it is important to beproactive with the administration. Technical decisionsthat have political implications are best made openly bywell-informed participants.

The right toolYour first consideration is whether a multiple-regressionsalary review is the appropriate tool to accomplishyour objectives. Multiple regression's strength is inrevealing group effects. It can tell you the exact aver-age effect of membership in a group, such as that offemale, full professor, or Asian. That is why it is themethod of choice for studying systemic bias. If weassume that all those in the group female are affectedby the existence of gender bias, then multiple-regressionis the best approach to explore the effects of thatsystemic bias.

But many faculty and administrators see the marketand institutional processes as acting fairly except in iso-lated situations. They hold what is called an individualperspective on bias and discrimination rather than asystemic or structural view. (Chapter 7 provides detailsabout these two different perspectives.) For this group,the objective of a salary study is to find the few individ-uals whose salaries have been affected by the rareexpression of personal bias. If that is your goal, multipleregression is not appropriate. Regression is a statisticaltechnique, not a formula for setting individual salaries.

Of course, you can obtain predicted salaries for indi-viduals from multiple-regression analyses, but individual-level predictions are much less precise than group-levelpredictions. Individual salaries commonly vary becauseof effects not represented by variables in multiple-regression analyses. As noted in chapter 1, these analy-ses rarely include productivity variables; neither dothey take into account such variables as being a relativeof the dean or provost. Factors affecting salaries but notincluded in an analysis are presumed to be distributedrandomly at the group level. As we pointed out in chap-ter 1, it is one thing to argue that an individual womanis less productive than an individual man; it is quiteanother to argue that women as a group are less pro-ductive than men as a group.

Decisions, decisionsThe decision to conduct multiple-regression analyses offaculty salaries is only the first of many choices that willhave a bearing on your results. Who, for example, willbe included in the study? If you exclude non-tenure-track faculty, the results will tell you nothing aboutthese academics, who are likely to be disproportionatelywomen or minorities. Moreover, excluding non-tenure-track faculty may substantially reduce the size of yourdata set and thereby restrict your ability to use somemethods. Similarly, if you decide to examine gender but

t)4

9

Lob Haignere and Donna Euben

not race, will you include all males or only white malesin your comparison group?

The variables you select can influence your results. Asnoted in chapter 1, if your institution confers adminis-trative or twelve-month positions disproportionately onwhite men, and you include these variables in youranalysis, they may mask bias by attributing some of thedifference in salary to the confounding variable ratherthan to gender or race. (You may be able to avoid anyneed to include these potentially tainted variables byadjusting the salaries in your sample to a nine- or ten-month basis and by removing the administrativesupplements.)

Current rank is even more controversial, since it isstrongly related to salaries but can still incorporate gen-der or race bias. Elizabeth Scott (1977) argues that quali-fied women who are denied promotion will appear tobe overpaid for their rank rather than frozen in it.Chapter 4 includes a more complete discussion ofpotentially tainted variables and how to assess theirimpact.

To further complicate the decision-making process,there are several different types of multiple-regressionapproaches for reviewing salaries, each giving a slightlydifferent picture. Depending on what you want to knowand the peculiarities of your data set, such as size andrange of salaries, you may judge one approach betterthan another for your purposes. Alternatively, you maydecide to conduct two or three different analyses basedon different approaches to determine if the results vali-date each other. But if you do so and the results differ,you will need to examine why.

If this all sounds daunting, don't despair. This guide-book is designed to help you. Chapter 6 goes into fur-ther detail about policy-related decisions. Here our goalis mainly to note that your choice of population, vari-ables, and methods will directly influence your finalresults.

A simpler method?If you find that multiple regression, computerizeddata, and the need to control for all of those variablesoverly complex, consider using scattergrams. A scat-tergram shows the pattern of two variables, such assalary and years of experience, by putting one variableon the vertical axis of a graph and the other on the hor-izontal axis. Points representing the intersection of thetwo variables for each case (or faculty member) form a"scatter" that gives a good visual image of the relation-ship between the two variables. See the glossary formore information and figure 6.1 for an example of ascattergram.'

10

You can create a scattergram with the old-fashionedtools of pencil and paper. If you want to look at differ-ences between two groups, say men and women, youcan use an x for the dots for one group and an o for thedots for the other group. If you want to control forrank, you can plot separate scattergrams for each rank.If you are adept with spreadsheet software, you canforgo pencil and paper in constructing these visualrepresentations.

If your college has a small faculty, or if you want toexamine only your department or discipline, scatter-grams may be the best option. That is because the valid-ity of multiple regression in examining data sets withfewer than fifty faculty members is uncertain. For addi-tional details about analyzing small data sets, see thediscussion of faculty size under "Basic Requirements"below. Even with larger groups, scattergrams can pro-vide preliminary information to help you decidewhether a full-scale salary study is needed.

Other considerationsWith computerization, the automation of personnel sys-tems and other data sets has increased, making it easierto conduct statistical analyses. Most colleges and uni-versities and many unions can now conduct multiple-regression analyses with minor additions or adjust-ments to already-existing data sets, and the growingcapacity of computers to store data encourages theinclusion of more specific information. The expansion ofinstitutional data sets increases the likelihood that insti-tutions will conduct statistical analyses like the onesdescribed in this guide on a variety of topics.' Facultyleaders and bargaining-unit policy makers thereforeneed to grasp basic approaches to statistical analysis.

Basic RequirementsIn order to plan your study, you will need to considerthe characteristics and resources of your college oruniversity.

Faculty sizeIf your institution has one hundred or more full-timefaculty members, you can probably validly conduct thesalary analyses described in this guide. If you do havefewer than a hundred full-time colleagues, you may wantto consider alternative methods, such as the scattergramsdiscussed above. We say "may" because of the otherfactors that bear on the validity of multiple-regressionanalyses, primarily the number of variables used andhow well they account for variations in salaries.

If salary increases on your campus have tended to takeplace only through annual increments and promotions,

22

Considerations Before Launching a Salary Study

then multiple-regression analyses could predict yoursalaries with a relatively small number of variables:years of experience and rank, for example. Adjusted Rmeasures can help you decide, after the fact, if your dataset was big enough. That is because the adjusted Rtakes into account the number of predictor variablesused relative to the number of cases (faculty members)in the data set. Unfortunately, you will not know if yourdata set was sufficiently large until after you have donethe analysis.

If your institution has fewer than a hundred full-timefaculty members, if salaries are not the result of a simpleand consistent pay policy, and if you cannot afford thetime and work involved in doing the analysis in orderto have the benefit of adjusted re hindsight, we suggestthat you not conduct multiple-regression analyses.

ExpertiseAlthough this guidebook is designed to help laypersonsunderstand methods of salary analysis and the outputthat results from them, you will need someone with sta-tistical and computer expertise to conduct the actualsalary analyses. If your institution is large and you areblessed with a cooperative, trusting relationship withthe administration, expertise may be easy to come by.Most universities have institutional research depart-ments with the personnel and computer resources toconduct these analyses. Small campuses may have fac-ulty members with the necessary expertise in depart-ments such as sociology, psychology, economics, orstatistics.

We do not mean to imply that knowledge of statisticalprocedures is all that is needed. An interest in the pro-ject and in helping others understand statistical proce-dures and output, a willingness to work cooperativelywith different constituencies to design the analyses, andthe trust and respect of key faculty and union policymakers and members are at least as important as exper-tise. It would be a mistake to ignore the political natureof faculty salary analyses when deciding who will dothem.

Decision makers often determine that the expertiseneeded to conduct the salary study can best be acquiredby contracting with an outside consultant. Hiring a con-sultant may bring more experience and neutrality to theproject than is available from within the institution.Later in this chapter, we provide insight into consultantsand the institutional processes involved in hiring them.

Computer resourcesWhoever is selected to carry out the analyses will proba-bly have access to the requisite computer resources,

whether an institutional mainframe or a personal com-puter. Most personal computers sold today have thepower and memory needed to conduct complex statisti-cal analyses. Although multiple-regression analyses canbe done with spreadsheet software, we recommendusing a statistical software package. The ease of usingsuch packages and of interpreting the results they gen-erate outweighs their cost. Some statistical packagesactually do the programming for you, prompting youconcerning what variables to include.

TimeHow much time will it take to conduct the analyses wedescribe in this guidebook? The process takes place infour main stages: data collection, data cleaning, runningof the analyses, and reporting of the results.

Data collection. Your institution's automated personnelsystem may already contain much of the data you willneed. For each variable you select, however, you mustdetermine whether data are missing and, if so, how longit will take to collect the missing information. Some ofthe variables you want to include may not be availablein automated form. If, for example, you have to gothrough the paper files in the personnel office to collectthe necessary degree data, it will probably take a lotlonger than if the data are available in a separate auto-mated file, such as the one for the campus catalog. Onlyyou can predict how long it will take to gather missingdata. Our advice is to make an estimate and thenincrease it by half. Our experience indicates that thiswould be a conservative calculation of the time actuallyneeded.

Data cleaning. Even data that appear to be completeand accurate commonly have anomalies that need to beexplained or corrected. You may, for example, find fac-ulty members whose reported initial ranks are higherthan their current ranks, faculty who appear to havereceived their doctorates at age twenty or younger, orthose whose discipline code differs from their depart-ment code. It takes time to verify or correct each anoma-ly. Although doing so is time consuming, it is impor-tant. As the well-worn adage says, "Garbage in, garbageout." The time needed will depend on the size of thepopulation you are studying. We recommend that youallow, at minimum, two months for data cleaning, moreif your faculty is larger than four or five hundred.Chapter 3, on developing a database, contains manysuggestions for verifying data.

Running of the analyses. Once the data have beencleaned, the next step is to code the appropriate vari-ables and program and run the analyses. This phasecommonly takes more time than anticipated. Consistent

11

Lois Halgnere and Donna Euben

with Murphy's Law, bugs, software glitches, and hard-ware failures will delay progress. Running analysesmay also reveal data errors that were not detected dur-ing data cleaning, making it necessary to rerun theanalyses.

In addition, there is a tendency for each statisticalresult to generate further questions. If, for example, youuse more than one method of multiple-regression analy-sis (we describe three types in this guide) and theresults differ, you will want to know why. You maydecide you want to see some analyses with and withoutcertain variables. If the results indicate bias in salaries,additional analyses aimed at formulating appropriatewage adjustments will probably be required.

Assuming a clean data set and appropriate expertise,we estimate that it will take a researcher about twentyhours a week for a month, maybe two, to complete themultiple-regression analyses. Another month or twowill be needed if the researcher carries out analyses ofbias in rank, tenure, or other potentially tainted vari-ables (see chapter 4). We suggest that the researcherwork half time on the project, because the activeinvolvement of the researcher will not be required con-tinually. Given the political nature of the research, it isimportant to build in time for disseminating informa-tion among interested parties and getting their feed-back. Of course, additional research questions mayresult from this exchange.

Reporting of the results. It is important to report theresults of the salary study in a way that faculty mem-bers can understand. It may also be politically impor-tant to provide a draft report to the primary con-stituents for their review before releasing the final docu-ment to a wider audience. Allow two to three weeks forwriting the draft, at least a week for the parties to pro-vide feedback on it, and another week to redraft it inlight of their comments. This process may also lead toadditional analyses. Sharing information and gettingfeedback can be time consuming, but it helps to ensurean open process.

An open processThe salary-equity investigation should be public andopen. Transparency helps gain support for the projectand promotes fairness. Regular newsletters, interimreports, and student and local press coverage are goodways to educate the campus community about theeffort. A salary-equity study should also involve facultymembers. If the administration limits opportunities toparticipate, or restricts the amount of faculty involve-ment, then faculty members can still critique the study'sfindings. Such critiques will have more legitimacy if fac-

12

ulty members have tried to participate in the process. If,after having participated, faculty members find thestudy's conclusions or recommendations unwarranted,they can prepare a minority report. They can also do soif they think the study's methods were flawed or theprocess was too political. Again, sharing informationand getting feedback can be time consuming, but ithelps ensure an open process.

Salary-Equity ConsultantsThis guidebook presumes that someone in your union,chapter, faculty senate, or administration will conductthe salary research. For various reasons, however, anoutside consultant is often sought to undertake such astudy. This section offers some insight into consultantsand the institutional processes for hiring them.

Competitive bidsCollege and university administrations rely on differentmechanisms to hire outside consultants. The most com-monly used is that of the request for proposal (RFP),which solicits competitive bids from interested parties.The RFP process is discussed below.

Administrations can usually find the means andmoney to accomplish the projects they favor. If the pres-ident's office wants to conduct a salary-equity studyand knows a reliable and experienced outside consul-tant, the money and mechanism to make the hire will nodoubt be found. Even public-sector institutions can hirenoncompetitively under what is often called the "singlesource" provision for hiring. This provision is some-times used when one consultant or firm can be shown tobe the only appropriate source of expertise, or when thecompetition is determined to be inadequate.

If an outside consultant or firm will be hired througha competitive process, the first step is to write an RFPdescribing the proposed project and specifying the pop-ulation to be studied and the data to be supplied by theinstitution. The RFP should ask the respondent for adetailed outline of the proposed undertaking, atimetable, a budget, a list of references, and descriptionsof the methods to be used. In addition, the RFP shouldask about the consultant's expertise in pay-equity stud-ies and the qualifications and experience of the pro-posed project staff.

Review the proposals you receive, taking into accountany regulations the university or college may have forcontracting with consultants. Interview, by phone or inperson, the consultants who have submitted the bestproposals. Any staff of the consultants who will beworking on the project should also participate in theinterview. When possible, get references from faculty at

24

Considerations Before Launching a Salary Study

institutions where the consultants have completed stud-ies. Members of bargaining units, faculty associations,and women's groups may be able to help with refer-ences. Finally, select the consultant who best meets yourneeds, and sign a contract with him or her.

faculty roleIf your chapter, faculty senate, or union decides to playan active role in the study, it must get involved early on,when the RFP is being drafted and a consultant selected.Once the study begins, it is often too late to changeaspects of it you do not like.

To ensure that you get in on the ground floor, reviewyour institution's options for hiring consultants. Whoneeds to approve such a hire? Can a consultant be hiredwithout going through a competitive process? If so,how? If an RFP will be circulated, make sure that theresearch design includes features you consider impor-tant. As you review the draft RFP, you may find it help-ful to read chapter 3 and chapter 6.

A faculty committee may want to provide names ofconsultants who have produced acceptable studies andask to review the bids received to determine whethercandidates have the requisite experience. Has the candi-date completed similar salary studies at similar institu-tions? Has she completed projects to the satisfaction offaculty groups? Does he have a good track record withunions and in unionized settings? Does she understandthe unique features of your institution and the proposedstudy?

Has the candidate submitted a clear proposal? (A con-fusing or overly technical proposal may be a sign thatthe consultant does not know the field well enough.)Does he have a staffing plan for completing the projecton time and within budget? Is she committed to thenotion that no faculty members should have theirsalaries reduced as a result of the study?

The faculty committee may also want to participate inthe final selection of the consultant and review the con-tract before it is signed for language specifying researchmethods and the scope of the undertaking. In addition,the committee should ensure that an appeals mecha-nism exists in case the faculty wants to challenge theconsultant's conclusions or recommendations.

Bottom fineA consultant works for the client. If you or your facultygroup are not represented among those who hire theconsultant or receive the final report, your views areunlikely to influence the research.

Consultants hired and paid unilaterally by the univer-sity or the college administration will probably be sensi-

five to the wishes of the administration only. If the insti-tution involves the faculty women's committee oranother faculty or advocacy committee in selecting andhiring the consultant, the consultant will understandthat the methodological concerns of committee mem-bers are important to the institution. By contrast, if theconsultant is ushered in and out of the president's orprovost's office and meets no one else, that will speakvolumes as well.

Not all consultants are hired unilaterally by theadministration. Your faculty group may be able to nego-tiate a contract under which the institution pays for thestudy even though the consultant must report to bothfaculty representatives and the administration. If possi-ble, the faculty group may want to contribute to theconsultant's payment so that the consultant under-stands that the project is for two distinct clients who arefully and equally involved.

If your union, chapter, or faculty group has theresources and data, you may even want to hire the con-sultant unilaterally. Consultants can be expensive, butthe expense may be justified if the consultant has solidexperience in doing salary-equity analyses. A consultantbrings the added benefit of appearing more neutral thaninternal faculty or institutional researchers.

Consultantsindividuals and firmsabound. Lookfor one who puts the validity of the research above allelse and who has a good history with faculty and facul-ty organizations.

Happy EndingsHundreds of institutions in the United States andCanada have conducted salary-equity studies usingmultiple regression. The analyses have been initiatedvariously by bargaining units, women's groups, facul-ty members, and administrators. We have collectedmost published and some unpublished reports of thesestudies, but we have not attempted to identify everyone undertaken. We suspect that those that find biasand result in awards are more likely to be publishedthan those that do not find bias or lead to salaryadjustments.

Below we describe eight studies that resulted inawards to remove bias in faculty salaries. The amountof salary adjustments varied. In our experience, mostawards range between an annual salary increment of$500 and $2,500.

Memorial University of NewfoundlandMotivated partly by a quantitative report published bythe Canadian Commission on the Status of Women,Memorial University commissioned a faculty salary

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Lots Halgnere and Donna Euben

study in 1973 (Rosenbluth 1967; Robson 1969). After ayear of collecting and cleaning data, which includedinformation on publications and research, multiple-regression analyses were conducted on a total of 598tenure-track faculty members, including 104 women.

The study found average annual salary disparitiesbetween men and women amounting to $705 when rankwas included in the analysis. Because of strong evidencethat women were discriminated against in promotion, afurther analysis was conducted omitting rank. Withoutthe rank variable, the annual salary disparity jumped to$1,766 (Schrank 1977).

The university president rejected the faculty associa-tion's recommendation that blanket awards be made toall female faculty and instead adjusted the salaries ofspecific women, most of whom were in the School ofNursing or the junior division, which was made up ofteachers of first-year courses. The awards amounted toroughly half of the disparity found by the regressionanalyses.

A follow-up study, conducted on 1982 data, againfound gender disparities, but not in cases in whichadjustments were made after the 1973 study. Where noadjustments had been made (the School of PhysicalEducation and the Faculty of Arts, for example), dispar-ities remained. Although the 1982 study resulted in noawards, the findings enabled the faculty association tonegotiate a salary grid system. By gaining placement onthis grid, many women, particularly those with the mostlongevity in the system, received substantial increases.One senior woman faculty member received a 65 per-cent increment.

Monroe Community CollegeThe women's caucus of the Monroe Community Collegefaculty association initiated regression analyses of the1983 salaries of tenured and tenure-track teaching facul-ty. The study found gender bias in both salaries andpromotion among a population of 99 women and 177men.

The faculty association filed a grievance in 1985,because the college declined to correct the situation vol-untarily even though sexual discrimination violated theassociation's contractual agreement. An arbitrator even-tually persuaded the college to negotiate with the facul-ty association regarding possible remedies.

As a result, 99 female faculty members receivedsalary increases of $700 and an additional amount ofabout $9 for each year of service. The remedy alsoaddressed the issue of unfair promotions and providedfor the monitoring of future promotions.

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University of Nebraska at OmahaIn 1984 the Chancellor's Commission on the Status ofWomen at the University of Nebraska initiated a seriesof studies that looked at the status of three differentgroups of women: clerical and technical, managerialand professional, and teaching professional (faculty). Ajoint administration-AAUP committee decided suchmatters as the variables and the statistical methods to beused, the population to be studied, and any pay adjust-ments to be made if disparities were found.

Conflicts occurred over the use of starting salary as apredictor variable. The administration viewed startingsalary as a reflection of historical market value. TheAAUP chapter believed that the starting salaries werethemselves affected by gender bias. Two studies wereconducted by the AAUP to examine starting salary asthe dependent variable. The results revealed genderbias in starting salary, and the university agreed toleave this variable out of subsequent analyses (see thediscussion of initial salary in chapter 6).

The population to be studied was also controversial.Discussion centered on two groups: faculty hired before1972 and temporary faculty members. The administra-tion wanted to exclude faculty members appointedbefore 1972 because their salaries had been adjustedbased on a 1971 study. Doing so would have left 37 per-cent of the faculty out of the analyses, substantially low-ering the population.

The administration also wanted to exclude temporaryfaculty, but the AAUP chapter argued that it was legallyresponsible for representing the entire bargaining unit.The parties eventually agreed to include the entire fac-ulty in the study. After more than eighteen differentanalyses, each woman faculty member received anaward of $1,000 to remedy the disparities found(Finider, Dyke, and Klawsky 1989).

University of ConnecticutA regression analysis of faculty salaries was conductedin 1988 in response to two factors: the requirements of acollective bargaining agreement between the universityand the local AAUP chapter and the state's commitmentto eliminating gender-based salary inequities.

The study found that female faculty were, on average,paid $1,806 less than their male counterparts, and thatfewer female than male faculty members received salaryincreases indicating high merit. In addition, only 29 per-cent of women received salaries higher than those theanalysis predicted they would have earned had theybeen male; 66 percent of women earned less than thesalaries predicted for them. The study concluded thatthere was no statistical indication that only a subgroup

Considerations Before Launching a Salary Study

of women faculty had been affected by gender-basedinequities, and it therefore recommended a salaryadjustment for every woman on the faculty.

The total amount of money to remedy the sex-basedinequity was estimated to be $470,553, or an average of$1,806 for each female faculty member. Two-fifths of themoney was awarded as a flat amount to all women fac-ulty members, two-fifths was awarded as a percentage(1.87 percent) of each woman's salary, and one-fifth wasdistributed to women faculty members on the basis ofmerit (Geetter 1988).

University of Connecticut Health CenterIn 1992 a multiple-regression study of the salaries of fac-ulty in the university's medical and dental schools wasconducted on the recommendation of a committee ofwomen faculty appointed by the administration. Thestudy, which resembled the one carried out earlier onthe university's main campus, revealed average dispari-ties between men and women faculty of $4,731. Theworking group on the status of women faculty reportedthe results to the administration and recommended thatall women's salaries be raised by $4,731 (Ferree andMcQuillan 1998).

The administration did not accept the study, express-ing concerns about the population included as well asthe accuracy of the human resources data and the vari-ables used. It preferred a "flagging" approach, whichidentifies as potentially underpaid those individualswhose statistically predicted salaries were higher thantheir actual salaries. The women's committee pointedout the problems with flagging, not the least of which isa lack of concern for women who are "top scholars" andare underrewarded for their productivity (see chapter 7).

Additional analyses were run to address the adminis-tration's concerns. As a result of this further study, theadministration instituted biennial salary reviews andrecommended to the board of trustees that salary-setting guidelines be developed. In June 1994 the admin-istration increased the pay of women faculty across theboard by $1,000 (prorated for part-time faculty).Additional awards were made to individuals based onthe administration's flagging model, which showed thesalaries of some of the women reviewed to be signifi-cantly below those of their male peers.

University of Hawaii at ManoaIn 1993 the University of Hawaii completed a salary-equity study as part of an affirmative action initiativeproposed by the university president. The proposalresponded to concerns expressed by the campusCommission on the Status of Women, other faculty

members, and the Office of Federal Contract Compli-ance Programs.

The study assessed the effects of both gender andethnicity on salaries. The database it relied on consistedof the 1991 personnel records of 1,004 faculty members.The results indicated that both women and persons ofJapanese descent were underpaid by about 4 percent.

Although external consultants recommended anacross-the-board remedy for the disparities, the univer-sity ended up implementing case-by-case reviews.Women and minority male faculty whose actual salariesfell below the median pay of comparable white-malefacultyor below the regression linecould apply for acase review. Those whose actual salaries were above thecomparable white-male median had to use other routes(grievances, federal agencies, or the courts) if theywanted redress.

An all-campus faculty equity panel with 35 mem-bers, including union representatives, worked for twoyears deciding the cases of the 223 women and minori-ty men who applied. (Only seven women eligible forreviews did not apply.) The total amount awarded tothe 171 women who received adjustments was about$1,525,351, an average of $8,920 each. Eighty-eightminority men received about $810,331, an average of$9,208 each.

State University of New YorkIn 1993 United University Professions (UUP) and theState University of New York (SUNY) completed astudy to assess gender- and race-based salary dispari-ties. The study was called for by the terms of the collec-tive bargaining agreement between SUNY and the UUP.The bargaining unit consisted of twenty-nine SUNYcampuses, including four major university centers, fourmedical schools, thirteen four-year colleges, six technicalcolleges, and specialized colleges such as the Colleges ofOptometry and Forestry. A joint labor-managementcommittee selected the methods to be used and madeother policy decisions, after which multiple-regressionanalyses were carried out on each of the twenty-nineinstitutions in the unit.

As a result of the analyses, SUNY made more than$2.2 million in wage adjustments went to women andminorities. These awards went to women and to thosein a given racial category if average salaries for thatcategory were found to be lower than those for compa-rable white males at a particular campus (Haignere, Lin,and Eisenberg 1993). The amount of money set asidewithin the contract for salary corrections paid onlyabout 25 percent of the amount of the salary disparitiesindicated by the research.

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Lois Halgnere and Donna Euben

University of Maine SystemAs part of the 1997-99 collective bargaining agreementbetween the Associated Faculties of the University ofMaine (AFUM) and the University of Maine System, ajoint committee was established to study the issue ofgender equity in faculty salaries. Regression analysescontrolling for the factors that are legitimately related tosalary were conducted at the systemwide level, at allseven institutions in the system, and at some of the larg-er colleges within the University of Maine and theUniversity of Southern Maine. Study findings werereported in October 2000.

The committee determined that systemic genderinequity existed when being female cost a faculty mem-ber 2 percent or more of the average male salary. Salarydisparities in excess of 2 percent were found at threeuniversities and within some of the colleges at the twolargest universities. The annual salary disparitiesranged from $1,438 to $3,079.

The committee recommended systematic adjustmentsto salaries where the 2 percent threshold was met orexceeded. The university and the AFUM reopenednegotiations upon receiving the committee's report andreached agreement on salary adjustments. Roughly 80

percent of the award amount was determined by a for-mula containing two components, each representingroughly half of the total: a flat dollar amount for eacheligible woman and an amount based on the number ofyears of university employment, up to twenty. If awoman's salary was already higher than those of mencomparable to her in terms of department, discipline,rank, and highest degree, then the formula awarded hera reduced amount or no amount.

The remaining 20 percent of the adjustment amountwas set aside for consideration of individual femalesalaries that, even after application of the formula,remained significantly below the earnings of men withsimilar qualifications and experience.

In addition to adjustments to base salaries, womenfaculty who had completed at least eleven years of ser-vice received a one-time payment, not added to basesalary, for each year of service between eleven andtwenty years. In total, roughly $400,000 was distributedto two hundred faculty members.

Notes1. Figure 6.1 contains more information than most two-variable scattergrams because the figures on the horizontalaxis (predicted salaries) are based on regression modelinginformation rather than on years of experience, age, or asimilar single variable.

2. Institutional research departments are increasingly ventur-

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ing into automated analyses that require extensive, precisedata. The Office of Institutional Research (OIR) at theUniversity of Delaware, for example, is conducting theNational Study of Instructional Costs and Productivity. With amajor grant from the Fund for Improvement of Post-Secondary Education, the OIR is collecting detailed informa-tion from many institutions of higher education in the UnitedStates on student credit hours and organized class sectionswithin disciplines.

3. See note 1, chapter 1.

It's never sex bias, just lack of time in service, bad negotiating skills, bad timing, wrong field, orbad-hair day that accounts for all these "discrepancies." So say the defenders of the status quo.

Ellen B. KimmelProfessor of Psychology

University of South FloridaTHREE

Database Decisions and DevelopmentBy Lois Haignere and Yangjing Lin

policy-related research projects usually begin withpolicy decisions, and faculty salary reviews areno exception. Determining what information to

include in the project database will require you to makepolicy decisions that will influence the outcome of yourstudy. Who makes those decisions will vary accordingto the political forces that bring the project to life. Atone end of the continuum, a faculty group unilaterallyconducts the study; at the other, the administrationdoes. Between these two extremes are a range of coop-erative arrangements with different degrees of faculty-administration control.

This chapter is geared toward those of you involveddirectly in designing and implementing a salary review.It will help you determine what data you need and howto collect and clean the information to be analyzed.

Policy-Making CommitteeDecisions about faculty salary reviews are often madeby committee. Strive to create a policy-making commit-tee that has representatives trusted by the different con-stituencies at your institution. Include men and womenfrom among the faculty and the administration whounderstand the importance of addressing a perceivedequal-pay problem. Of course, many of the effectivefaculty and administrators you want to involve willprobably be busy. To encourage participation, makesure to explain that the issue at hand goes beyondpotential salary improvements for minority andwomen professors: faculty morale and productivity, thereputation of the school, and alumni support will all beaffected.

To help you determine who belongs on the policy-making committee, you may want to revisit the "BasicRequirements" section of chapter 2 and take an advancelook at chapter 6. Here we list some questions with whichthe policy-making committees will have to grapple.

Should the study include non-tenure-track and part-time or adjunct faculty? What about nonteaching fac-

ulty and faculty from the evening division and satel-lite sites? How about faculty from professionalschools, department chairs, and other departmentaladministrators?

What gender and race categories should be examined:Asian women, all minority women, Latino men? Whichvariables should be included: initial rank, current rank,publications, previous experience, teaching quality, dis-cipline, and tenure? What outcome measures will beused to diagnose bias: standardized or unstandardizedcoefficients, residuals, adjusted R2, or statistical signifi-cance? Each of these questions can have political impli-cations, and each can affect the study results. How thequestions are answered may depend on who is on thepolicy-making committee.

When other considerations are equal, it is best toappoint people who are comfortable with research andstatistics. They do not need to know a lot about statisti-cal methods, but they must not be intimidated by statis-tics or afraid to insist on basic explanations about theorigin and the importance of the numbers. Appendix Acontains information committee members will needabout regression analyses.

Avoid statistical snobspeople who know a lot aboutstatistics, but who cannot or will not explain the impli-cations of statistical findings to others. If you end upwith a "trust me, I know it all" type on your committee,you will need to read this guidebook very carefully orfind someone with knowledge equal to that of your col-league to cut through the verbal fog.

Policy decisions that seem neutral to some committeemembers may be viewed as an affront by others.Ensuring good communication is the best way to mini-mize confrontation and arrive at effective outcomes.But even the best communication cannot eliminate alldifferences. If you cannot gain the cooperation of theadministration in designing a valid study or in address-ing salary inequities, you may find the strategies inappendix E helpful.

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Study PopulationWho should be included in the study? It might be betterto ask this question in the negative: who should not beexcluded from the data? Non-tenure-track or temporaryfull-time faculty, whose ranks tend to include manywomen and minorities (Chronister et al. 1997), are oftenleft out because their jobs are deemed "different." Thisdifference is usually vaguely defined as their having toteach lower-level courses or their being governed byseparate hiring and promotion criteria. Comparable dif-ferences in teaching expectations and in appointmentand evaluation standards are found across assistant,associate, and full professor ranks, making this logicunpersuasive. (This issue is dealt with in more detail inchapter 6.)

Excluding non-tenure-track faculty from the analyseswill almost surely mean that they will not be consideredfor any salary adjustments that may result from thestudy. In other words, a group of low-paid and oftendisproportionately female and minority faculty mem-bers will be denied the opportunity to have any bias intheir salaries corrected (Gray 1993; Hamermesh 1996).

Besides, multiple regression can separate out pay dif-ferences that are unrelated to gender or race, as long asrank or tenure status is taken into account. In our analy-ses of the twenty-nine SUNY campuses, for example, weincluded all full-time faculty members. To allow theequation to account for salary differences caused bytenure status, we included a variable for lecturer, whichis the non-tenure-track rank at SUNY. That way, thesalary differences based on gender and race within thelecturer category could be measured as part of the coef-ficient for the gender and race variables, while salarydifferences related to non-tenure-track status wereattributed to the coefficient for lecturer, not to race orgender. In short, we recommend that all full-time facul-ty, including those not on the tenure track, be includedin the database.

But what about part-time faculty? Here again, womenand minorities constitute a high proportion of the popu-lation. Many must piece together an existence by teach-ing part time at several institutions. Unfortunately,including part-time and less-than-full-time adjunct fac-ulty in a multiple-regression salary assessment is almostimpossible. Institutions keep little automated informa-tion on such faculty, among whom the turnover rate ishigh. In addition, part-time faculty tend not to respondto questionnaires, making systematic collection of dataon them difficult.

Another issue is that many part-time faculty are paidon a per-course basis rather than according to careerattributes such as experience. Thus a retired part-time

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professor with many years of teaching experience maybe paid no more than a graduate student. You maywant to consider examining per-course pay rates foruniformity across gender and race.

If part-time faculty at your institution are paid on asalary rather than on a per-course basis, and if you havedata on them that parallel the data you have on full-timefaculty, include them in your analyses. To do so, youwill need to adjust their salaries to make their pay com-parable to that of full-time faculty. If, for example, part-time professors at your institution work half time, youwould double their salaries to approximate what theywould make as full-time faculty members. You will alsoneed to include a part-time variable in your analyses.

If, as is likely, you do not have data on part-time fac-ulty that are comparable to what you have on full-timefaculty, consider extending any remedies for bias foundin the full-time analyses to part-time employees, prorat-ed to the proportion of time they work.

Data CollectionUnless your campus is way behind the times, it has anautomated personnel and payroll data system. This sys-tem houses the information needed to ensure the accu-racy of paychecks and usually includes date of initialhire, date of appointment to current rank, current rank,discipline or department, salary, and contract length(nine-month or twelve-month year). It may also recordgender, race, and age in order to meet federal reportingrequirements.

On some campuses, the database including personnelinformation, such as race and year of hire, may be sepa-rate from payroll data. If that is so at your institution,obtain a separate download of each database, makingsure that a common identifier, such as social securitynumber or first and last name, is attached to the infor-mation for each individual. The common identifier canbe used to merge the two data sets.

Larger campuses will probably have an institutionalresearch department that relies on the personnel andpayroll data set for the faculty information it maintains.Such departments conduct statistical analyses and pro-vide descriptive statistics to assist and advise campuspolicy makers. Some institutional research departmentshave added useful information such as initial rank,highest degree attained, and year of highest degree tothe database.

As the automation of data increases, more institution-al research departments are collecting data on prior fac-ulty experience, performance measures, and the year ofeach promotion. We address the relative importance ofyears of experience at hire and proxies for that informa-

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Database Decisions and Development

tion later in this chapter and in chapter 5. Chapter 1 dis-cusses productivity and performance measures and theuse of current rank as a proxy for them.

Of course, "low-tech" or "hard-copy" sources of datastill exist. These include the personnel forms filled outby new hires, paper-based personnel records, and cam-pus catalogs (which may contain highest degreeattained, source of degree, and year of initial hire inaddition to rank and department). Having been spoiledby the convenience of automated data, we shudder atthe thought of the labor-intensive task of collecting andentering data from these sources. If you are lucky, youwill have to rely on such sources only to check the accu-racy of inconsistent data for a few individuals.

Your access to institutional data will depend, ofcourse, on your relationship with your campus adminis-tration. The more cooperative the administration is, theeasier it will be to access, collect, and verify data.Faculty groups that are not recognized bargaining unitsor unions may have more difficulty than recognizedgroups in gaining administrative cooperation, especiallyat institutions at which there is no public access tosalary information. In the United States, faculty salariesat public institutions are technically open to publicscrutiny under freedom-of-information legislation, andprivate colleges and universities can be forced to pro-vide pay data by a court order. (In Canada, however,public-sector salaries can be kept secret.)

Fortunately, it is often unnecessary to go to extremes.Many institutions, even private, nonunionized collegesand universities, have been responsive to the concernsof women and minority faculty groups and haveworked collaboratively with them to study facultysalaries. For the purposes of this discussion, however,we will assume that you will have little, if any, coopera-tion from the administration.

Under collective bargaining agreements, most unionsreceive information about their members, such as name,social security number, address, phone number, depart-ment, current rank, and salary. Can you "make do"with this limited data set? If you add gender and race,you can do a regression analysis of salary to see if gen-der or race bias seems to be present when you controlfor discipline and current rank. Of course, additionalmeasures, like years in rank or years at the institution,would account for more of the variation in salaries andprovide a higher adjusted R2.

If a preliminary assessment indicates bias, adminis-trators will probably protest that the apparent biaswould disappear if you controlled for additional vari-ables. They could be right. If women and minoritieshave less time at the institution and in their current

rank, controlling for these variables may make the evi-dence of bias disappear. But then again, it may increase,or decrease just a little.

Tell the administration that you would be happy tosee if the bias disappears with more control variables,and ask for information on the relevant variables.Administrators may do their own analysis. If the evi-dence of bias disappears, they will, in all likelihood,give you the data so you can verify its findings. Anunwillingness to provide you with the data may indi-cate that the bias persisted or perhaps even increased inthe administration's analysis.

When pressed for data, the administration may offerto do the research and show you the results instead.That is a tempting offer. Whether to accept it willdepend on how much you trust the administration andthe individual or individuals who will do the analyses.Meet with them. Discuss the data set they will use, thevariables, and the types of analyses. Chapter 6 explainsapproaches that can mask bias. Are they proposing touse any of these approaches? Can you agree on the spe-cific variables and statistical approaches to be used?

If you are at a public-sector institution and you haveexhausted friendly persuasion, you may be able toacquire most of the data you need through the Freedomof Information Act (FOIA). With the passage of theFOIA in 1966, federal records became more accessible.All states have subsequently passed similar laws. Thesalaries of public employees as well as most job-relatedinformation such as rank (or job title) and education arecovered by these laws. To find out how to request suchinformation, consult your state's law. A limitation inusing the FOIA is that personal characteristics such asrace, sex, and age are specifically protected againstrelease. You will have to collect these data through com-mon knowledge or other means.

Variables and Possible SubstitutesIn both our original analyses of the twenty-nine SUNYcampuses and our reanalyses of twelve campuses con-ducted to inform the writing of this guidebook, we usedeleven principal variables: salary, gender, race, highestdegree, completion date for highest degree, years sincehighest degree at time of hire, date of hire at institutionunder study, current rank, date of promotion to currentrank, contract length, and discipline.

SalarySalary is, of course, the necessary dependent variable ina study of salary equity; there are no alternatives for it.To analyze the effect of gender and race on salary, accu-rate information on the base salary of each individual in

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the data set is vital. Annual salaries are usually the basicunit of analysis, although monthly salaries have alsobeen used. Temporary summer pay or temporary incre-ments associated with administrative duties should beexcluded; only base salary should be considered. Anadjustment for the amount of time worked may beneeded (see the discussion under "Contract length"below).

GenderGender is another variable for which there is no alterna-tive. Studying the effect of gender on compensationrequires the ability to distinguish men from women.Gender assumptions based on first names are accuratefor about 90 percent of Anglo-Saxon names. Foreignnames, initials, and gender-neutral first names requireverification. Without gender information, a gender anal-ysis is not possible.

RaceRace is also an essential variable. You may ultimatelyconclude that there are too few minority faculty mem-bers at your institution to warrant an analysis of theeffect of race on compensation. But you will need toidentify the racial minorities to make this determination.

Remember that if minority males are underpaid, theirinclusion will lower the average male salary relative tothe average white-male salary. Preliminary analysis candetermine whether or not bias is evident in the salariesof minority men. If it is, exclude minority men from themale reference category. The comparator category fordetermining whether or not bias exists is properly thatof white males.

Legally, certain racial groups are specified as protect-ed classes, but some may be more important at yourinstitution than others. If your campus is in the vicinityof a Native American reservation or near the Mexicanborder, for example, regional demography will influ-ence your concerns.

Our SUNY data included a racial category called"alien," which is made up of noncitizens who are work-ing legally in this country. Noncitizens are not a legallyprotected class, but many faculty members who are notcitizens, most notably Asians, Latinos, and Africans,may be in a protected class. If your data include a non-citizen category, give this group special attention todetermine which of its members are in racial categoriesthat may experience discrimination.

Highest degreeHighest degree earned is an important variable. Anindividual's educational attainment determines many

career markers, such as initial rank, initial salary, andpromotions. Higher degrees garner more prestige andbetter pay than lower degrees, so you will want to havethis variable in the model.

At two-year colleges, a higher proportion of facultymembers will have a master's, bachelor's, or associatedegree, or a vocational certificate, not a Ph.D. Make sureto review the distribution of degrees and code the rela-tive distinctions at your institution.

At some institutions, the data for highest degreeincludes an ambiguous category with a label such as"professional degree." We have found that this label canapply to a range of degrees, including those formedicine, law, business, social work, mechanical draw-ing, and pottery. Categorizing professional degrees mayrequire reviewing the data on each individual in orderto ascertain the level of educational attainment (doctor-ate, master's, or below master's) and coding it to theappropriate category.

Most data on highest degree attained fail to notewhere the degree was earned. Many campuses do, how-ever, have information on the institutions that granteddegrees to faculty in a separate automated file, becauseit is included in the campus catalog. The status or typeof institution can be coded (doctoral, comprehensive,baccalaureate, two year). If you can acquire it, suchdetailed information could prove valuable, particularlyfor initial rank or initial salary analysis. Once an indi-vidual has been working in a field for some time, theorigin of a degree tends to become less important.

An alternative variable for highest degree attained ishighest degree earned at time of initial hire. Some insti-tutions collect degree data when a faculty member isappointed, but never update this information. In ourSUNY study, about 20 percent of academics receivedtheir highest degrees (usually a Ph.D.) after being hired.If your information on highest degree is not current, tryto update it by consulting the college catalog, deans orchairs, or the faculty members themselves.

Completion date for highest degreeCompletion date for the highest degree is a time vari-able used to estimate experience. After receiving theirhighest degrees, faculty begin to acquire experience intheir field. Those who finished their degrees many yearsago are likely to be more experienced and more valu-able to the institution than recent graduates.

Years since highest degree at time of hireIf, however, you measure experience by calculating theyears since the highest degree was completed, thatinformation will overlap with the variable for date of

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Database Decisions and Development

initial hire (discussed below). To make the data lessredundant, create a variable for previous experience bycounting the years since highest degree at time of hire.Those who received their degrees before being hiredwill have a positive value for the variable, while thosewho completed their degrees after being hired will havea negative value.

Although years since degree at time of hire is indeeda possible proxy for previous experience, its useinvolves an assumption that once a degree is received,the recipient begins working in her field and continuesin it until being appointed at your institution. But thecontinuity of employment after degree completion mayvary by gender. Women may be more likely to take timefrom employment for family work. Using data sets fromthe twelve SUNY campuses we studied, we comparedthe number of years since degree with the variable forexperience prior to hire. Women had fewer years ofexperience recorded for their years since degree thanmen did. As we discuss below, we have no way ofknowing how carefully this information was gathered atthe various campuses. Our data are, however, consistentwith the hypothesis that women are more likely thanmen to take time out from continuous appointments.Thus, using years since degree prior to hire as a proxyfor previous experience may credit women with toomany years in their field.

Age is sometimes used as a substitute for years sincedegree at time of hire, but we do not recommend it.People tend to proceed from kindergarten throughgrade twelve and sometimes even through undergradu-ate college with little time out. But education beyondthe bachelor's degree is less age-specific. Moreover, theage at which degrees are received may vary by genderand race, with women and minorities receiving degreesat older ages on average.

We suggest proxies (alternative variables) to measureprevious experience because most campuses do notinclude information on relevant experience at the timeof hire in their automated data sets. Even when theinformation is available, its quality varies depending onwho collected and quantified it. It can easily be tar-nished by gender or race bias. A man who was anadministrative assistant in the business world, for exam-ple, may have his experience counted as relevant for afaculty position in the business department, yet awoman who gained similar work experience but had atraditionally female title, such as office manager, mayhave her experience discounted as "only clerical."

If you collect data on previous experience, we recom-mend that you create a list of acceptable positions and areliable method for calculating the number of years of

such experience. Although the SUNY data included avariable for relevant previous experience at time of hire,we suspect that the level of care taken in collecting andcoding these data varied from campus to campus.Assessing work experience after the fact is complicated.You may have to consult paper files in the personneloffice or look through vitae and resumes. This processcan be time consuming; is it worth the time?

To answer that question, we performed a test on thedata from our twelve SUNY campuses. We dropped theprevious experience variable and reran our regressionanalyses for each of the campuses. The adjusted le tend-ed to decrease by less than three percentage points. Outof the twelve schools, it increased at only two campuses,and then only slightly. (See chapter 1, appendix A, orthe glossary for discussion of R2.) The effect on indica-tors for gender and race bias was mixed, with half of theschools showing less bias and half of the schools show-ing more. At only four institutionstwo universitiesand one two-year and one four-year collegedid theresults indicate increases in bias in excess of $100, thelargest increase being $500.

Our mixed findings led us to conclude that whetheror not you take the time to collect detailed data on pre-vious experience depends on two factors. First, if policymakers at your institution are concerned that yourproxy variable for previous experience credits womenwith more than they actually have, you should collectthe necessary data about actual previous experience.

Second, you should also do so if you are being pres-sured to include initial rank in your regression analysis.Our categorical modeling of this variable suggests sub-stantial gender bias in assignments to initial rank. Youwill want to use the previous experience data you col-lect to assess whether initial rank is tainted. Chapter 6discusses in detail why we believe it is inappropriate toinclude initial rank in regression analyses.

Date of hireDate of initial hire in a faculty line at the institutionunder study is another measure of experience. It allowsfor calculation of important time variables, such asyears at institution and years at institution prior toachievement of current rank. These time variables arecritical to analyses of both rank and salary.

If you do not have date-of-hire information, you canapproximate it if you know the number of years facultymembers have been at your institution (subtract thenumber of years from the date of the database creation).There is a potential disadvantage to using this kind ofcalculation: a person entering data in January 2002, forexample, may credit everyone starting in 2001 with a

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Lois Haignere and Yangjing Lin

year of experience regardless of whether an individualwas hired in January or September 2001. Using the dateof hire to calculate the variables associated with time atthe institution is a more accurate approach.

What about part-time experience? Your analysis willprobably include only full-time faculty because of thedifficulties associated with maintaining accurate recordsfor part-time faculty. But some of those who are nowfull-time faculty members may also have had part-timeexperience at this campus. If such experience were dis-tributed equally among men and women, then all part-time histories could reasonably be disregarded in thesalary analysis. At the twelve SUNY campuses we stud-ied, we found that women were about four times aslikely as men to have part-time experience. Not consid-ering this experience in the analysis would tend, there-fore, to make any salary disparity between men andwomen appear to be less than it would be when part-time history is taken into account.

Of course, one year as a part-time faculty membershould not be equated to one year of full-time service;part-time employment should be translated into a full-time equivalency. We took the conservative approach,treating each year of part-time service as equivalent to athird of a year of full-time experience. We did so bymultiplying the part-time variable by 0.33. Thus, twoyears of part-time service equaled 0.66 years of full-timeemployment.

Do you need to go to all of this trouble? We examinedour data and regression analyses with and withoutincluding part-time experience to answer that question.We found that part-time experience influences theregression results when either of two conditions exist:(1) when 20 percent or more of the faculty have part-time experience, or (2) when the average number ofyears of part-time experience is greater than three. If thepart-time experience in your population does not meeteither of those conditions, then you can probably drop itfrom your analyses. The difficulty is that you have tocollect the data on years of part-time service to know ifeither of the two conditions exists on your campus. Inthe SUNY study we found that dropping part-timeexperience changed the results of the analyses at twofour-year colleges and two two-year colleges. Droppingpart-time service did not substantially change theresults at the remaining eight schools.

Current rankCurrent rank is the most hotly debated type of informa-tion included in regression analyses. It reflects the insti-tution's assessment of a faculty member's performanceand is therefore viewed by some as a proxy measure for

22

performance. At most colleges and universities, howev-er, the same people and processes that control salariesgovern promotions to rank. If bias affects salaries at aninstitution, it probably also influences rank (see chapter4). Whether or not you ultimately decide to use currentrank in your analyses, you should collect rank data toassess its appropriate use and potential bias.

Because gender bias can affect current rank, it is agood idea to gather consistent, accurate information onthe performance variables that determine rank.Information on these variables, which include publica-tions, research grants, teaching, and community service,is difficult to collect and quantify. To create valid dataon publications, for example, the value of books ormonographs relative to journal articles would need tobe coded according to how a discipline assesses them.Each journal article, in turn, would need to be weightedby the prestige of the periodical in which it appeared.For grant funding, it would be best to consider both theamount of money going for overhead and the totalaward. Regarding teaching, should teaching load orteaching quality be included? If so, how should thisinformation be collected?

It is unclear how these performance variables wouldaffect study results. Because of the unwieldy size anddiversity of the SUNY system, we made no attempt tocollect performance data. As a result, we cannot assessthe implications of substituting such data for currentrank.

Date of current rankDate of promotion to current rank is another measure ofexperience. Without such a variable, we have no way todistinguish between a professor who reached her currentrank within the past year and one who has been in therank for fifteen years. We would expect the fifteen-yearveteran to have more experience and a higher salary.

If possible, collect dates for each promotion through-out your faculty members' careers. Having each promo-tion date simplifies any modifications that may be nec-essary if rank analyses show substantial bias. It also pro-vides the detail necessary to conduct event history anal-yses of promotions (see chapter 4).

Contract lengthContract length is a variable that indicates whether afaculty member's annual salary is earned over aneleven- or twelve-month calendar year or a nine- or ten-month academic year. Perhaps the most direct way toadjust for differences in contract length is to use month-ly salary rather than annual salary as the dependentvariable. Your institution's automated database may

Database Decisions and Development

not, however, include monthly salary figures.Remember also that if salaries are earned in ten monthsbut paid out over twelve, they are still ten-monthsalaries and must be adjusted accordingly. Anotherdirect way to adjust for differences is to change thesalaries of those working eleven or twelve months toreflect the amount of money they would have made ifthey worked only nine or ten months. Institutions thathave a nine-month academic year usually adjust allcalendar-year salaries to the fraction 9/11. The fractionused for adjustment varies relative to the paid vacationtime awarded to those working the calendar year. Somestudies have included the contract-length variable in theanalyses even when the dependent variable has beenadjusted for academic- and calendar-year salary differ-ences. That should not be done unless it can be demon-strated that the contract-length variable is not tainted(see chapter 4).

DisciplineDiscipline is a control for market differences. Including avariable for discipline in the salary analyses ensures thatpay differences related to discipline are not attributed toeither race or gender bias. In essence, that means that westatistically measure the effects of gender and race bycomparing faculty who are in the same discipline.

University studies have indicated that the greater theproportion of women in a discipline, the lower the aver-age salary (Staub 1987; Be llas 1997, 1994). The relation-ship between the proportion of women in a disciplineand the salaries its practitioners receive is relevant tothe movement outside academia for equal pay for com-parable worth. In this guidebook, however, we addressonly within-discipline salary bias (equal pay for equalwork), not across-discipline salary bias (equal pay forcomparable work).

Chapter 1 noted that college and university depart-ments enjoy much greater autonomy than do equivalentdivisions of many other public and private employers.The result is that the vagaries of the market and of indi-vidual administrators can affect salaries in higher edu-cation. In the public sector, entry-level professionals byand large make the same salary whether they begintheir careers in the State Department or in theDepartment of Education. And entry-level K-12 teach-ers generally receive equal remuneration no matterwhat they teach.

In most institutions of higher education, however,faculty members are not treated in the same way. Thesalaries entry-level professors expect and receive varywidely according to their discipline and department.Faculty members on the same campus who teach the

same number of classes and students for the same hourscan be paid quite differently depending on what theyteach. That is so even at two- and four-year undergrad-uate institutions that emphasize teaching over research.

To allow for salary differences across disciplines, weincorporate a measure for discipline into the analyses.That may sound simple enough, but this measure is nota single variable but many. Variables that are categorical(male and female, for example) as opposed to numerical(years in rank) must be entered as dummy variables. Insimple terms, to specify ten academic disciplines, youwould need nine discipline dummy variables and atenth one as the default category. (See chapter 5 andappendix A for information on dummy variables.)

The number of disciplines that can be entered validlyinto a regression analysis depends on the number ofindividual faculty members in the database. If the num-ber of variables entered comes close to the number ofcases being examined, the regression model will not bevalid. In research vernacular, such a situation is called"overspecifying the model." Generally, you need atleast five cases (faculty members) for each independentor predictor variable. But that is a minimum; for robustfindings, it is best to minimize the number of variablesby maximizing the size of the discipline units used. Useonly the discipline units that have a substantial impacton determining faculty salaries at your institution.

The Classification of Instructional Programs (CIP)codes developed by the U.S. National Center forEducation Statistics combine departments into disciplinecategories that logically relate to both subject matter andmarket salaries. We have used CIP codes in many facul-ty salary studies and generally recommend their use.

Alternatively, you may choose to cluster departmentsinto disciplines based on common administrative units.You may, for example, count departments in the samecollege or under the same dean as disciplines. A statisti-cal procedure called cluster analysis can also be used todetermine which departments are statistically similarbased on a set of categories including salary but exclud-ing gender and race. Whichever approach you use tocombine departments, it is important to eliminate orminimize clusters that contain fewer than five facultymembers.

Variables for Verification of DataIn our analyses, we commonly use five categories ofinformation (name, social security number, birth date orage, department, and initial rank) to verify individualdata points that seem to be in error.

Name and social security number are useful identi-fiers when data problems are discovered. Without them,

33 23

Lois Haignere and Yangjing Lin

you will be unable to verify or correct the data thatappear to have errors. If confidentiality is important, aunique identifier for each individual can be substituted.Although the researcher need not know from whom thedata are derived, someone will have to be able to traceeach unique identifier to an individual in order to checkon data errors and inconsistencies.

Information on birth date and age also help in screen-ing for potential errors in the data. If, for example, vari-ables for age and completion date for the highest degreeindicate that an individual received a doctoral degreebefore age twenty, that individual's data should be veri-fied. The use of birth date and other variables are dis-cussed below ("Inconsistencies").

Department name is important to ensure that individ-uals are categorized in the correct discipline. It will alsoassist you in determining how to recode degree infor-mation for those with "professional" degrees.

Information on initial rank can help you check theaccuracy of current rank, years at the institution, andyears in current rank. In our database, we found manyinstances in which initial rank was the same as currentrank and yet years at institution was not the same asyears in current rank. Without initial rank data, wewould not have been aware of these inconsistencies.

Cleaning of DataChecking the accuracy of data is time-consumingdrudge work and requires a tolerance for tediousdetails, but it is essential to the validity of your findings.Even if the data have been very carefully collected, youwill probably find errors. The data-cleaning processinvolves finding and eliminating missing values, irregu-larities, and inconsistencies.

Missing valuesMissing values are easy to spot but hard to eliminate.Gaps in the data usually come about because of difficultyin getting information about particular individuals. Butlack of data about a faculty member effectively excludesthat person from the analysis and may affect the validityof the results (N. Moore 1992). If data on a variable aremissing for many faculty members, either the informa-tion should be collected and added to the data file or thevariable should be excluded from the analysis.

IrregularitiesIrregularities in the data are values that are impossibleor illogical. If, for example, your data for educationalattainment has eleven codes (1 = less than grade 7; 11 =doctoral degree), any code other than 1 through 11amounts to an irregularity that should be corrected. If

24

you have a collective bargaining agreement that speci-fies minimum salaries for each rank, use the minimumsas screening criteria to flag all those who are belowthem. A below-minimum salary may result from a data-entry error, or it may signify a part-time faculty membermistakenly counted as a full-time faculty memberor itmay call attention to a full-time faculty member who isbeing underpaid and should receive a salary adjustmentto reach the minimum. Printing out all of the data on acase that appears to have an irregularity may allow youto make sense of it based on the person's total profile.

InconsistenciesAlthough eliminating inconsistencies is more time con-suming than locating missing data or removing irregu-larities, it is just as important. Locating inconsistenciesinvolves comparing the data on two or more variables.The criteria for screening out inconsistencies should bedecided by the members of the research team. Here aresome of the criteria we have used to clean data sets.

Initial rank versus current rank. Note any cases inwhich a person's current rank is lower than the initialrank. A faculty member may have moved from assistantprofessor to a non-tenure-track rank such as lecturer toavoid the tenure clock. But it is unlikely that a facultymember who was initially an associate professor wouldbecome an assistant professor. Although we haveencountered cases of faculty being downgraded, appar-ent downgrading usually indicates an error.

Year of highest degree versus year of birth. Data indicat-ing that a faculty member born in 1949 received a Ph.D.degree in 1960 are suspect. In screening for potentialproblems, we project that most people will be twenty-one before completing a bachelor's degree, twenty-threebefore finishing a master's degree, and twenty-fivebefore earning a doctorate.

Total years of experience versus year of birth. If you haveseveral different measures of experience (years in rank,years at the institution, years since highest degree at timeof hire), you can create an estimate for total years of expe-rience and compare it to the age variable. How young istoo young to have acquired relevant experience? Wescreen any case in which a person seems to have acquiredrelevant faculty experience by age twenty-two.

Assistant professor rank versus years in current rank.According to the tenure system, assistant professorsmust achieve tenure, which is usually accompanied bypromotion, before their fifth, sixth, or, most commonly,seventh year in rank. If they fail to do so, their appoint-ment is expected to terminate. So if your data showtenure-track assistant professors who have been at theinstitution for more than seven years and who were not

36

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appointed initially in a non-tenure-track rank, you prob-ably have errors. Look for an error in current rank oryears at the institution. Some assistant professors, albeita small minority, receive tenure without promotion andremain in the rank indefinitely. You can use informationon tenure to screen for this possibility.

Years in current rank versus years at the institution.Logically, years in current rank should be the same as orless than years at the institution. If, for example, yourdata show that a faculty member has been in the currentrank for fifteen years but at the institution for onlytwelve, you need to investigate the three-year discrep-ancy. Such inconsistencies sometimes arise as a result ofleaves of absence, but they should be checked.

Current rank and initial rank versus time in current rankand time at the institution. When initial rank is the sameas current rank, years in current rank should be thesame as years at the institution. But we have found indi-viduals who had more years in current rank than yearsat the institution and vice versa. Some of these inconsis-tencies can be technically correct but need clarificationin order to judge the probable impact on salaries. Wefound, for example, a faculty woman who was appoint-ed as an assistant professor in 1976, became a nonteach-ing professional (academic counselor) in 1981, and wasrehired as an assistant professor in 1989. Her reportedinformation was initial rank: assistant professor; currentrank: assistant professor; years at the institution: fifteen;and years in current rank: two. We recoded her years incurrent rank to reflect the time she spent as an assistantprofessor (1976 to 1981 and 1989 to 1991, for a total ofseven) and her years at the institution to those when shewas in a faculty rank, which was also seven years.

When initial rank is not the same as current rank,years in current rank should be less than years at theinstitution. Check also for instances in which facultymembers have moved more than one promotional step,for example, from assistant to full professor, in only oneor two years. We examine the data for anyone advanc-ing more than one rank in five or fewer years and findthat data errors account for most of these apparentmoves. But there are indeed fast-track faculty who risetwo or more ranks in five or fewer years.

Your goal is to rectify any gender- or race-basedsalary inequities that exist at your institution. To accom-plish this goal, you and everyone involved must haveconfidence in the accuracy of the data collected.Ensuring accuracy is therefore necessary. When youhave selected the right variables and gathered completeand accurate data, the results of your study will be seenas a valid basis on which to assess bias in salaries anddetermine any adjustments needed to correct it.

Notes1. At the SUNY institutions we studied, we found that includ-ing part-time experience added complexity to collecting,cleaning, and coding the experience variable for years at theinstitution. Our data consisted only of total years of part-timeexperience and total years of full-time experience, leaving usto wonder whether the part-time experience occurred duringthe current rank or during the years prior to current rank, andwhether date of hire referred to the date a person startedworking part or full time. These questions plagued us whenthere were data inconsistencies between years in current rank,years at the institution, and date of hire.

2. Toutkoushian (1994b) has made interesting use of citationsas a measure of performance and found that considerableunexplained salary differences still existed between men andwomen. This finding may be consistent with Valian's (1998)observation that while women publish less, their publicationshave a higher rate of citation.

3. In our original study of the twenty-nine SUNY campuses,we did not deal with differences in contract length by adjust-ing the dependent variable for salary because of concernsabout differences in the academic year across the campusesunder examination. Instead, we entered the contract lengthvariable in the analyses. Thus we held constant the differencesin months worked with a control variable. We do not neces-sarily recommend this approach. Subsequent to completingthe SUNY analyses, we have become aware of a potential forbias in the disproportionate awarding of calendar-year con-tracts, and the administrative responsibilities often tied tothem, to white men (see "Problem 4" in chapter 6).

4. In chapter 5 we indicate how creating a continuous variablefor discipline using average salaries circumvents the regres-sion analysis and why such a variable should not be used.

5. Some institutions have non-tenure-track or visiting scholarsenior ranks. They are common at professional schools thatrun clinics, but they also exist elsewhere. At these institutions,the inconsistency of having moved from a higher to a lowerrank may be related to moving from the nontenure track to thetenure track.

25

Our study revealed that one of the major sources of differential is the rate at which women arepromotedor not promotedand the longer period of time they remain in rank. It's not easyto pursue equity; it can be a lonely and even debilitating experience. Yet I have found thatworking together provides more than just better salaries. The sense of solidarity and empower-ment is tremendously rewarding. I firmly believe that those of us who have been able to makegains must use our experience to help other women faculty achieve equity.

Wendy Wassyng RoworthProfessor of Art History and Women's Studies

University of Rhode Island

FOUR

Gender and Race Bias in Current RankBy Lois Haignere and Bonnie Eisenberg

Unlike the rest of this guidebook, this chapter doesnot focus on assessing bias in salaries. Instead, itexplains methods for estimating whether or not

bias affects the awarding of rank. Making such a deter-mination is important because of disagreement overusing current rank as a predictor variable. Warning: thischapter contains technical terms. You may need to con-sult the glossary for definitions.

Some argue that the current rank variable is potential-ly tainted and that its inclusion in the regression modelwill underestimate the gender or race bias in facultysalaries (Scott 1977; Allen 1984; Ransom and Megdal1989). The people and processes involved in settingsalaries at an institution probably influence rank andtenure decisions. Thus, if salary patterns are biased, pro-motion patterns will probably be so as well. Researchshows that women and minorities disproportionatelyhold lower ranks and that women spend more years inlower ranks before receiving promotions (Gray 1993,1990, 1988, appendix H). Little wonder that includingvariables for current rank and tenure in studies of salaryequity has led to a major debate in the literature.

Most studies, however, do include current rank as anindependent variable, usually without apology or justifi-cation (Schrank 1988; Gray 1991). Those who offer justifi-cation argue that salary discrimination should be definedas unequal pay for equal work. Two people in the samejob level or rank have equal work; any discrimination inthe awarding of rank is irrelevant to a study of salaryequity. Nelle Moore adds that current rank is a strongdeterminer of salary and the best available proxy for pro-ductivity measures such as research, publications, andteaching. In "Using Regression to Study Faculty Salaries"(1991), mathematics professor Mary Gray summarizes thepredicament over whether or not to include current rank:

The dilemma is that if rank is not used in aregression model of salaries, differences per-ceived to be based on gender may be just theresult of differences in rank distributionbetween men and women. On the other hand,the differences in rank distribution may be theresult of discrimination . . . resulting from place-ment of equally qualified men and women indifferent ranks.

Excluding current rank from the analyses can overesti-mate bias; if it is tainted, including it can underestimatebias. To illustrate the effect of a tainted variable, we rananalyses on a SUNY data set with and without a variablefor initial rank, which statistical analysis had shown to besubstantially gender biased. We included current rank inthese analyses. When the tainted variable for initial rankwas used, it masked about a third of the gender bias oth-erwise shown. The methods described in this chapter donot solve the "taint problem," but they can help you findout where it may exist and approximate its magnitude.

Details and OptionsThe level of detail available in your data will affect bothyour ability to test for bias in rank assignments and thestatistical methods you select. On the low end of thescale, you may know only the proportion of men andwomen faculty at each rank. At the high end, you mayhave data for each faculty member indicating eachcareer transition, including when he or she earned thehighest degree, was hired, and moved from initial toeach subsequent rank.

The level of detail available for current rank analysesat most colleges and universities falls between the lowand the high end. Automated filing systems commonly

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Lois Haignere and Bonnie Eisenberg

include data for each faculty member on the date ofhire, the highest degree, the year of highest degree, cur-rent rank, initial rank, gender, and race. With this levelof information, categorical modeling methods can beused to estimate the existence of gender bias across thecategories of current rank.

If you are fortunate enough to have complete detailsconcerning the career histories of your population, youcan employ event history analysis to ascertain the pro-portion of men and women reaching a certain promo-tion at a specific point in their career.

Later in this chapter, we will discuss how to use cate-gorical modeling and event history analysis to assessbias in rank. First we will illustrate how frequency tablescan help you discover potential bias in rank assignmentsif you do not have the detailed data necessary to do cate-gorical modeling or event history analysis.

Frequency TablesIf you know the current rank and the gender or race cate-gory of the faculty members in your population, you cancreate distribution tables that will give you a sense of theproportional distribution of men, women, and minorityfaculty throughout the ranks. In table 4.1 we present afrequency distribution for a hypothetical institution toillustrate how this information can be displayed so as toshow whether or not women and minorities are repre-sented proportionally throughout the ranks.

The percentages in the table cells reveal the distribu-tion of the different gender and racial groups across theranks. Since, for example, there are a total of five minor-ity faculty members, the one minority lecturer in thefirst cell and row represents 20 percent of the minoritiesat this hypothetical institution. You can see a higherproportion of white males at the senior ranks compared

with any other racial or gender group. A frequencytable like this one can make visible the total lack orunderrepresentation of a race or gender category, suchas minority females in this example. Thus frequencytables may suggest recruitment and hiring problems aswell as those related to rank placement and promotion.

Unfortunately, distribution tables do not control forother variables while looking at gender and rank. Thesetables cannot, for example, address concerns about the"pipeline." Studies of the distribution of men andwomen at U.S. and Canadian institutions of higher edu-cation have found a larger proportion of women at thelower ranks and a larger proportion of men at the high-er ranks. But since a faculty member cannot get intohigher ranks without first passing through the lowerranks, it may be that women and minorities have justnot been in the faculty pipeline long enough to be pro-portionally represented at the senior ranks.

Categorical ModelingOther "yes, but" issues besides the pipeline are some-times offered to explain the lower ranking and pay of fac-ulty women. Some people argue that women are at lowerranks because they are less likely to have a Ph.D. andhave fewer years of experience. To do statistical testing ofany of these arguments, you need the data we describedabove as commonly available in most automated filingsystems: date of hire, highest degree attained, year ofhighest degree, current rank, initial rank, gender, andrace. If you are conducting research on bias in salaries,you probably have individual-level information, whichwill allow you to proceed with a categorical modelinganalysis for bias in rank.

Categorical measures, such as current rank, can beused as independent variables in a multiple-regression

model, but they can-not be used as thedependent variable.3Linear multiple-regression statisticalmethods require thedependent variableto be a continuousvariable, such assalary. Studying thecategorical variableof current rankrequires a differentstatistical method,multinomial logitmodeling; we call thismethod categorical

Table 4.1

Frequency Distribution for Hypothetical InstitutionRANK CATEGORIES

Assistant Associate Fun Row

Race and Gender Lecturer Instructor Prof. Prof. Prof. TotalsCategories # % # % # % # % # %

All Minorities 1 20 0 0 3 60 0 0 1 20 5All Whites 2 4 9 9 30 29 34 33 27 26 102All Females 0 0 6 23 7 27 7 27 6 23 26All Males 3 3.5 3 3.5 26 33 27 33 22 27 81White Males 2 2 3 4 23 30 27 36 21 28 76Minority Females 0 0 0 0 0 0 0 0 0 0 0

Rank Totals 3 5 9 8 33 31 34 32 28 24 107

28 39

Gender and Race Bias In Current Rank

Table 4.2

Categorical Modeling: A Pairwise Comparison for Gender Bias

Number of femalesin rank A

Number of females in thenext higher rank

The Odds

Ratio

compared to

Number of malesin rank A

Number of males in thenext higher rank

modeling for simplicity (appendix F includes technicalinformation on categorical modeling).

Like regression modeling, categorical modeling has adependent variable and predictor variables and cancontrol other predictor variables while it tests the effectof gender or race. Years of experience and educationalattainment are held constant by the categorical model-ing procedure while it examines whether women andminorities are found in the same proportion as whitemen across ranks.

Categorical modeling cannot handle many predictorvariables. This limitation arises from the lower range ofvariability in faculty ranks compared with salary. Onehundred faculty members, for example, may have ahundred different salaries but only five or six differentranks (even if we count the less populated ranks of lec-turer, instructor, and distinguished professor).

As a rule, reduce the number of variables in a categor-ical model whenever possible. Instead of including eachgender and race category (white male, white female,African American male, African American female,Asian male, Asian female, Latino male, Latino female,and so on), try reducing these categories to white,minority, male, female, and an interaction term (seeglossary) for minority female.

The results of categorical modeling are odds ratios,where the odds of women (or minorities) being in onerank rather than another are compared with the sameodds for men (or whites). Table 4.2 illustrates the oddsratio, which can also be thought of as a pairwise compar-ison of adjacent ranks. Categorical modeling is actuallymore complicated than calculating these simple ratios,because it controls the independent variables, such asprevious experience, educational attainment, and yearsat the institution. Also, to produce the best estimates, themodel uses all available information, even for thoseranks not involved directly in the particular comparisonunder review. (All the data for instructors, lecturers, andfull professors are used to create estimates comparingassistant to associate professor, for example.)

ConstraintsIf your campus has a smallfaculty or few women andminorities, can you test for biasin current rank? The answerdepends on three factors: (1) thenumber of faculty in relation tothe number of predictor vari-ables included in the model; (2)the number of faculty in eachrank; and (3) the presence ofzero cells.

Number of predictor variables. With ten predictor vari-ables, we were able to conduct categorical modeling atall but our smallest SUNY school. At this campus,which had only ninety-nine faculty members, categori-cal modeling worked well with five predictor variables.Schools with fewer than a hundred faculty may have tolimit the number of predictor variables or forgo categor-ical modeling.

Number of individuals in a rank. If a rank included inthe study has fewer than three people, categorical mod-eling will probably not work. In such a situation, youshould either combine that rank with the next closestone, or drop it from the analysis. If you choose to com-bine ranks, the results become more complicated tointerpret. If, for example, instructors are combined withassistant professors to create a new category, the resultswill estimate the bias affecting promotions from instruc-tor or assistant professor to associate professor. But howlikely is it that an instructor will be promoted directly toan associate professor?

Choosing to drop a rank from the analysis may havepolitical ramifications. In our experience, the only rankswith fewer than three incumbents have been the lowest(lecturers or instructors) and the highest (leading, dis-tinguished, or named professors). If the low rank con-sists mainly of females and minorities while the highrank consists mainly of white males, you may mask biasby dropping either.

Zero cells. A zero cell is a cell with no one in it. If, forexample, your school has no minority associate profes-sors, it has a zero cell for minority associate professors.You would therefore be unable to use categorical mod-eling to test for race bias between associate professorsand other ranks.

There is a hidden danger in zero cells. Any emptyrank (zero cell) that is included in the model will bedropped from the analysis. If you review the resultswith the impression that the rank was included, youmay misinterpret the findings. So, before starting anymodeling, identify the ranks in which faculty are

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Lois Haignere and Bonnie Eisenberg

found and drop all others. Among our twelve SUNYtest campuses, categorical modeling worked for all butthe smallest school (the one with ninety-nine facultymembers) as long as there were no zero cells.

Variables for categorical modelingGiven that categorical models are sensitive to zero cells,we recommend that you include only those variablesthat are the best predictors of current rank. We alsoadvise you to combine levels of categorical variableswherever possible to reduce the number of zero cells.Your population, for example, may have eight types ofterminal degrees, ranging from a high school diploma toa Ph.D. But if most faculty members have Ph.D.'s, theeight levels of educational attainment can be reduced totwo: Ph.D. and non-Ph.D. Below we summarize the vari-ables we have included in our categorical models, andwe discuss how the number of variables can be reducedto a minimum without losing necessary information.

Response variable. The dependent variable, known asthe response variable in categorical modeling, is thevariable you are studying. This chapter focuses exclu-sively on the response variable for current rank.

Keeping in mind the problem of zero cells, includeonly those ranks that have individuals in them. Avoidcombining ranks unless there are fewer than three peoplein a rank. For the twelve SUNY schools in our sample, wecombined ranks only after modeling failed owing to thepresence of fewer than three individuals in a rank. At oneuniversity and one college, we combined two instructorswith assistant professors. At two colleges, we combinedone leading professor with full professors.

For our analyses of current rank, we included predictorvariables for gender, race, highest degree attained, yearssince highest degree at time of hire, and years at institu-tion. We also used quadratic terms to control for curvilin-earity (see glossary and chapter 5 for discussions of quad-ratic terms and curvilinearity). Keep in mind the need tolimit the number of variables, and include only thosethat most influence achieving rank at your institution.

Gender and race. As we noted above, we did notinclude every possible gender and race combination inour model, because we wanted to avoid zero cells.Instead, we analyzed gender and race, white facultyversus all other race categories, and male versus female.We included an interaction term for race and gender toprovide information on minority women. Combiningall minorities may mask bias when there is substantialbias against only one minority type. Despite this poten-tial problem, we suggest combining categories to avoidzero cells and to produce better estimates by creatinglarger pools of data.

30

Highest degree. Although our SUNY sample had ninelevels of educational attainment, we found that 90 per-cent or more of the faculty at SUNY universities andfour-year colleges had either a master's or doctoraldegree. As a result, we reduced the variable to two lev-els: Ph.D. and non-Ph.D. At SUNY two-year colleges,most faculty had a master's degree as their highest levelof attainment. Thus we used two categories: M.A. andabove, and below M.A. We recommend that you exam-ine the distribution of highest degrees at your institu-tion and limit your variable for educational attainmentto two or three categories.

Years since highest degree at time of hire. This variablecan serve as a proxy for the amount of experience aperson acquired before coming to the institution. It isimportant to give proper credit to those hired withmore experience. (See the discussion of this variableand other variables for previous experience inchapter 3.)

Years at institution. We chose years at institutionrather than years in current rank as a predictor variablebecause years in current rank cannot logically predictthat current rank; the number of years a faculty mem-ber has been an associate professor is not a factor inthat person getting to be an associate professor in thefirst place.

Quadratic terms. We suggest including a quadraticterm for each variable that is a time measure (years atinstitution or years since highest degree at time of hire)to control for curvilinearity. A quadratic term is createdby multiplying a variable by itself. Chapter 5 discussesthe problem of curvilinearity and how quadratics reme-dy the situation. Be aware that although quadratic termssolve one problem, they cause anotherredundancy.For a discussion of redundancy and solutions for it, seeappendix G.

Interpretation of resultsTable 4.3 shows results from a categorical modelinganalysis of current rank at one of our SUNY test cam-puses in which all of the predictor variables listed abovewere held constant. For the promotional step from lec-turer to assistant professor, the odds ratio for the vari-able female is 2.96. That means that women are 2.96times more likely than men to be lecturers rather thanassistant professors. For the same step, the odds ratiofor the variable minority is 3.69: minorities are 3.69times more likely than whites to be lecturers rather thanassistant professors.

Table 4.3 shows little or no bias in the minority towhite category at the two higher-rank transitions. Theodds ratios for the assistant to associate professor step

41

Gender and Race Bias in Current Rank

Table 4.3

Example of Categorical-Modeling Analysis of Rank

Lecturer toAssistant Professor

Assistant toAssociate Professor

Associate toFull Professor

Odds Ratio p-Value' Odds Ratio p-Value' Odds Ratio p-Value'

Female to Male 2.96 0.0741 2.62 0.0006 5.21 0.0001Minority to White 3.69 0.1505 1.08 0.1245 0.82 0.6598

1. The p-Value is a measure of statistical significance. For details, see the entry for statistical significance in theglossary and "Problem 5" subheading in chapter 6.

(1.08) and for the associate to full professor step (.82)are close to 1. An odds ratio of 1 indicates that the twocategories being compared are equally likely to be ateither rank. Thus we can safely conclude that the cate-gorical modeling results indicate little race bias in pro-motions from assistant to associate and associate to fullprofessor.'

But what constitutes substantial bias? Unfortunately,there are no guidelines for assessing that. It would seemthat the odds ratio in the female to male category forassociate to full professor (5.21) indicates substantialbias. It shows that male faculty are five times more like-ly than comparably qualified female faculty to be fullprofessors rather than associate professors. Odds ratiosof this magnitude were rare in our SUNY analyses andseen mostly at the associate to full professor level. Inour opinion, they indicate bias.

But what about the 2.62 odds ratio in the female tomale category for the assistant to associate professorlevel? Does the finding that female faculty are two and ahalf times less likely than comparably qualified malefaculty to be at the associate rather than the assistantrank indicate substantial bias? Our judgment would bethat it does. We suggest that campus policy makers tryto agree on the magnitude of odds ratios that will indi-cate bias before they conduct analyses.

Model ValidityIt is important to know how well the predictor vari-ables account for the differences in the dependent vari-able. If we substituted less valid information, such asnumber of siblings for years at institution, or maritalstatus instead of highest degree, we would still get anodds ratio. But no matter what its magnitude, that oddsratio would not tell us much, because the measures weused would not account for variation in rank levels.What is needed is a measure that indicates the amountof the variation in the dependent or response variableaccounted for by the independent or predictor variables.

For multiple-regression analysis,this measure is the adjusted R2.For categorical modeling, therelative quality of the model isindicated by the R-square sub-L(R2). Appendix F explains thismeasure further.

Summary of steps1. Condense any race or minoritycategories to the smallest num-ber feasible.2. Create a frequency table of

gender and race categories by current rank to identifyany zero cells and to provide a general understandingof the distribution of men and women throughout theranks.3. Where no zero cells appear in pairwise adjacent rank,proceed with categorical modeling using the selectedpredictor variables to produce odds ratios for each ofthe adjacent rank comparisons.4. Calculate an R2, model statistic to estimate theamount of the variation in the dependent or responsevariable accounted for by the independent or predictorvariables.5. Consolidate the results in a table like table 4.3.

Limitations of Categorical ModelingThe categorical modeling analyses described above donot test for bias in promotion over time. They can onlydetect bias in current rank assignments (not promo-tion) at a single point in time, that is, the point atwhich the data are collected. They assess the relativeodds of being in one rank or the other at that moment,and they answer the question: are white men withspecific educational attainment and years of experi-ence more likely to be at a higher rank than women(minorities) with the same educational attainment andyears of experience?

These analyses rely only on demographic variablesconcerning education and experience, and the resultsshould therefore be interpreted with caution. Still, theycan indicate whether the variable current rank is taintedbased on the predictor variables entered, and they cansuggest where rank assignments create glass ceilings forwomen and minority faculty.

Event History AnalysisIf you are fortunate enough to have data showing howmen and women have progressed through the ranks overtime, you may want to conduct event history analyses.Event history techniques can help you answer questions

4231

Lois Haignere and Bonnie Eisenberg

such as: what is the probability of an assistant professorbeing promoted to an associate professor after four yearsof being in rank? How do these probabilities differ forwhite men and women and for minorities?

Like categorical modeling, event history analysescompare the odds of women and minorities to the oddsof white males while controlling for years of experienceand education. Data for every faculty member in thedatabase are used, no matter when the person was eligi-ble for the rank transition being studied. Event history'sadvantage is that it provides results that directly assesspromotions rather than just rank assignments.

The difficulty is that the data needed to conduct theanalyses are not commonly available. The automateddatabases of most colleges and universities maintainyear of appointment information for only the mostrecent appointment, which is current rank. If that is thesituation on your campus, you can do categorical mod-eling analyses but not event history analyses.

To conduct event history analyses, you need to knowthe year each faculty member received each promotionat the institution. The twelve SUNY campuses on whichwe tested the methods described in this guidebook didnot have the promotion details needed to do event his-tory analyses. Fortunately, we were able to test theimpact of different event history approaches on a non-SUNY database. See appendix H for a case study con-ducted at Kent State University using event historyanalyses. Appendix H also provides technical informa-tion and discusses the impact of common expectationsconcerning the timing of promotion.

Population and time frameBecause faculty members that are hired at the seniorranks have been promoted elsewhere or have negotiat-ed rank in conjunction with hiring, we recommend thatyou restrict your study population to those hired at thejunior ranks of lecturer, instructor, or assistant profes-sor. These faculty are more fully subject to the promo-tional mechanism of your institution.

Likewise, it makes sense to restrict the time frame youexamine to the period when a faculty member is eligiblefor the promotion being studied. In the event history ver-nacular, the analysis is best confined to the time duringwhich the individual is at risk of experiencing the event.

Still, we know that events that happen before a per-son is eligible for promotion can affect how soon she orhe gets promoted. Having completed postdoctoral workor having been an instructor, for example, may influencehow quickly an assistant professor is promoted to associ-ate professor. It is therefore tempting to include theseyears in the dependent variable when we examine pro-

32

motion to associate professor.6 But including years as aninstructor in the dependent variable years in rank for ananalysis of promotion from assistant to associate profes-sor would be to consider years when the possibility ofpromotion to associate professor is remote or impossi-ble. Confining your analysis to the years when facultyare truly eligible to experience a promotion does notmean that you have to ignore prior career investments.Predictor variables such as years of experience at timeof hire and years at institution prior to current rankallow the event history analysis to control for theimpact of such periods. In this way, postdoctoral workor experience gained as an instructor can be consideredin predicting the odds of being promoted from assistantto associate professor. But only the years when facultyare eligible to be promoted to associate professor areincluded in the dependent variable.

Person-year unit of analysisThe unit of analysis for most of the methods discussedin this guidebook is the individual person. Each recordor row of data corresponds to an individual facultymember and includes his or her salary, current rank,years in rank, gender, race, discipline, and so on.When conducting event history analyses, however, thebasic unit is a person-year, rather than a person. Thatmeans that a faculty member who has been at an insti-tution for ten years would contribute ten records to anevent history database, one record for each year at theinstitution. The data you obtain for gender and raceanalyses will probably be for persons, not person-years. One way to reorient your thinking to person-years is to physically construct a database in whichyou create a record for each person-year. The data fora faculty member who has been at your institution forten years would be reentered so that the informationwould constitute ten records or rows of data. Eachrecord would contain a code for each variable neededto test for bias in promotion rates. (See the list of pre-dictor variables for categorical modeling given earlierin this chapter.)

Unfortunately, you cannot simply copy an individu-al's record and reenter it ten times. Although there arevariables that do not change with time (race, gender,and years since degree at time of hire), other variables(years in rank and years at institution) change eachyear. Furthermore, some faculty members may nothave received their Ph.D. degree until after theybecame assistant professors. If the data for an individ-ual indicate that she received a Ph.D. in 1978 butbecame an assistant professor in 1975, her first threeperson-year records will have non-Ph.D. as her

43

Gender and Race Bias In Current Rank

educational attainment. For the fourth person-year, the highest degree code will change toPh.D.

In addition to creating the predictor vari-ables for every year an individual contributesto the database, you will need to create a tran-sition variable. All of the faculty members whoreceive a promotion (or transition to a higherrank) in a given year score 1 on the transitionvariable. All of the faculty members who donot receive a promotion in that same year score0 on the transition variable. An individualhired in 1992 as an assistant professor and pro-moted in 1998 would have a transition variableequal to 0 for his person-years from 1992 to1997. In 1998 the code would change to 1.

Probabllhy tablesIf you have complete career history data, youcan construct promotion probability tables toassess the odds of being promoted at eachyear in rank and the proportion of unpromot-ed faculty who have reached a certain year ina specific rank. The figures for the cells in theprobability table are calculated using an equa-tion based on logistic or Cox regression analy-ses that include only years in rank, the genderor race category you are examining, and thetransition variable for the promotion.Probability tables, like frequency tables, donot control for other variables like Ph.D. oryears of experience at time of hire.

The beauty of probability tables is that foreach year in rank examined, the data for allfaculty who have ever reached that year inrank are considered, whether they reached itfifteen years ago or last year. All faculty members whohave reached their sixteenth year as an associate profes-sor, for example, can be studied to compare the differ-ence in the proportion of unpromoted men and womenafter sixteen years as an associate professor.

Table 4.4 shows the relative probability at one insti-tution of male and female faculty members being pro-moted to full professor during each year they serve asan associate professor. The annual promotion rate indi-cates the probability of a faculty member experiencinga promotion from associate to full professor at eachyear. At year 9 as an associate professor, for example,women faculty have a 4 percent chance (.041) of beingpromoted to full professor, while male faculty membershave about double the chance (8 percent or .078) in thesame year.

Table 4.4

Analysis of Promotion-Probability Table:Transition from Associate to Full Professor

Females Males

Annual Cumulative Annual CumulativePromotion Proportion Promotion Proportion

Year In Rank Rate Unpromoted Rate Unpromoted

1

28

458

788

1011

121814151817181920

0.007 0.989 0.0130.011 0.979 0.0210.016 0.963 0.0310.022 0.941 0.0430.029 0.912 0.0550.129 0.783 0.0660.039 0.743 0.0750.042 0.701 0.0790.041 0.660 0.0780.038 0.622 0.0720.033 0.589 0.0630.027 0.562 0.0510.020 0.542 0.0390.014 0.527 0.0280.009 0.518 0.0180.006 0.512 0.0110.003 0.509 0.0060.002 0.507 0.0030.001 0.506 0.0020.000 0.506 0.001

0.9790.9590.9280.8850.8300.7640.6890.6110.5330.4600.3970.3460.3070.2790.2610.2500.2430.2400.2380.237

Note: Event history statistical methods are commonly used to examine certain hazards suchas illness and death. Most event history studies therefore report "hazard rates" and "propor-tions surviving." For applicability to promotions, we have renamed the hazard rate the "pro-motion rate" and the proportion surviving the "proportion unpromoted."

The cumulative proportion unpromoted reports onfaculty remaining in the lower rank of associate profes-sor.' By year twenty, the cumulative proportion ofunpromoted females is .51 (rounded from .506), whilethe cumulative proportion of unpromoted males is .24(rounded from .237). After twenty years at the associateprofessor rank, then, more than half of female facultymembers have not been promoted to full professor. Bycomparison, less than one-quarter of male faculty mem-bers have not been promoted to full professor aftertwenty years at the associate rank. See appendix H foradditional information on promotion probability tables.

Logistic and Cox regressionIf you have created a database in which person-year isthe unit of analysis and each record is one year of a

4'4' 33

Lois Haignere and Bonnie Eisenberg

faculty member's career, you cananalyze this data using a basiclogistic regression proceduresuch as that of Proc Logistic inthe SAS statistical analysis pack-age. As long as you have correct-ly coded variables such as yearsin rank, years at institution, andperhaps highest degree, andchanged them accordingly witheach person-year, you need notworry about time-dependentvariables.

If your database unit of analy-sis is the individual (not person-years), the analysis can beaccomplished using a statistical technique called Coxregression.8 Cox regression can reconstruct a databasewith individual records so as to analyze person-years. Butyou will need to have someone on hand who understandsand can program the Cox regression procedure. There arecomplexities. One is that the procedure needs to correctlyinterpret cases that are never promoted, called censoredcases. Another is that time-dependent variables requirespecial programming for proper entry into the Cox regres-sion calculations.

The computer output for logistic and Cox regressionprovides a coefficient for the gender and race categoriesyou use. The exponential value (see glossary) of thiscoefficient is the relative odds of those in one such cate-gory (e.g., women) being promoted compared with theodds for those in the default category (e.g., men). Table4.5 illustrates gender results from a logistic regressionanalysis including the coefficient, odds ratio, and statis-tical significance (p-value) values for the variable female.

The coefficients resulting from logistic regression areactually log odds. For ease of interpretation, the log oddsare converted to antilogs. In table 4.5, for example, theassistant to associate professor transition coefficient is-0.2197. The exponential of this number yields an oddsratio of 0.803. This odds ratio tells us that female facultyare, on average, 80 percent as likely as comparably expe-rienced male faculty to be promoted to the rank of asso-ciate professor in any one year. For the promotion fromassociate to full professor, the odds ratio indicates thatfemale faculty are, on average, about 51 percent as likelyas male faculty with comparable experience and educa-tion to be promoted to full professor in any one year.

Female to Male

Table 4.5

Event History of Promotion ResultsAssistant to

Associate ProfessorAssociate

to Full Professor

Coefficent Odds Ratio p-Value

-0.2197 0.803 0.309

Coefficent Odds Ratio p-Value

-0.6824 0.505 0.182

Note: The control variables are years at institution, years of experience at time of hire, highest degree, andthe quadratic terms for the "years" variables. p-Value refers to statistical significance (see the glossary entryfor statistical significance and "Problem 5" subheading in chapter 6).

Summary of steps1. Determine if you have the level of detail needed toconduct event history analyses. Do you have completecareer history information for the individuals in the

34

database? Does your database contain the year each fac-ulty member received each promotion at the institution?2. Restrict your study population to those fully subjectto the promotional mechanism of your institution. Atmost colleges and universities, that means includingonly those hired at the junior ranks of lecturer, instruc-tor, or assistant professor.3. Restrict the time frame being studied, that is, thedependent variable years in rank, to the period when afaculty member is eligible for the promotion being stud-ied. Use the independent variables to control for influ-ences before that period, such as time spent as a lectureror in postdoctoral study.4. Transform the individual-level database to a person-year database. The change can be accomplished eitherby constructing a database in which you create a recordfor each person-year or by using Cox regression.5. Construct promotion probability tables that allow youto view differences that may exist in the odds of beingpromoted at each year of academic pursuit. Such tablesindicate the proportion of unpromoted faculty whohave reached a certain year in a specific rank.6. Conduct logistic or Cox regression computer analysesfor each promotion you are studying. These analysesestimate the relative odds of promotion for the genderand race categories you enter.

Next StepsSo far, we have described how you can use frequencytables, categorical modeling, and event history analysesto diagnose gender or race bias in current rank. Now wewill consider your alternatives for analyzing bias in fac-ulty salaries relative to your findings concerning dis-crimination in current rank.

Findings of little biasFour of the twelve SUNY schools we studied using cate-gorical modeling showed little bias in current rank.

4 5

Gender and Race Bias in Current Rank

Indeed, gender and racial bias in rank assignment is notuniversal, and some institutions have developed rela-tively equitable promotion processes. If your resultssuggest no bias in current rank, then you can include itin your regression analyses of salaries without fear ofrecrimination.

You may, however, want to analyze your institution'sinitial rank assignments. Three of the four SUNY cam-puses with relatively little bias in current rank displayednotable evidence of bias in the assignment of initial rank.

Findings of notable biasIf you have found bias in current rank and want to pro-ceed with multiple-regression analyses of salaries, whatare your options? You can omit current rank from theanalyses and assume your results overestimate salarydisparities based on gender or race. We do not, howev-er, recommend this option. Current rank is widely seenas related to job level and as a legitimate determinant ofsalary. If you leave it out, many academics will dismissthe results of your salary analyses despite the care youhave taken to demonstrate that current rank incorpo-rates bias. But if you include the tainted variable in youranalyses and still find gender or race bias in salaries,these results cannot be easily discounted. Althoughthere may be evidence of bias in current rank assign-ment, current rank directly reflects the institution's for-mal recognition of individual status and performance.

Another option is to substitute performance data forcurrent rank. If your current rank data are tainted, onesolution would be to replace them with comprehensivedata on publications, research, and teaching. The litera-ture notes that it is difficult and time consuming togather and score this information (Scott 1977; Gray1990), so we do not suggest that you embark on collect-ing it unless someone has already automated a substan-tial proportion of the data. Even if you do have suchdata available, building appropriate measures may becomplex. In measuring publications, for example, areyou interested only in quantity or also quality? Howshould you rate a newspaper article versus a bookreview versus a paper in a refereed journal versus abook? How can you assess teaching effectiveness? Is itnecessary to score the productivity variables differentlyfor different disciplines?

Yet another option if you have found bias in currentrank is to clean the variable up by excluding the biasedcategories. It may be that your analyses of current rankwill indicate bias across only two or three ranks. If youremove the distinctions between these tainted ranks,you will remove the bias and the potential to mask biasin salaries. If, for example, you find women are substan-

tially more likely to be instructors than assistant profes-sors but are appropriately represented in all other ranks,you can create a new current rank category that com-bines instructors and assistant professors.'1

Unfortunately, this approach has a major drawback. Ifmost faculty members are in the ranks you combine,you will eliminate a substantial amount of current rankinformation. This situation may arise if you find biasbetween the associate and full professor ranks, for thesetwo ranks often contain 70 percent or more of the facul-ty at a given institution. Combining the two would blurimportant job level distinctions for most of the faculty inyour analyses.

Still another option is to include current rank andassume that the results underestimate bias. Although itis troubling to include a variable that can mask bias insalaries, we prefer this option over that of leaving cur-rent rank out of the regression analyses. The only com-pensation for doing so is that it justifies the assumptionthat any gender or race bias indicated by the regressionanalyses underestimates the amount of discriminationthat actually exists.

Given the options we have described, is it worth con-ducting analyses for taint in rank? Yes, for three reasons.First, you may find that current rank is not biased.Second, if it is biased, you can choose from among thefour options we have noted (or other options that youmay design), and assess your multiple-regression resultsaccordingly. Third, you may choose to use the results onbias in current rank to diagnose where glass ceilings maybe blocking the promotion of women and minorities.

Among the twelve SUNY institutions we studied, weobserved different patterns depending on institutionaltype. At two-year colleges, for example, a glass ceilingseems to exist for women at the associate professorrank, but once a woman breaks through and achievesthe rank, she is just as likely as a man to be promoted tohigher levels. At four-year colleges, women consistentlyhave lower odds of getting into the rank of assistantprofessor than they have of getting into senior ranksonce they have achieved the assistant professor rank.Women faculty at universities seem to continue to havesubstantially lower odds of reaching senior ranks evenafter obtaining the assistant professor rank. Having theodds ratios for the ranks at your institution may enableyou to flag and change institutional processes thatcreate barriers.

Notes1. Studies that control directly for productivity still find gen-der bias in assignments of current rank (Downey et al. 1985;Long, Allison, and McGinnis 1993).

46 35

Lois Haignere and Bonnie Eisenberg

2. Note that for most institutions of higher education, thesedata are available through the AAUP's Annual Report on theEconomic Status of the Profession.

3. There are other potentially tainted categorical variables. Themost likely culprits are administrative positions and initialrank. As chapter 6 explains more fully, there are good reasonsto exclude both of these variables from salary analysis. Tenureis also likely to be a tainted variable. If you have tenure data,you can conduct categorical modeling similar to the analysisdescribed for current rank in this chapter.

4. The interaction term is created in the following way: allminorities are assigned a value of 1 for the dummy variableminority, and all females are assigned a value of 1 for thedummy variable female. The interaction term is obtained bymultiplying the minority variable by the female variable andcreating a dummy variable with a code of 1 for all minorityfemales and a code of 0 for everyone else.

5. Such a conclusion, of course, assumes an adequate numberof cases in all of the cells being compared, and no zero cells.

6. Unlike categorical modeling, event history analysis exam-ines each rank transition separately. The chance of experienc-ing a transition from assistant to associate professor is a sepa-rate analysis from the chance of transition from associate tofull professor.

7. To understand the relationship between the annual promo-tion rate and the cumulative proportion unpromoted, subtractthe promotion rate for each year from the cumulative propor-tion unpromoted column of the previous year to get thecumulative proportion unpromoted for that year.

8. If you are using the SAS statistical package, the procedurethat will run Cox regression is called Proc PHREG.

9. Schrank (1988) raises the question whether the decisions ofjournal referees and grant review committees incorporate gen-der bias.

10. Allen (1984) suggests that variables measuring teachingquality are probably unnecessary because it has never beensuggested that women are less effective teachers than men.

11. A complication of this approach is that the years in currentrank variable must be modified to reflect the time spent in thenewly created combined rank, but the dates of promotion toprevious ranks may not be available.

36

Currently, widespread gender discrimination in wages in universities throughout this countryis supported and sustained by our tax dollars. To eliminate pay inequity, universities shouldconduct independent wage studies to diagnose gender bias. By correcting salary disparitiesshown in these studies, universities will affirm a commitment to equal pay in the workplace.

Norma SadlerProfessor of Elementary Education and Specialized Studies

Boise State University

FIVE

Gender and Race Bias in SalariesBy Lois Haignere

This chapter takes up where chapters 1 and 2 leftoff on the use of multiple regression to assesssalary equity. If you have skipped those chapters,

you may want to read them now, particularly the con-ceptual overview. Better yet, look at the discussion ofmultiple regression in appendix A. Even readers famil-iar with multiple regression may find this appendixhelpful in understanding the relative strengths andweaknesses of the different types of regression models.Again, many of the terms used in this chapter aredefined in the glossary.

The strength of using multiple regression to studysalary equity is that it sorts out how race and genderaffect salaries as if all elsehighest degree, years ofexperience, and disciplinewere equal. As a result,multiple regression is commonly acknowledged to bethe most useful statistical tool for studying salary equi-ty, and there have been many multiple-regressionreviews of faculty salaries.

But not all multiple-regression approaches are alike.The first section of this chapter discusses some ways ofmodifying predictor variables to improve their use inmultiple-regression salary analyses. The second sectiondescribes three regression model approaches that arecommonly reported in the literature and summarizestheir strengths and weaknesses. The final section pre-sents our findings and recommendations concerning thethree regression approaches, based on their impact onthe results of salary studies for four universities, fourfour-year colleges, and four two-year colleges.

Re-engineered VariablesChapter 3 enumerates the variables that are desirable ina data set. Here we suggest ways of adapting some ofthese variables before entering them in multiple-regression analyses.

Redundancy in time variablesExperience and longevity variables all involve time, andoverlap between time variables should be avoided.Years in current rank and years at the institution areoften used as indicators of seniority and experience.Using both introduces substantial redundancy.Therefore, we recommend redesigning years at theinstitution to be years prior to current rank, whichwould be the time between initial date of hire andappointment to the current rank. This eliminates theoverlap with years in current rank.

Years since highest degree at time of hire and years ofexperience prior to hire are both measures of previousexperience. We recommend using both, although theyare somewhat redundant, because each has a disadvan-tage that is lessened by use of the other. Years sincehighest degree at time of hire is the more reliable of thetwo measures because this variable represents a setevent that can be confirmed: graduation. However,some people may not acquire professional experiencefor every year since highest degree. Our data suggestthat women are credited with less experience than menrelative to their years since highest degree at time ofhire. But estimates of relevant work experience prior tohire are subjective, and employees and personnel officesfrequently disagree over this issue. (See the discussionof this variable in chapter 3.) Nevertheless, we believe ayears of experience prior to hire variable should be usedif you have it. The problem of overlap between thesetwo variables is reduced because some people acquireprevious experience prior to their year of highestdegree, and some do not get their degrees until afterthey are hired.

If your campus has no automated data on years ofexperience prior to hire, should you collect them? Toassess the importance of this variable, we ran regression

48 37

Lois Haignere

analyses on salary with and without the years of expe-rience prior to hire variable. Without this variable, theresults for eight of the twelve SUNY analyses did notchange substantially either in terms of the R or thebias indicated. For the remaining four schoolsonetwo-year and one four-year college and two universi-tiesthe results did indicate an increase in both gen-der and race bias when experience prior to hire wasomitted. The increase in the amount of bias shown atthese four schools was not, however, substantial, thelargest increase being $500. Whether this limitedimprovement in precision merits the time and workinvolved in collecting the relatively subjective data onyears of experience prior to hire is a judgment call forpolicy makers. As noted in chapter 3, however, it isimportant to collect previous experience information ifthere is pressure to include initial rank in the regres-sion analyses. Data on experience at the time of hireare important in statistically assessing whether or notinitial rank is a "tainted" variable and, therefore, willmask bias in salaries.

Age is rarely used in salary-equity analyses, aslong as better measures of experience and longevityare available. To the extent that women interrupttheir careers more oftenor for more yearsthanmen, the use of age could overestimate gender differ-ences in salaries. Moreover, our findings indicatethat inclusion of the age, variable does not add moreinformation (raise the R ) or change the estimates ofgender and race bias. In light of these factors, and tominimize redundancy, we recommend leaving ageout of the model.

Curvilinearity: The problem and some solutionsMultiple regression assumes that there is a linearrelationship between the independent and depen-dent variables. According to this premise, for eachyear of additional experience, there is a correspond-ing unit of increase in salary. Unfortunately, salarydoes not always change in a truly linear way acrosstime. In fact, there are opposing nonlinear pressures,particularly when a union represents the faculty.Percentage raises that are negotiated by the unioncause salaries to grow at a faster rate as raises buildon raises over time. This effect, when graphed, pro-duces an accelerating curve (see figure 5.1). The othereffect is that, as faculty acquire more years of experi-ence, their salary growth may slow because they arereaching the end of the promotion ladder and therelated raises (Gray 1991). (See figure 5.2.) If thesetwo pressures offset each other, curvilinearity maybe minimized so that linear multiple

38

Figure 5.1

Accelerating Curve

Years

Figure 5.2

Decelerating Curve

regression correctly measures the relationships betweenthe time variables and salaries. If they do not offset eachother, either type of curvilinearity can adversely affectthe predictive power of multiple regression.

49

Gender and Race Bias In Salaries

The solution to the problem of curvilinearity, as weindicated in the previous chapter, lies in adding to theregression analysis a quadratic term for each time-related variable. A quadratic term is the square of avariable, the variable multiplied by itself. The methodsused in the regression do not change (Pedhazur 1982;Hays 1991); the regression is just run with the quadrat-ic term included. The new equation represents both thelinear aspect (the time-related variable itself) and thecurvilinear aspects (the quadratic term for the time-related variable) of the data. If the regression result forthe quadratic term is negative, the data have some ele-ment of a decelerating curve. If the result is positive,the data have some element of an accelerating curve(Gray 1991). The amount of curvilinearity is shown bythe amount of variance accounted for by the quadraticterm. You can examine this by noting the amount ofimprovement in the R2 when the quadratic term isentered.

As is so often the case, this solution creates anotherproblem: variable overlap or redundancy. A variable andthat variable multiplied by itself are very similar.2Thisproblem can easily be solved by centering the original lin-ear variable. Centering involves subtracting the mean ofthe variable from each measure of that variable, so thatthe new mean is equal to zero (see appendix G).Quadratic terms calculated on centered variables havesubstantially less overlap. Another solution is to drop thequadratic term, if it does not add anything to the analysis.

Redesigned Categorical Variables: DummiesVariables like rank, gender, race, and discipline are cate-gorical, rather than continuous. That is, they have afinite number of categories that are probably not equalin size. In contrast, continuous variables like years anddollars deal in quantities and have units that are equalin size (see the glossary).

Special steps need to be taken before categorical vari-ables are included in multiple-regression analyses.Specifically, a categorical variable must be transformedinto a set of dummy variables (see appendix A). Eachdummy variable has only two possible values, 0 or 1.For example, for the variable female, all women arecoded 1, and all others are coded 0; for the variableassociate professor, we assign the value of 1 to thosewho are associate professors and the value of 0 to allothers. Where there was originally one variable for cur-rent rank, there are now several current rank dummyvariables, that is, full professor, associate professor,assistant professor, instructor, and lecturer. Therefore,the transformation to dummy variables involves a sub-stantial increase in the number of variables.

For each categorical variable, the total number ofdummy variables entered into the regression equation isone less than the total number of categories. The reasonis that all necessary information is present when youenter all but one of the dummy variables. For example,in gender there are two categories, male and female. Ifwe have a dummy variable for female, then we do notneed one for male. If you are not female, then you aremale. When there are more than two categories, thesame situation applies. If there are only four race cate-gories and you are not African American, Latino, orAsian, then you must be white, so we do not need toenter a white variable in the regression equation.

The dummy variable category that is excluded from theregression analysis becomes the default or referencegroup and is crucial in interpreting the parameter esti-mates of the other dummy variables. This is the group towhich all other groups are compared. For example, ifwhite is the default category, the parameter estimate forAsian tells us how much more or less money Asians makethan whites with the effects of all the other variables in themodel held constant. The Latino parameter estimate tellsus how much money Latino faculty make compared towhites. To see how much Latinos make compared toAfrican Americans, just subtract one parameter estimatefrom the other. (This discussion presumes that the param-eter estimates are unstandardized. See chapter 6.)

Since creating dummy variables substantially increas-es the number of variables in the regression equation, itis important to know how many variables are too many.The answer depends on the size of the faculty data set.Gray (1993) indicates that as few as five cases for eachvariable are acceptable, if statistical significance is not aconcern. (See also Blalock 1979 and the discussion onstatistical significance in chapter 6.) This would meanthat with a faculty population of 250, you could use 50variablesmore than we have ever used. The differencebetween the R2 and the adjusted R2 is one way to assessthe effect of the number of variables. The adjusted R2takes into account the number of variables, whereas theR2 does not. Both measures are provided by the comput-er output of the regression model. As a general princi-ple, trim the number of dummy variables to the smallestnumber needed.

Suggested Categorical VariablesYou can follow these guidelines for including categori-cal variables in your study.

Current rankCombining rank categories is not recommended, unlessyou do so specifically to erase the bias embedded in

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them (see chapter 4). Different ranks are rewarded atdifferent salaries. Therefore, we suggest entering evenrank categories with small populations separately in theregression model.

Highest degreeYou will probably find, as we have, that most facultymembers have either a master's or a Ph.D. for theirhighest degree. In this case, you can reduce the numberof dummy variables for highest degree to two or three.At the SUNY university centers and colleges, wereduced nine categories to two: Ph.D. or equivalent andnon-Ph.D. Some disciplines have degrees that are desig-nated "terminal" even though they are not Ph.D.degrees. If the information concerning these degrees isavailable, you may want to use a separate variable forterminal nondoctorate as well.

At SUNY two-year colleges, where the majority offaculty members had master's degrees, we used threevariables: above master's, master's, and below master's.Some data sets include professional degrees. As weindicated in chapter 3, we recoded these to appropriatelevels. In most cases, outside of medical and law schoolanalyses, medical and law degrees were recoded asequivalent to Ph.D. degrees. M.B.A. and M.S.W. degreeswere recoded as master's degrees.

DisciplineWhile there are a limited number of ranks or levels ofeducational attainment, there are usually many depart-ments, which may add too many dummy variables tothe regression model. Therefore, as indicated in chapter3, it is best to combine departments into disciplines. Aspreviously mentioned, the federal government hasdeveloped Classification of Instructional Programs, orCIP, codes for this purpose. Alternatively, you maycombine departments into discipline groups based oncommon administrative units such as those in the samecollege or under the same dean, or through the use of astatistical technique called cluster analysis (seeglossary).

Instead of creating dummy variables, someresearchers transform discipline into a continuous vari-able by using salaries. This approach uses the averagesalary for each discipline within the institution, or theaverage market salary for each discipline, to create acontinuous variable. We caution against this approach.When we conducted analyses to observe its impact, wenoted that the R2 declined measurably when such con-tinuous variables were used. Using averages ignoreshow departments varyfor example, whether thedepartment is a new one with many junior faculty or a

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more established department with many senior faculty.Using average market salaries ignores whether the dis-cipline is one that brings great prestige to the institutionand, therefore, is allowed to pay top dollar to attract thebest in the field, or whether the discipline is one lesswell regarded nationally. Entering each discipline as aseparate dummy variable allows the regression equa-tion to assign the appropriate value for each discipline,given the faculty salaries paid in that discipline by theinstitution being studied.

Race and gender categoriesWhether to combine race and gender categories is acomplicated question. Several factors need to be takeninto account: political consequences, potential maskingof bias, and the number in each category. Politically,each racial constituency usually wants its own analysis,and the women in each group also want their own anal-ysis. The racial categories we analyzed at SUNY wereAfrican American, Latino, and Asian. Other categoriesmight be appropriate for your study. For example,schools in New Mexico and Alaska may want to includeNative Americans.

Different dynamics affect each group, so breakingeach category out is reasonable. But doing so can meanfewer than ten people in many race-gender categories,depending on the size of your institution (see table B.1in appendix B). Even though you are using a populationrather than a sample, results based on larger groups aremore convincing than those based on one or two facultymembers. If the regression results show ten or moreAfrican American males at a salary disadvantage, youcan be more confident that this group is being subjectedto systemic bias than if there are only one or twoAfrican American males on the faculty.

Statistically, there is a danger of masking bias whendifferent race-gender groups are combined. For example,at two of the SUNY universities, Asian male facultymembers as a group experienced a salary advantage rel-ative to comparable white males, whereas AfricanAmerican male faculty members were disadvantagedcompared with white males. Combining these twominority male groups would have masked the salarydisparity experienced by the African American males.The opposite pattern occurred at the four SUNY col-leges. Asian males as a group had substantially lowersalaries than white males, while African American maleson average had a salary advantage over white males.

If you have several small race-gender groups andyou are wondering if it is all right to combine them,first try running regression analyses with the groupsseparate. This allows you to assess the degree to which

Gender and Race Bias In Salaries

masking could be a problem if you do combine thesegroups.

What about minority women? Should they be includ-ed as minorities, as women, or separately as their ownrace-gender category? There may be more incentive forcombining minority women than minority men.Judging from all twelve of the schools in our analyses,there are fewer minority women than minority men onfaculties. The results from the twelve SUNY schoolsindicate that minority women's salaries are more similarto those of white women than to those of the men intheir same minority category, and that minority womenexperience greater salary bias than their male counter-parts. Our findings are consistent with other studiesthat indicate that minority women's ranks and salariesare below those of minority men (Exum 1983; Fairweather1991; Tuckman 1979). Therefore, if you want to combineminority women to create a larger pool, we suggest com-bining them with each other or with all women, but notwith their minority male counterparts.

Finally, there is the question of whether to conductrace analyses at all. Unfortunately, most of the studiesreported in the literature assess salaries for gender biasbut not for race bias. Of the studies that have examinedrace, some have found that minorities are paid as well as,if not better than, white men, while others have found theopposite (Exum 1983; Fairweather 1991; Tuckman 1979).We encourage you to conduct assessments for both raceand gender bias, bearing in mind that individual charac-teristics can unduly influence analyses where there areonly a few individuals in a minority category.

Ignoring race may mask gender bias, since lower-paidminority men could lower the male average salary. Inother words, if the average salary for male minority fac-ulty is less than the average salary for white males, thetotal male average will be lower than the white-maleaverage, thereby decreasing the gap between women'sand men's salaries. Our assessment indicated thatomitting race information did not substantially changethe amount of gender bias shown, or the adjusted R2, atmost SUNY institutions we studied. At one college,however, the gender bias shown dropped by one-thirdwhen minority men were included with white men. Weurge you retain the race variable unless the number ofminority males is very small.

Three Multiple-Regression ApproachesThe three types of multiple-regression models reviewedhere are the ones most commonly reported in the litera-ture.' You need not choose among them. You can use allthree to examine the consistency of the results. If theresults agree, the information provided here on the

differences between the three approaches may be of lim-ited interest. If the results differ, or if you decide to limityour study to a single approach, this section will behelpful. First we describe each approach along with itsprimary advantages and disadvantages; then wedescribe our general findings relative to each approach,and our resulting preference.

Total populationactual salary analysisThe first approach uses the total population of faculty inderiving the regression equation. Men and women,minorities and nonminorities are included in the analy-ses. The dependent variable is salary in actual dollars.Gender and race are accounted for by entering thedummy variables for each race-gender category, such asLatino male, Asian female, and so on.

An advantage of this model is that the regressioncoefficients (parameter estimates) can be directly andeasily interpreted in real dollar amounts. For example,the coefficient for the variable white female is the aver-age salary difference between the default category,white male, and white female, with all other variablesheld constant. If the coefficient is -3,000, white femalesare paid $3,000 less than white males with comparablepredictor variable scores. If the dummy variable AfricanAmerican male is entered, then the average salary dif-ference between African American males and thedefault category, white males, is indicated by the coeffi-cient for this variable. Appendix A explains this regres-sion approach thoroughly.

The total-population regression analysis can maskinequity because it assumes that every factor that influ-ences white-male salaries affects female and minoritysalaries at the same rate. As a result, some discriminato-ry differences get averaged away. For example, if, onaverage, males are rewarded $1,000 for having a Ph.D.and females are rewarded $500, this model masks thisinequity because it looks only at the average reward forPh.D. Later in this chapter, we indicate how to comparethe results of the total-population analysis with thewhite-male analyses to reveal whether women and menare being paid differently. If this problem exists, oneway to eliminate it is to use the "white-male popula-tion" approach.

Natural logarithm of salary analysisThe second model we tested was a total-populationmodel using the natural logarithm (ln) of salary insteadof actual salary as the dependent variable. Taking thenatural log of salary means that you are no longerstudying dollar units and that the parameter estimatescan no longer be directly interpreted in dollars. Rather,

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they become proportions by which a salary is changedwhen an independent variable increases by one unit;multiplied by 100, they become percentages (Hodson1985; Gray 1991; Becker and Toutkoushian 1995;Halvorsen and Palmquist 1980). For example, if whitemales are the default group and the coefficient for thevariable female is -0.0634, then the average female in thepopulation is making 6.34 percent less than the averagewhite male.4

The natural log of salary transformation can create amore "normal" (see glossary), less skewed and lesscurvilinear, distribution. It is generally felt that the morenormal the shape of the data distribution, the better,particularly if you are using a random sample to makeinferences about a population, rather than studying thetotal population as is commonly done in faculty salarystudies (see "Problem 5" in chapter 6). The improve-ment in the distribution of the data so that it is a "betterfit" for linear regression analyses is usually indicated byan increase in the adjusted R . Gray (1991) notes that the"log model generally allows us to get a better fit to thedata, but at the sacrifice of simplicity."

Using the natural log of salaries lowers the highestsalaries, bringing them closer to the mean and the restof the distribution (Hodson 1985), and reduces the effectof very high salaries on the regression results. If thereare extremely high-paid individuals who make morethan ten times as much as most people in the salaryanalysis, using log salaries could be very important inreducing the impact of these individuals' salaries on theregression results. The log of salaries also pushes thelowest salaries further from the mean and the rest of thedistribution, thus tending to increase their impact on theregression results.

The log of salary is conventionally used in the field ofeconomics, and faculty salary-equity studies frequentlyattract the attention of faculty economists. Economists'affection for the natural log of salary is related to theirfocus on returns for investments and frequent researchon populations with an extremely wide range ofsalaries. When focusing on return for investment, itmakes sense to report the results in percentage rates. Toreport results in actual dollars means that you alwayshave to know the baseline. If an investment nets $100,you need to know the size of the original investment.On the other hand, if an investment nets 30 percent, youknow it has done well. Hodson (1985) notes thateconomists find this useful because they can report find-ings such as "each year of investment in educationbrings a 13 percent increase in earnings. "5 But if you arestudying the effect of gender and race on salaries, thelogic of "investments" disappears. It makes no sense to

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say that for each year of investment in being a whitemale, earnings increase by a certain percentage. Genderand race are not investment choices.

Because using logs lessens the gap between the meanand the high end of the salary distribution, they arecommonly used in studies of the general populationwhere the highest salaries may be a hundred times oreven a thousand times higher than the lowest salaries.But the occupational and institutional context of facultysalaries restricts their variations to a much narrowerand less skewed range than in the general population.Observing this, Ferree and McQuillan (1998) concludedthat "converting salaries to logarithms offered more costin loss of ready interpretability than it was worth" (23).We suggest that you weigh the importance of conduct-ing the log salary analyses based on the range ofsalaries. You can do this by dividing the highest facultysalary by the lowest. If the result is greater than ten, sayfrom a lowest salary of $30,000 to a highest salary ofmore than $300,000, you should conduct log analyses. Ifyou do have such a wide range of salaries, we suggestyou also visit the section on outliers in chapter 6 andappendix I on how to locate outliers.

White- male - population salary analysisThe third approach, the "white-male-only" model, hasbeen widely promoted because it solves the total-population problem of masking different rates of payfor women and men (Braskamp, Muffo, and Langston1978; Gray and Scott 1980; Scott 1977).6 The HigherEducation Salary Evaluation Kit by E. L. Scott (1977) rec-ommends the white-male analysis because it provides"an estimate of what the salary of the woman or minori-ty faculty member would be if she or he were a whitemale with the same attributes and experience."

To apply this method, you calculate a regressionequation using only the white-male faculty. There is noneed to use race-gender variables because there is onlyone gender and race in the analysis. This "white-male"equation is used to predict what the salaries for womenand minorities would be if their career attributes wererewarded in the same way as those of white males. (Seeappendix A for how to calculate a predicted salaryusing regression parameter estimates.) The differencebetween each woman or minority's predicted salary,based on the white-male equation, and his or her actualsalary is called that person's salary residual. The averageresidual for a race-gender category measures the differ-ence between the actual salaries of those in the groupand what they would have been paid if their race hadbeen "white" and their gender "male." A negativeaverage residual indicates that the actual salaries of the

Gender and Race Bias in Salaries

category in question (for example, Latino men) are lowerthan their predicted salaries based on how white malesare paid. A positive average residual means that therace-gender category's actual salaries are higher thantheir predicted salaries using the white-male equation.

Gray (1993, 1991) indicates that while this model istheoretically better because it shows what femaleswould be paid if they were male, it may be more diffi-cult to use. A problem occurs any time there are nowhite males in a category where there are women andminorities, making it impossible to derive an accuratepredicted salary for these women and minorities. Forinstance, if there are no white males in the school ofnursing, then there is no parameter estimate for this cat-egory and the salary worth of this discipline willdepend on the default discipline. Any category with noparameter estimate is treated the same as the defaultcategory.'

To get around this problem, Scott (1977) suggestsagreeing on another discipline that is similar to the dis-cipline with no males in it. For instance, the pharmacywhite-male coefficient could be used in calculating thepredicted salaries for nursing faculty.

The smaller the white-male population, the more like-ly you are to have disciplines or other categories (forexample, a rank like instructor, or an educational attain-ment like master's degree) that have women andminorities but no white-male counterparts. Even if thereare men in all categories, there may simply not beenough white males to create a valid regression model.We advise that there be at least five white males in eachdiscipline, rank, and degree category to apply thismethod; otherwise, having one or two uncharacteristicwhite males in a category can throw the validity of thewhite-male analysis into doubt (see "Headaches"below). If there are fewer than fifty white males amongthe faculty, the accuracy of the white-male regressionresults are questionable. As is the general rule forregression modeling, there should be at least five cases(faculty members) for each independent variable in theanalysis. Since twenty or more variables are common infaculty equity studies, a count of a hundred or morewhite males is desirable for these analyses.'

RecommendationsIf you had only a single type of multiple-regressionanalysis available to you, you would probably want it tobe the first method we described in this chapter, thetotal-population salary analysis. It is easy to under-stand. The unstandardized results represent the actualsalary variations. It does not exhibit the frequent prob-lems experienced with the white-male analysis caused

by too few or uncharacteristic white males. The resultsare in actual dollars and, consequently, more readilyinterpreted and understood than log of salary.

But you may nonetheless find it worthwhile to try allthree models. If all three confirm a similar level of bias,then they validate each other. (In three of the twelve fac-ulty data sets we analyzed, one two-year and two four-year colleges, our results were consistent across all threeanalyses.) If the findings differ somewhat, you will needto assess why, but in the process you will gain under-standing of the salary anomalies that exist at your insti-tution and how they relate to gender and race. Reportingthree estimates of bias also avoids overconfidentlyreducing a complex issue to one summary number.

HeadachesIf white males are paid more for a Ph.D. or for a year ofexperience than women and minorities, this source ofbias is hidden in the averaging done by the total-population approach. How prevalent is this problem,and how does the white-male population approach cor-rect for it?

Our analyses of the twelve SUNY institutions showedthat the white-male results supported the total-population results in six of the twelve analyses. In otherwords, at half of these institutions, there was no sub-stantial differences by gender and race in the rewardsfaculty received for career attributes such as Ph.D.'s oryears of experience. In fact, when differential rewardsexisted, our findings indicated that the white-maleresults were most likely to be based on anomalies in thesalaries of white men that are accentuated by the white-male population approach.

The results of the white-male analyses showed sub-stantially higher bias than the total-population salaryanalyses for only two of the twelve SUNY data sets. Inboth cases, the higher estimate of bias was based on theaberrant salary of one white male. At one college, awhite male speech pathologist was paid $13,000 morethan the average for all the faculty members in this dis-cipline.' As a result, the predicted salaries of the womenand minorities in this department were substantiallyhigher using the white-male method, and their actualsalaries seemed to be biased by comparison. When wedropped this discipline from the analysis, the amount ofbias indicated by the white-male analysis was the sameas that for the total-population and log of salary results.At a two-year college, an inconsistency resulted from awhite male in construction technology whose educa-tional attainment was below a master's degree but whowas paid more highly than most of the Ph.D. facultymembers. The result was that the women and minorities

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whose highest degree was below a master's appeared tobe low paid by comparison, and their predicted salaries,based on the white-male analysis, were substantiallyhigher than they would have been as a result of thetotal-population analysis.

At one two-year college and one university, thewhite-male analyses indicated substantially lower biasthan did the total-population salary analyses. Onceagain, the presence of one white male with an atypicalsalary caused the misleading white-male results. At thistwo-year college, there was only one low-paid whitemale in public service and early childhood education.By comparison, the nine women and minorities in thedepartment looked overpaid. At the university, therewas only one white male in the school of nursing, andhis pay was relatively low. By comparison, the twenty-three women in the school of nursing appeared to beoverpaid.

We concluded that when the number of white malesin a category is fewer than five, and when the white-male results differ from the total-population results, thetotal-population analyses are more likely to accuratelyreflect the amount of bias present in salaries.

At two other SUNY institutions the white-male analy-ses were problematic because there were no compara-tors in disciplines where there were women and minori-ties. Thus, six of the twelve white-male results are prob-lematic. These problems were not confined to the small-er schools. Three of the six institutions (one universityand two colleges) had more than two hundred white-male faculty members. If our twelve SUNY analyses arecharacteristic, a white-male analysis at any one institu-tion has a fifty-fifty chance of displaying incongruentfindings that take time and resources to investigate.Before deciding to conduct a white-male analysis, werecommend that you check for disciplines or degree cat-egories at your institution with no white malesorfewer than five white malesand consider whether youhave the time and resources to investigate any anoma-lies that may result.

The argument that white-male analyses avoid averag-ing away greater rewards given to white males fordegrees and experience implies that the white-maleanalyses reveal higher bias than total-population analy-ses. We have not found that to be true.

Improved analysisWhen the white-male results show inconsistencies, webelieve that using total-population analysis is more logi-cal and defensible. Regression equations using theentire faculty population include more information and,thus, may be more accurate than the regression equa-

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tions based only on males. For example, a male-onlysalary regression equation might include only two orthree faculty members in a particular discipline, but theall-faculty salary regression at that campus may includetwo or three additional faculty members in that disci-pline. Thus, the all-faculty regression would have twiceas much information concerning how salaries in thatdiscipline vary relative to salaries in other disciplines.

If you are concerned about whether a total-populationanalysis is masking differences in the way men andwomen are paid, this problem can easily be assessed.Place the regression-equation computer output for thewhite-male analysis and the one for the total-populationanalysis side by side.' Compare the coefficients (param-eter estimates) for each of the variables. If you find asubstantial difference for a category, examine howmany white men are in that category. If there are four orless, perhaps their salary-related rewards for thisattribute are very dissimilar from the others in this cate-gory. If you find that the differences noted between thewhite-male and total-population results are not due toone or two aberrant salaries, you can correct for the dif-ference by adding an interaction term to the total-population analysis (Gray 1993).

An interaction occurs when the effect of one variablechanges across levels of another variable. Suppose thatthe effect of not having a Ph.D. changes across gender.An interaction term variable is created by multiplyingthe two variables together." Create an interaction termby multiplying the Ph.D. variable by the gender variable,and include this interaction variable in the analysis. Theparameter estimate for the interaction term tells what thedifference is between men with a Ph.D. and women witha Ph.D. For statistical purposes, it is important not to addany more interaction terms than are needed.

ComplexitiesThe primary disadvantage of using log of salary as thedependent variable is the complexity it adds to inter-preting the results. When dollars are converted to logdollars, the intervals between the values of differentsalaries change. One person earning more than anotherwill also have more log dollars, but the distancebetween the log salaries of the two people grows small-er as the size of their salaries increases. Complexity ofinterpretation is more important in reporting findingsthan it is in deciding which analyses to do. As indicatedearlier, if the range from the lowest to the highest facul-ty salary is greater than a factor of ten, we suggest youconduct log of salary analyses. But when it comes towriting the report of your findings, assuming that theresults do not differ substantially, consider reporting on

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the salary results instead. Our preference for reportingthe salary rather than log of salary results is based onsimplicity and on the logic of reporting on what peopleactually take home in their paychecks.

Using the natural log of salary usually results inslightly higher adjusted R2 values, commonly in therange of two or three percentage points. At the twelveSUNY schools we studied, institutional type did notseem to play any role in the amount or direction of thechange in R2 values. Closer examination indicated thatthe slight improvements in the adjusted R2 values wereprobably primarily due to the reduction of the positiveskew of the dependent variable at the universities andcolleges.

Two Additional ChecksOnce the analyses have been completed, two importantadditional tests remain to be conducted: a test for out-liers and an examination of the residuals.

OutliersAlthough we do not generally recommend droppingoutliers, it is best to check for them (see "Problem 3" inchapter 6). Assessing the impact of outliers is a goodvalidity check on your data and results. For a discussionof methods of checking for outliers, see Appendix I. Asnoted there, we recommend the Cook's Distance (CD)approach. The advantage of Cook's Distance is that itpinpoints those cases that greatly influence the parame-ter estimates rather than just aberrant cases on one ofthe variables. Cases that are not distorting the resultsneed not be examined or eliminated before you certifythe accuracy of your analyses.

The developers of the Cook's Distance procedureindicate a CD cutoff value of 1.0. Out of twelve SUNY-campus analyses, we found only one case that exceededthe CD cutoff value. A check of this professor's datashowed him to have been a full professor for only twoyears, but he had actually been a full professor for sev-enteen years. The erroneous "two years in current rank"referred to the time at which he stepped down from adean's position. If your analyses include cases with CDvalues above 1, review their data for accuracy. You mayfind errors that explain their outlier status.

If you note CD values that are substantially higherthan those of most of the population, examine these forpotential data errors. For example, if the highest CDvalue is 0.63 and the next highest CD value is 0.15, thedata for the case with the CD of 0.63 should be checkedfor accuracy. If you are assessing a small population offaculty salaries (under a hundred), consider how repre-sentative that case is. At one small college, such a case

turned out to be a non-Ph.D. male instructor who hadreceived tenure thirty-five years ago but never pro-gressed in rank. After running the analysis with andwithout this outlier, the joint faculty-administration com-mittee at this institution decided he was not representa-tive of the population and left him out of the analysis.

Although the detection of outliers is a recommendedstatistical procedure, dropping them is as much a politi-cal decision as a methodological one. Drop outliers onlyif they distort the real picture.

Residuals: The ungreat unknownRegression analysis looks at the variation in the depen-dent variable (salary) and all of the information provid-ed by the predictor variables, and creates an equationfor the straight line that best predicts your institution'ssalaries. But real-world salaries do not dutifully line upon the straight line provided by the equation. They maycluster tightly around it; how tightly is indicated by R2.But even when the R2 indicates that 70 or 80 percent ofthe variation in salaries has been accounted for with thepredictor variables, there is scatter around the line (seefigure A.2 in appendix A). This scatter of 20 or 30 per-cent variation in salaries is called the unexplained varia-tion or residual. It results from factors you have notmeasured or cannot measure precisely. Some examplesmight be unmeasured productivity, administrativefavoritism, and being hired in a financially dry year.

The residual or unexplained variation is the differ-ence between a person's actual and predicted salaryfrom his or her actual salary. As explained in appendixA, the regression equation provides a formula that cancreate a predicted salary for each faculty member basedon the predictor variables. All of the widely used statis-tical computer software programs provide the predictedsalary for each individual based on the regression equa-tion (when properly asked, of course). They also pro-vide the residuals or unexplained variations. You cancreate a scattergram of the residuals by plotting eachfaculty member's actual salary on the vertical axis andthe unbiased predicted salary on the horizontal axis. Forexamples, see figures 6.1 and 7.1.'2

When you use the white-male regression equationand arrive at the women and minorities' predictedsalaries by plugging in their career attributes (the pre-dictor variables), the result is a direct measure of whatwomen and minorities' salaries would have been if theywere white men. But the predicted salaries and, byextension, the residuals provided by the total-populationregression analysis output include the salary bias varia-tion related to the female and minority variables. Regres-sion analyses let us know how much of the variation in

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the dependent variable, salary, is accounted for by theindependent and predictor variables. We provide pre-dictor variables that are seen as both legitimately relatedto salary (experience, degree, discipline) and variablesthat are seen as illegitimate predictors of salary (genderand race). The regression equation that results does notdistinguish between these. It tells us mathematicallywhich variables predict the women and minorities'salaries. If it finds that, after accounting for all the vari-ables that we consider legitimately related to salaries,women and minorities' salaries are best predicted bysubtracting something from their salaries, it includesthat subtraction in the equation that calculates thewomen and minorities' predicted salaries. It is our job toremove that part of the equation reflecting gender orrace bias.

If, for example, the coefficient for female is -1,000, thesalaries of the women faculty members are predicted tobe $1,000 less, on average, than if they were male facul-ty. The predicted salaries for the female faculty must becorrected by the amount of the coefficient for female: itwould be necessary to add the $1,000 back to eachfemale faculty member's predicted salary. Once youhave corrected the predicted salaries to remove anygender and race effect, you can subtract them from actu-al salaries to get a corrected residual. Alternatively, asdescribed above, you can create a scattergram of theresiduals by plotting each faculty member's actualsalary on the vertical axis and the "corrected-for-bias"predicted salary on the horizontal axis.

There are both political and methodological reasonsfor examining the residual or unexplained variation insalaries (see chapter 7 for more on the political implica-tions). You may observe a pattern of the residuals thatsuggests an additional variable not included in theanalysis. Including that new variable could account formore of the variation in salaries, thus raising the R2. Forexample, you may note a cluster of faculty paid morethan their predicted salaries, all of whom are named ordistinguished professors. By including this as a catego-ry you may improve your analyses. Or you may dis-cover a group of faculty whose actual salaries are muchlower than their predicted salaries and who are all in aparticular subunit or discipline. As Ferree andMcQuillan (1998) note, such a result could point to apocket of bias caused by a particularly prejudicedadministrator.

Notes1. In technical terms, redundancy means high correlations thatmake it difficult, if not impossible, to determine the separateeffects of the two predictor variables on the dependent variable.

46

2. To determine whether variable overlap is a problem, run acorrelation matrix to show how much each variable and itsquadratic term overlap. If any correlation reaches 0.9 or above,you have a problem.

3. There are, of course, many variations in the literature. SeeToutkoushian (1994) for a statistical discussion of the alterna-tive approaches and their potential impact on salary adjust-ments. In the next chapter, we discuss why we believe twovariations, one that is called stepwise regression and one thatomits the gender and race variables from the equation, shouldnot be used. There is also the complex Oaxaca (1973)approach, which uses both male and male regression analyses,but, in practice, the results are very similar to using just thewhite-male analysis.

4. When interpreting percentage rates, be aware that the ratefor one group is not the inverse of the rate for the other. Sincethe percentage rate is based on the average salary of thegroup, there is no common denominator. In actual dollars, ifwomen need to make $1,000 more to be equal to men, thenmen would need to make $1,000 less to be equal to women.However, with percentage rates, the numbers are not thesame. If men make $1,000 and women make $900, then a 10percent decrease in male salaries would constitute equality,but an 11.11 percent increase in female salaries would beneeded to achieve equality.

5. Hodson points out a very important implication resultingfrom the use of natural logarithm of salary and the associatedrates of return, like the rate of return for a year of education. Arate of return is always calculated based on the mean of thegroup being analyzed. For example, if separate analyses aredone for men and women, the calculated rate of return isbased on increments above their separate average loggedsalaries. Because women make substantially less, on average,than men, women can appear to gain more, even though theiractual salaries are increased by less. Hodson (1985) notes thatwhereas men make more in dollars ($66), which translates to a0.54 percent rate of return, women make less ($46), but thistranslates into a 1.25 percent rate of return, because of themuch lower average earnings of women. Thus, when differ-ences in mean earnings between groups are substantial, theanalysis of logged salaries may create apparent differenceswhich are artifactual and very difficult to unravel.

6. For simplicity of explanation, this section assumes that thedependent variable used in white-male population analysis issalary as opposed to natural log of salary. Although there areadded complexities, it is, of course, possible to conduct awhite-male population log of salary analyses.

7. The impact on the predicted salaries of the nursing facultyof having no white-male counterparts can be high or lowdepending on which discipline is in the default category. Thatis because any group or category with no parameter estimate(coefficient = 0) is treated the same as the default category. If

5r

Gender and Race Bias In Salaries

the discipline left out of the equation is psychology, then thenursing faculty women will be paid like white-male psycholo-gists. If the default discipline is the highest paid, the predictedsalaries of the nursing faculty will be based on their being inthe high-paid discipline; if the default discipline is the lowestpaid, the predicted salaries of the nurses will be based onwhat they would make in this lowest-paid discipline.

8. If your primary analyses use a white-male regressionapproach, it is advisable also to conduct a female-only regres-sion analysis to check whether it underpredicts male salaries.It is possible, although in our experience not probable, for themale model to predict higher female salaries and for thefemale model to predict higher male salaries (Gray 1991).

9. Speech pathology was the only department in the healthprofessions discipline.

10. Alternatively, a female- or minority-only analysis can berun and its coefficients compared with the white-male linecoefficients. Some researchers recommend running the femaleor minority regression and assessing the male faculty salarieswith this model. That is sometimes suggested to assesswhether the female-only model indicates that the male facultyare underpaid (Gray 1991), just as the white-male-only modelindicates that female faculty are underpaid. Although thispotential is important to check, in reality it is rarely the casethat men are found to be underpaid using the female model(Gray 1990). At most institutions of higher education, men stillconstitute the bulk of faculty and are the basis for institutionalnorms; it therefore makes more sense to fit the women to themen's model than vice versa.

11. Using interaction terms involves complexities. If the non-gender variable involved has more than two categories, thedefault category used changes the interpretation. This is par-ticularly noteworthy if you are doing interaction termsbetween gender and a category like discipline or college withthe objective of deciding the relative salary bias in each disci-pline or college. When interaction terms are used, the interpre-tation of the regression coefficients changes (see Jaccard,Turrisi, and Wan 1990).

12. With regard to white-male equation analyses, Ferree andMcQuillan note a second approach to examining the residuals.The residual standard deviation units can be arrayed in a barchart that will approximate a normal curve. Creating onearray for the white males and another for the women andminority categories may display "humps" in the residuals thatindicate pockets of bias that are not systemic. (See chapter 7and Ferree and McQuillan 1998 for more information.)

5S 47

I have always believed that contemporary gender discrimination within universities is partreality and part perception. True, but I now understand that reality is by far the greater part ofthe balance.

Charles M. VestPresident

Massachusetts Institute of Technology

SIX

Small Errors with Big ConsequencesBy Lois Haignere

For many readers, this chapter will be the mostimportant in this guide. In designing a statisticalstudy, you will have to make many decisions. Too

often, these decisions are touted as strictly methodologi-cal, and their subjective nature and potential politicalimpact are ignored.

Even if you are one of the policy makers involved,you may be concerned that those conducting the salary-equity analyses for your institution will, wittingly orunwittingly, design them in a way that masks gender orrace bias. This chapter helps alert you to what to guardagainst and what questions to ask. Some common cir-cumstances with which this chapter will assist youinclude the following.

The administration has handed you its study,expecting you to accept the results as "objective truth."

Institutional researchers, or others with more statis-tical knowledge than you, have suggested a researchdesign for your approval.

You are a member of a joint faculty-administrationplanning committee to design a salary-equity study,and you are suspicious of some suggested approaches.

You are conducting your own analyses, and youwant to know what procedures to avoid.

Problem 1: Standardization of the CoefficientsThe regression coefficients (also called the parameterestimates) are the values that indicate how much influ-ence each variable has on the dependent variable,salary. Most statistical computer packages provideunstandardized regression coefficients by default,because they are easier to interpret. Getting standard-ized coefficients requires extra computer programmingto override the default. Unstandardized results indicatethe average dollars associated with each variable. (Seeappendix A for a detailed explanation and an exampleof computer output.) An unstandardized coefficient of

-1,500 for female faculty indicates that, on average,women faculty are paid $1,500 less than comparablemale faculty.

Standardization of the coefficients does not mask gen-der and race bias per se, but it does change the results ofthe regression analyses from a form that almost anyonecan understand to one that only researchers and statisti-cians can interpret.

To obtain standardized coefficients, both the indepen-dent and dependent variables are changed to standarddeviation units. The standardized coefficient for a par-ticular independent variable represents the amount ofchange in that variable's standard units needed to pro-duce a change in the dependent variable of one stan-dard unita far cry from the direct dollars interpreta-tion of the unstandardized coefficients. Standardizedcoefficients can be converted back to dollar equivalents.'However, this should not be necessary, since the analy-sis can simply be rerun specifying that the output be inunstandardized units.

Problem 2: Exclusion of Certain CategoriesSome higher education institutions direct their researchwhere they may be least likely to find gender and racebias in salaries, and then declare that they just can't findit. They do so by systematically excluding the academicgroups where women and minorities predominate. Forpart-time faculty, exclusions may be a necessary evil(see "Study Population" in chapter 3). But all too often,the full-time non-tenure-track faculty are unnecessarilyexcluded without any methodological or theoreticaljustification.

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Exclusions based on track or rankNon-tenure-track teaching ranks are often excluded forreasons that, if explained at all, are described vaguely aseither different teaching and research expectations(Gray 1993) or different hiring and personnel policies

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Lolls Haignere

(N. Moore 1992).2 Some institutions of higher educationhave an array of non-tenure-track faculty, including"visiting," "research," and "clinical" assistant, associate,and full professors. But most campuses confine non-tenure-track faculty to one or two lower ranks, such asinstructor or lecturer. At the SUNY institutions, mostnon-tenure-track faculty are lecturers, long-term teach-ing faculty who rarely have research obligations. But inregard to teaching, their work is much the same as thatof tenure-track faculty. Most variations in teachingexpectations and hiring and personnel policies that existbetween non-tenure-track and tenure-track teaching fac-ulty are no greater than those that exist across mostranks. Just as rank differences are methodologicallyaccounted for by the inclusion of dummy variables forthe different ranks, non-tenure-track salary differencescan be measured by the regression equation through theaddition of a non-tenure-track dummy variable.

There may be different research expectations for thefaculty who are on tenure track than for those who arenot, but research expectations are not prevalent on allcampuses. In fact, teaching rather than research is theprimary focus at many two- and four-year colleges.Even at research universities, the expectations regardingresearch may depend as much on discipline as onwhether faculty are on track for tenure. If a departmentis recognized as one of the best in its field, the researchexpectation for those hired into it is often greater thanthat for faculty in less prominent departments.

Moreover, differences in policy regarding research,teaching, hiring, and other personnel issues are takeninto account by multiple-regression analyses. Multipleregression can separate out pay differences that areunrelated to gender and race as long as the separaterank and discipline categories are named in the analy-ses. By entering a variable for each discipline and rank(see the discussion of dummy variables in appendix A),we enable the regression equation to properly attributesalary differences related to discipline or rank to the dis-cipline or rank variables and not to gender or race.

We can do the same for non-tenure-track ranks. Allfull-time faculty members, including those not ontenure track, were included in our SUNY analyses. Asindicated in chapter 3, to account for non-tenure-tracksalary differences, we entered the variable lecturer as asynonym for "nontenure track." This means that anygender or race salary differences within the lecturer cate-gory can be captured by the equation and attributed tothe coefficients for the gender and race variables. Anysalary variations due to different teaching or researchexpectations or personnel policies for lecturers will beattributed to the coefficient for the variable lecturer.

50

To assess whether dropping non-tenure-track facultyimproved the quality of the analysis, we reran the anal-yses, excluding those in the rank of lecturer at the nineSUNY schools that have this non-tenure-track rank.Neither the adjusted R2 measures nor the amount ofgender or race bias shown changed substantially whenwe dropped lecturers. At two campuses (one universityand one four-year college), the amount of bias increasedmodestly, suggesting that, at these schools, those in thenon-tenure-track lecturer rank experienced less biasthan those in the tenure-track ranks. At two campuses,the amount of bias measured did not change. At theremaining five campusesone two-year college, twofour-year colleges, and two universitiesthe amount ofbias decreased slightly, suggesting that the non-tenure-track faculty at those schools probably experiencedmore salary bias than those in the tenure-track ranks.

Nevertheless, it is important to examine the regres-sion results carefully for indications that the non-tenure-track ranks could be masking bias in the tenure-trackranks or vice versa. This lesson was made clear by astudy that we conducted recently at a private-sector col-lege on the East Coast. The results indicated a modestamount of gender bias in salaries. But a comparison ofthe parameter estimate of the total-population andwhite-male equations showed major differences for thenon-tenure-track variable. Interaction-term analysesindicated that the bias was greater among the non-tenure-track faculty. When we dropped the non-tenure-track faculty from the analyses, the indication of salarybias disappeared. As is true at many institutions, therewere too few full-time non-tenure-track faculty to sup-port a separate analysis within the non-tenure-trackranks, but the interaction-term results provided clearevidence of salary bias in the salaries of those in thenon-tenure-track ranks.

The tendency to exclude non-tenure-track faculty insalary analyses may be due in part to an assumptionheld by many higher education policy makers that thereis less bias at the lower-status levels, where women andminorities predominate. There is also an inclination tobelieve that recent hires are treated more equitably thanless recent hires, and that the non-tenure-track ranksinclude a higher proportion of recent hires. Our analy-ses suggest that these commonly held assumptions areoften not supported by study results.3

The most important consequence of excluding non-tenure-track faculty from the salary analyses, as weindicated in chapter 3, is that they will be ineligible forany salary adjustments that may result from the study.That means that the lowest-paid faculty, who are likelyto be disproportionately minority and female, are

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Small Errors with Big Consequences

denied the opportunity to have any bias in their salariesassessed and corrected. We know of no theoretical ormethodological justification for this unfortunate exclu-sion. All full-time faculty, including the non-tenure-track ranks, should be included in the multiple-regressionsalary review.

Potentially legitimate exclusionsDifferent campuses and institutions rely on an array oftitles, positions, and funding mechanisms to provide forthe diversity of staff needed. We have conducted analy-ses at institutions that have research and clinical facultylines (sometimes called rank modifiers) that span theassistant, associate, and full professor ranks and alsoinclude both tenure-track and non-tenure-track faculty.These are all considered faculty lines and should beincluded in the faculty salary study.

By contrast, campuses also commonly have nonteach-ing grant-funded positions, such as research assistantsand associated positions. Those holding these non-tenure-track research assistant and associate positionshave much in common with faculty: they may holdPh.D.'s and work right along with faculty in a specificdiscipline. But they are usually not in faculty lines anddo not teach, and their salaries may be determined inwhole or part by outside funding sources rather than bythe higher education institution. Here you may need tosort carefully so that your study includes only teachingfaculty, both on and off the tenure track, whose salariesare determined by the campus administrations.

Exclusions based on disciplineAt some institutions the faculty members who special-ize in teaching students basic reading, writing, andmathematics skills are clustered in a special department.At SUNY institutions these skills are taught in EqualOpportunity Programs and Equal Opportunity Centers.Segregating the remedial education function in a sepa-rate organizational unit can result in excluding thesefaculty members from a salary-equity analysis.

Here too, regression analyses can sort out the effectsof gender and race from those due to membership in aseparate discipline unit. All that is needed is inclusionof a dummy variable for remedial education. Again, notheoretical or methodological reason exists for exclud-ing remedial educators. All full-time faculty should beincluded in the multiple-regression salary review.'

Problem 3: Dropping of OutliersTrimming the outliers, those whose pay is way out ofline with that of others, sounds like a statistically legiti-mate, innocent thing to do. If your school has a Pulitzer

Prize-winning professor who was recently hired at avery high rate of pay, why should she be allowed tomask bias against other minority women? If your schoolhas kindly kept on staff, at a token salary, a severelyinjured white-male professor so as to continue provid-ing his health insurance, why should he be allowed tomask bias? If the gender and race of these exampleswere reversed, the logic would not change. The drop-ping of such outliers should be discussed and agreedupon by all parties. Appendix I explains three statisticaltests for locating outliers.

The problem comes when more statistically lazy orpolitically expedient methods of "trimming" outliersare used. If the hands-on researchers inform you thatthey have dropped all "outliers" with salaries morethan two standard deviations from the mean, this isnot as innocent as it may sound. By definition, approx-imately 2.5 percent of the faculty will be more thantwo standard deviations above the mean and another2.5 percent will be two standard deviations below it. Ifthe analysis involves four hundred faculty members,that means dropping about twenty peopleten withactual salaries much higher than their predictedsalaries and ten with actual salaries much lower thantheir predicted salaries.

If gender and race are randomly distributed amongthese two groups, dropping them from the analyses willprobably make no difference. Such randomness was notthe case at any of the twelve SUNY institutions in ouranalyses; rather, those on the high-paid side were oftenwhite males, and those on the low-paid side tended tobe females and minorities. The practice of dropping theoutliers is predicated on the assumption that they dis-tort the real picture. If the so-called outlier faculty donot distort the picture but are simply the highest- andlowest-paid cases in the picture, there is no real reasonto drop them; doing so can peel off a chunk of thegender and race bias.

Problem 4: Tainted VariablesThe choice of predictor variables included in multiple-regression analyses is critical in determining the accura-cy of the results. If you include a predictor variable thatis biased, then some of the salary estimate that mightproperly be attributed to being female or minority willinstead show up as part of the biased or tainted vari-able's estimate.

For example, suppose height were included in asalary-disparity analysis where gender bias exists.Because women are shorter on average than men, anygender differences in salaries could largely be explainedby the inclusion of height as a predictor. The salary

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Lois Haignere

disparity related to gender would be proportioned outby the regression analysis to both height and gender,masking the true magnitude of the gender bias.

While no one would include a height variable in asalary study, there are several common variables thatcan be tainted. Chapter 4 discusses in detail how to testthe categorical variable current rank for any taint thatmight mask bias. We also discuss what to do if you findthat current rank is tainted. Our conservative recom-mendation is that you still include it as a variable in theregression analyses, but assume that the results under-estimate the amount of bias. In this section, we warnagainst inclusion of three variables that are likely tomask bias even though it may not be possible to demon-strate statistically that they are tainted: current or previ-ous administrative appointment, initial rank, and initialsalary.

Current or previous administrative appointmentBecause being appointed to dean, assistant dean,department head, or another administrative position ismuch more common for male than female faculty(Johnsrud and Heck 1994), we thought it best to checkthis variable for taint before including administrativeappointment data in our SUNY analyses. Unfortunately,we found that for most of the twelve SUNY schools, thestatistical checks for bias in this variable were not reli-able. The categorical modeling approaches detailed inchapter 4 gave low R2L measures, indicating that thevariables in the model (years at the institution, years ofexperience prior to hire, highest degree, gender, andrace) were poor predictors of receiving an administra-tive appointment. Perhaps these variables will be betterpredictors of administrative appointment at your insti-tution. Or your data set may include other variables thatare more directly related to who is appointed to admin-istrative positions.

At some institutions, the extra pay associated withadministrative appointments is awarded only while anindividual is in that office, and is dropped afterward. Ifyour institution is one of these, you can simply drop theextra salary stipend of all current administrators, run-ning the analyses on base salary.

For most institutions, however, the situation is not thatsimple. Many campuses in theory remove the stipendwhen the faculty member no longer holds an administra-tive position, but in practice many faculty keep some orall of the administrative salary increment after they stepdown. Other institutions openly allow those who wereonce in administrative positions to continue to berewarded at a higher rate, based on their history in anadministrative position. It may also be that those who

52

have formerly served in administrative positions are dis-proportionately awarded discretionary raises.

Although in our SUNY studies we were unable todocument gender bias in the awarding of administrativepositions using categorical modeling, we did notinclude this information in our regression analyses. Wedid this based on the substantially higher proportion ofwhite-male faculty that had received administrativeappointments. In our opinion, if former administratorsare allowed to keep the extra salary stipends associatedwith their previous administrative roles, including thisvariable is likely to mask bias in salaries.

Initial rankIf women are hired at lower initial ranks than men withsimilar credentials on a systemic basis, and if the variableinitial rank is included in the analysis, then initial rank,like height, could be interpreted as explaining salary dis-parities more appropriately attributed to gender.

Studies reveal that department chairs, deans, andmembers of faculty search committees prefer curriculavitae attached to male names over the same vitaeattached to female names (Fide 11 1970; Steinpreis,Anders, and Ritzke 1999; Davidson and Burke 2000).Fidell found that the descriptions attached to malenames were, on average, 10 percent more likely to bejudged as deserving appointment at the tenured level(associate and full professor) than those attached to thefemale names.

Consistent with Fidell's findings, our categoricalmodeling results at SUNY institutions indicated sub-stantial gender bias in initial rank assignment. Womenwere consistently at least two to four times less likelythan comparable men to receive senior rank (associateor full professor). At two universities and one two-yearcollege, women were more than six times less likely tobe awarded initial ranks of associate and full professorthan men with similar highest degrees, years since high-est degree at hire, and years of experience prior to hire.Racial minorities were more likely to be hired as lectur-ers and instructors rather than assistant professors.

These findings of bias in initial rank are consistentwith the results of a study at the University of Hawaii.Male faculty there "have more than twice the chance ofwomen of being hired initially into upper ranks"(Hauser and Mason 1993, 10). Both the Hawaii studyand the analyses of twelve SUNY institutions lackeddata on the relative supply of male and female candi-dates, information that would ideally be included in anystudy of bias in initial rank. Nevertheless, in our opinion,the levels of bias shown for initial rank were striking andsuggested bias in hiring practices.

Small Errors with Big Consequences

To test the effect of omitting initial rank, we ranregression analyses with and without this variable.Although for many of the twelve SUNY institutions, theamount of salary bias indicated did not change substan-tially, at one university the bias indicated by the white-female coefficient decreased by about 30 percent wheninitial ranks were included in the model. This schoolwas also the university with the greatest amount of gen-der bias in the assignment of initial rank. This resultoffers a clear case of a tainted-rank variable maskingsalary bias.

Based on this information, we omitted initial rankfrom our SUNY analyses. We would also note that it isillogical to include initial rank in accounting for currentsalaries. The rank assignment that should account forcurrent salary is current rank.

Initial salaryAlthough we have not experienced pressures to includeinitial salary in current salary analyses, otherresearchers have. In negotiating the variables to beincluded in a study examining gender bias in salaries atthe University of Nebraska, for example, the bargainingunit representatives discovered that the universityadministration intended to include starting salary as avariable to explain existing salaries (Finkler et al. 1989).The problem with including such a variable involvesboth the likelihood that there is gender bias in startingsalaries and the substantial redundancy or overlapbetween initial salary and current salary variables. In alllikelihood, this overlap will mean that most of the vari-ance in current salaries will be explained by the vari-ance in starting salaries, leaving little to be explained byany of the other predictor variables, including genderand race.'

If the administration on your campus suggests suchan approach, you may find it helpful to know how thisissue was handled by the AAUP bargaining unit repre-sentatives at the University of Nebraska. The adminis-tration claimed that starting salaries were not gender-biased and, therefore, could be used in the analysis. Thebasis for this claim was a regression analysis with start-ing salary as the dependent variable. However, thisanalysis included only faculty members hired since aprevious adjustment for discrimination in 1972. Thislimitation meant that only 266 of the total 422 facultymembers were included. The results of this regressionanalysis showed a disadvantage for women of $1,231 instarting salaries, with a significance level of 0.0522 (seeglossary). The administration claimed that since thisfinding was not statistically significant (the significancelevel was not at or below 0.05), the variable starting

salary was not gender-biased and could be used in thecurrent-rank regression analysis.

The bargaining unit researchers responded thatalthough a significance level of 0.0522 meant that thesalary disadvantage could technically be considered sta-tistically insignificant, it was not evident that there wasgender equality in starting salaries. They conducted twoadditional analyses of starting salaries. The first ana-lyzed the initial salaries of all 422 current faculty, ratherthan just the 266 hired after 1972. That analysis foundgender bias at $1,038 with a significance level of lessthan 0.02, which is highly significant. The second studylooked at all of the 600 faculty hired since 1974 regard-less of whether or not they were still on staff. This analy-sis found gender bias at the level of $810 with a statisti-cal significance level of less than 0.01, indicating a veryhigh degree of significance. The administration droppedits insistence on the inclusion of starting salaries.

There are two morals to this story. First, multipleregression can assess gender bias in starting salaries justas it can in current salaries. Unless starting salaries canbe shown to be bias free, they should not be used as apredictor variable for current salary. Second, amountsthat would not reach statistical significance in smallerdata sets may become statistically significant with largerpopulations or data sets. Whereas bias at the level of$1,231 fell short of statistical significance when the dataset contained only 266 faculty, bias at the level of only$810 was statistically significant when the data setincluded 600 faculty. This is important backgroundinformation for our discussion of the "significance ofsignificance."

Problem 5: The Significance of SignificanceIf our results concerning salary bias are "significant,"they are assumed valid. The question is, if regressionresults indicating salary bias are not statistically signifi-cant, are they invalid? The answer is no; to understandwhy, we must look at the technical meaning of statisti-cal significance.

Significance levels are also called probability levels.Probability is a less misleading term, because what isbeing measured is the probability of replicating thefindings in another sample. Probability levels weredeveloped for use with inferential statistics. Inferentialstatistics make inferences about a whole populationbased on a sample. If we wanted to draw inferences orconclusions that extended beyond the faculty membersin our data set, significance levels would be important.If we took a random sample of faculty members on acampus and found a salary difference related to genderor race, we would use a significance test to estimate

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Lois Haignere

whether this finding was due to chance or whether wecould expect the same difference if we selected anothersample or examined the entire population.

Most faculty salary studies directly examine the entirefaculty population at a higher education institution, nota sample of that population. Nelle Moore (1993) notesthat faculty salary-equity studies should always involvetotal populations: "There is no reason to draw a samplewhen the complete data are available" (119). Any salarydifference found in that population is an actual salarydifference between the white male and female or minor-ity faculty categories.

When you study a population of faculty members,there is no sampling error, because there is no sample.But when you ask the computer to do a multiple-regression analysis, it does not know that a population,rather than a sample, is being studied. It has been pro-grammed to provide the sampling error and relatedlevels of statistical significance on the presumption thatit is looking at a sample. Since the figures are rightthere, it is difficult to ignore them. But the focus shouldbe on substantive rather than statistical significance.

If women or minorities are, on average, affected byeven a few hundred dollars, this could be a "significant"amount to them. At one of the four-year SUNY collegeswith a faculty of only 117, the regression result for beingfemale was -1,488, with a significance level of 0.06. Inother words, on average, female faculty members werepaid $1,488 less than male faculty, all other independentvariables held constant. Is this a substantial amount ofmoney for those involved? Given that $1,488 is an actualdifference within a population and not an inferentialfinding from a sample, should a salary disparity of thismagnitude be ignored?

It is particularly important to understand that statisti-cal significance is directly tied to the size of thedatabase. (Note the example of the University ofNebraska study in the previous section.) The smaller thedata set, the less likely that the results will be statistical-ly significant. A regression analysis on a data set withfewer than two hundred faculty members is unlikely toyield a statistically significant finding. With large datasets, a small dollar difference can be statistically signifi-cant but of little practical significance.

The size of the race-gender category being examinedis also important. Even when you have a large data setof, for example, over a thousand faculty, if the numberin the group being assessed is very small, the amount ofbias indicated has to be substantial to achieve statisticalsignificance. If there are twenty Asian women profes-sors, and the results indicate bias in their salaries, thisresult is more likely to reach statistical significance than

54

if there are only two Asian women. We do not have tobe statisticians to understand that. The salary disparitycalculated from a population of two Asian women ismore likely to be affected by unusual and random fac-tors than it would be based on a population of twentyAsian women.

The implications of this connection between the num-ber of faculty in a category and statistical significancebear noting. An institution with hiring practices thatkeep the number of women or minorities low could con-ceivably use the resulting lack of statistical significanceto exonerate them of salary bias. This possibility under-scores the suggestion that significance levels should beconsidered just one piece of information in the interpre-tation of the results. If, for example, there are very fewLatino men on the faculty and the results indicate a sub-stantial but not statistically significant bias in theirsalaries, this result should be interpreted in light of pat-terns for this campus. If there are few women andminorities and the analyses show that they are paid lessthan comparable white men, there may well be biasagainst the Latino men. If, on the other hand, this col-lege has hired many Latino women and other minoritiesand if these groups are paid relatively fairly, the resultsregarding Latino men might be considered to be chancefindings.

The issue of database size in relation to statistical sig-nificance can become the focus in struggles betweenthose who do and do not want the study to indicatesalary bias. For example, in court cases the defendantuniversity will argue that deans or even departmentheads determine salaries and that, therefore, smallerunits should be studied separately. Those suing the uni-versity for salary discrimination will argue that theprovost or president has the final say on salaries and theoversight responsibility to make sure that bias insalaries does not exist, so the analyses should be con-ducted at the university level.'

In our opinion, the appropriate approach is to recog-nize the limited role of statistical significance when apopulation is being studied and, therefore, to look at thesubstantive importance of the results. A small salarydifference at a large university may not be importanteven though it is statistically significant. A large salarydifference at a small college may be important even if itis not statistically significant. If eliminating a salary dis-crepancy could improve morale, recruitment, retention,and fairness, asking if it is statistically significant is thewrong question.

Nelle Moore notes that statistical significance hasbeen confused with substantive importance in partbecause of the normal usage of the word significant.

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Noting that significance testing provides an illusion ofobjectivity built on fantasy (Carver 1978), she concludesthat it has no meaning in salary-equity studies of insti-tutional populations. She notes, "There is nothing ran-dom about the data, about the hiring process, or aboutthe awarding of salaries. There is no sampling proce-dure. There simply is no context within which the use ofsignificance tests could be considered appropriate" (N.Moore 1993).

Gray (1991, 1993) is less emphatic about ignoring sig-nificance levels. She agrees that no question of inferenceexists when you study a population. However, she sug-gests that statistical significance still be noted as an indi-cator of whether the observed difference could be theresult of random variations in faculty salaries. Forexample, salary increments for promotion may besmaller in a low-funding year. Being both a lawyer anda statistician, Gray notes that many courts have movedfrom "complete disregard of the concept of statisticalsignificance" to an almost "mystical reliance" on the0.05 significance level. She also indicates that there arejudicial decisions to suggest that the intent to discrimi-nate can be inferred from sufficiently large statisticallysignificant differences (Gray 1993).

We recommend that tests of statistical significance beused as one piece of information in weighing theimportance of the results. The importance of any salarydifferences found should be evaluated in light of thegeneral pattern of the findings and should not be strict-ly a statistical decision. We agree with Snyder et al.(1994) that the absence of statistical significance shouldnot be viewed as proof of the absence of bias. Theauthors note that if there is a pervasive pattern of nega-tive residuals for the female variable across ranks andcolleges, there is cause for concern despite an absenceof statistical significance.

Problem 6: Divide and HideThe objective of most multiple-regression studies offaculty salary equity is to check for systemic genderand race bias at the institutional level. But in studies atsome institutions, the total institutional analysis (theforest) is skipped over in favor of separating the tenuretrack from the nontenure track or senior ranks fromjunior ranks. At this tree level, the decision is to look atseparate colleges or schools within the institution.Within a set of disciplines or a large discipline, the sug-gestion is made that the problem is really due only to afew departments. At the department level (the twigs),the problem is attributed to a few individuals. So weget down to the leaves, the individual female andminority faculty members.

Why bother to use regression analysis if you have dis-carded the idea that discrimination is systemic andaffects all those in the group?

Failure to understand that regression analyses mathe-matically control for discipline and rank may lead poli-cy makers to accept the misguided practice of studyingonly subsets of the faculty population. Studies of bias infaculty salaries include the variables discipline, rank,degree, and years of experience in order to control anysalary differences related to these variables while gen-der and race are examined. Thus, by design, these anal-yses do not address different jobs, but rather very simi-lar ones, for example, associate professors in disciplinex. The result is an equal-pay-for-equal-work study,where gender and race differences across disciplines orranks are statistically controlled. There is no reason toconduct separate studies of the different disciplines andranks to accomplish this.

The problem with subdividing the population intodiscipline or rank groups is that the data sets becomesmaller and smaller. As a result, the regression analysesmay be less valid. As previously noted, for regressionanalysis, it is recommended that there be at least fiveobservations (faculty members) for each independentvariable in the model (Blalock 1979). With fewer people,the analysis has less information to go on. This will bereflected in the deterioration of the significance levelsreported in the computer output. Even if significancelevels are ignored, the significance of the results will beless clear when the data set and the numbers in the indi-vidual race-gender groups are small. For valid results,stick with data sets that have at least five faculty foreach independent variable.

There is some diagnostic appeal to looking for theinstitutional subsets in which bias is more prevalent. Seechapter 7 for a discussion of when and how to validlyassess subunits like certain ranks and disciplines forsalary inequities.

Problem 7: Stepwise AbuseThe statistical procedure called stepwise regression pro-duces results that at best are difficult to interpret and atworst can mask a substantial gender or race salary dis-parity simply by ignoring gender and race.

There are two types of stepwise analyses: forwardand backward. The forward stepwise procedure is themore problematic for salary studies. In this procedure,the researcher enters a long list of variables whoseeffects are unknown, to discover which meet the test ofa specified level of significance. The procedure selectsthe predictor variable that has the strongest relationshipwith the dependent variable and enters it on the first

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Lois Haignere

step. Next, it searches for the second variable based onthe second strongest correlation with the dependentvariable and enters that variable on the second step.This process continues until the procedure finds nomore variables that are related to the dependent vari-able at the level of statistical significance specified. Suchfishing expeditions or exploratory studies are some-times necessary, but Pedhazur (1982) and N. Moore(1993) note that the researcher should be responsible forselecting the variables, not the computer.

Stepwise procedure has its proper uses, but in salarystudies it is commonly used to conceal gender and racerelationships. If the forward stepwise procedure is usedwith a restrictive level of significance, the stepwise pro-cess may stop before the gender and race variables enterthe analysis.' The race and gender variables are thendeclared "insignificant," and salaries are declared biasfree. This procedure is not designed for use when vari-ables that are predictive of the dependent variable are aswell recognized as they are for salary analyses.Moreover, since stepwise regression relies blindly on sta-tistical significance, it should be avoided for all of thereasons indicated in our discussion of significance levels.

If those conducting the research at your institutioninsist on using a stepwise analysis, make sure that theyuse a backward stepwise procedure. Pedhazur (1982)notes that the use of the forward stepwise procedure isproblematic and that the backward is preferred.Backward stepwise regression starts with all of the vari-ables in the analysis and drops those variables that donot reach the significance level specified, one at a time.Thus, the computer output for the initial step of thisanalysis allows you to view the results for the genderand race variables even if these variables are dropped inlater steps for failure to meet the specified significancelevel. Unless their intent is to hide the magnitude of thegender or race relationship by using stepwise proce-dures, the administrations should not object to using thebackward (rather than forward) stepwise procedure andproviding the computer output for the initial and subse-quent steps.

While backward stepwise procedures are moreacceptable than the forward approach because they donot hide the effect of gender and race, the results are dif-ficult to interpret. Because they do not meet the signifi-cance levels required, some of the dummy variables donot enter the analysis. The smaller your faculty, themore likely some dummy variables will be dropped bythe analysis. This means that some ranks enter the anal-ysis and others do not. What does it mean, for example,when lecturers and leading professors are left out of theanalysis because there are too few individuals in these

56

categories to reach statistical significance? For one thing,it means that both ranks are treated like the default orreference current-rank category, that is, the dummyvariable rank that has been left out of the analysis or setto zero. If full professor is the default, both lecturers andleading professors are treated as full professors. Ifinstructor is the default, both lecturers and leading pro-fessors are treated as instructors. Similar problemsoccur when a highest degree or discipline dummy vari-able is dropped by the backward stepwise procedure.

In our opinion, there is no reason to use stepwise pro-ceduresforward or backwardto assess gender andrace bias in faculty salaries. Faculty salary-equity stud-ies are explanatory, not exploratory, analyses.

Problem 8: Dropping of Gender and RaceStepwise regression is not the only way that race andgender variables get excluded from multiple-regressionsalary studies. Some salary reviews, even when theypurport to check gender and race bias, leave these cru-cial variables out of the analyses. The common excusefor doing so is that since race and gender should not beallowed to play a role in determining pay, they shouldnot be used to create the predicted salary of the individu-al faculty member (see appendix A).

This sounds good in theory, but in practice the predict-ed salaries are not the actual salaries. If we could get ridof the effects of gender and race on actual salaries just byleaving these variables out of regression analyses, howwonderful that would be. What we need is to know howmuch of the variation in actual salaries is attributable torace and gender. If the variables are omitted from theequation, the degree to which they explain actual salariesis never determined. It is easy enough to remove race andgender effects from predicted salaries. For example, ifbeing female is found to cost $1,500 on average, you sim-ply add this amount to each woman's predicted salary.Alternatively, you can calculate all faculty members' pre-dicted salaries as if they were white males.

In addition, omitting these variables from the regres-sion model embeds any gender or race bias that may bepresent against white men, making them appear statisti-cally to be overpaid. This happens because, in theabsence of any information on gender and race, theregression procedure takes the entire population intoaccount, averaging the salaries of all faculty. Comparedto this overall regression line, most white men willappear to be overpaid. By contrast, when race and gen-der variables are entered, white men are compared totheir own average line. Half of the white men are abovethe line and half below it, so their average residual iszero. This is true for each of the race and gender groups.

6 6

Small Errors with Big Consequences

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Salaries for a Two-Year College, State University of New York

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Figure 6.1 helps to make this clear. This graph showsa scatter of actual salaries against predicted salaries fora SUNY two-year college. Note that most of the femalefaculty are in the lower part of the scatter and most ofthe male faculty are in the upper pare The dark linerepresents the regression line of the male scatter, andthe light line, that of the female scatter. If the gendervariable had not been entered in this analysis, theregression line would be between these two lines,pulled down by the lower salaries of the women faculty.More of the male faculty scatter would then be abovethe average line, making more men appear "overpaid."If we gave all females enough money to bring theiraverage salary up to the average for the total popula-tion, general scatter for the female faculty would still bebelow that of the male faculty, indicating that there wasstill bias in pay.

Without the race and gender variables, the regressionprocedure creates an overall pay line that, because ofthe lower salaries of female faculty, makes the male fac-ulty look overpaid and fails to provide the proper esti-mate to remove the bias in the female faculty pay.

SummaryIn this chapter I have discussed eight ways method-ological decisions can affect the outcome of the analy-ses so as to mask gender or race bias. This list is farfrom exhaustive. Every new research design bringswith it the potential for subjective methodological deci-

sions that influence the results. I hope, however, thatthis chapter has alerted you to issues to guard againstand questions to ask concerning the research designand results.

Notes1. If you are stuck with interpreting standardized coefficients,divide the standard deviation of the dependent variable by thestandard deviation of the independent variable. (The multiple-regression computer output from most statistical softwarepackages provides the standard deviations for the indepen-dent variables.) Then multiply the result by the coefficient ofthe independent variable. This lengthy, unnecessary processgives you the unstandardized regression coefficient dollarestimates.

2. Chronister et al. (1997) report that the proportion of non-tenure-track faculty has increased to 27.3 percent, with non-tenure-track women faculty now making up more than half ofthe faculty at two-year and master's-level institutions.

3. Our regression analyses examine whether faculty hiredwithin the last five years at a specific institution are less likelyto have gender or race bias in their salaries. We usually findlittle evidence of less bias in the salaries of recent hires. Bycontrast, Toutkoushian (1998), using 1988 and 1993 data fromthe National Center for Education Statistics, finds evidencethat the wage gap for younger women is smaller than that forolder women in academe. Given the difference in methodolo-gies and the populations being studied, there could be a num-ber of explanations for these different findings.

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4. If your institution separates out remedial educators, therebyproviding an institutional mechanism through which they canbe paid less than others in their discipline despite their needfor special teaching skills, you may be able to use the occasionof this study to correct their salary inequities. At the request ofEqual Opportunity Program members at a SUNY university,we assigned these educators to the discipline they teach,rather than the discipline of "remedial education." The aver-age difference between their predicted and actual salariesgives an estimate of the degree to which they have been sys-temically underpaid.

5. Gray (1990) noted that a justification offered for using start-ing salary as a variable to predict current salary is that if raiseshave been equal for men and women, there is no current dis-crimination. She cites a 1986 Supreme Court decision thatemployers have a continuing obligation to equalize salariesand that giving equal raises is not sufficient.

6. Ferree and McQuillan (1998) note that competing implicitconceptions of discrimination also play a role in these strug-gles. See chapter 7.

7. Most computer procedures set a nonrestrictive significancelevel recognizing that fishing expeditions are best when theyallow many variables, even those with low predictive power,to enter the analysis. SAS, for instance, has a default signifi-cance level of 0.50 for forward stepwise procedures and 0.10for backward stepwise procedures. If, however, theresearchers so choose, they can set much more restrictive sig-nificance levels. That was done for a faculty study at a univer-sity in Ontario. Forward stepwise regression was used with asignificance level of 0.05 rather than the common, less restric-tive significance default of 0.50. Not surprisingly, the gendervariable did not enter this analysis. Lois Haignere was askedby the faculty association to comment on this study. She usedinstitutional data from SUNY to demonstrate that a lessrestrictive significance level would have, in all likelihood,revealed a gender effect.

8. The only minorities in this data set are four Asian males.

58 sS

At first, we were surprised that our argument for an across-the-board settlement that it wouldbe fairer to the best women on the facultywas rejected. Ultimately, we imputed this resistanceto both the administration's tacit view of discrimination as an individual process and its desireto keep salary information and decisions in its own hands.

Myra Mary FerreeProfessor of Sociology

University of Wisconsin

Julia McQuillanProfessor of Sociology

University of Nebraska

SEVEN

Diagnosis Dynamics and Treatment TurmoilBy Lois Haignere

The researchers analyzing faculty salaries at yourinstitution are likely to reach a point at which theybelieve the job is done and a diagnosis of whether

or not salary inequities exist has been made. Other par-ties in the process may have other ideas. In this chapter,we note the practical side of the political dynamics ofdiagnosis as the parties progress from research resultsto remedy.

Diagnosis DynamicsBefore looking at remedies, faculty and administrationshould attempt to come to an understanding of themeaning of bias findings.

Two views of biasUnderlying many debates over how to study and correctfaculty salary disparities are assumptions about how dis-crimination comes to be embedded in salaries in the firstplace. Ferree and McQuillan (1998) have described thetwo primary conceptualizations of discrimination as theinstitutional and individual perspectives. The institutionalperspective views discrimination as systemic, generallyaffecting all those in the women or minority category inquestion. The individual perspective sees discriminationas resulting from isolated personal prejudices that causepockets of salary disparity.

According to the institutional-systemic view, the basicreason for gender bias in salaries is that women andwomen's work have traditionally been undervalued.There is a pervasive cultural attitude that women aresecond-class citizens and, by extension, their work isworth less than that of men. This cultural devaluing of

women and their work permeates all realms of our soci-etyour psychological, political, and economic exis-tence. "The market, as it functions in the daily lives ofpeople, is not independent of the values and customs ofthose who participate in it" (Kessler-Harris 1990, 117).Paying women less than men for equal work was notmade illegal until 1963; the acceptability of payingwomen less remains an implicit social norm.

"Gender is present in the processes, practices, images,and ideologies, and distributions of power in the vari-ous sectors of social life" (Acker 1992, 567). Gender dis-tinctions are created and maintained by everyday socialinteraction and accumulated past practices and policies.A basic tenet of the institutional-systemic perspective isthat historical and ongoing prejudice becomes embed-ded in institutional processes, and the resulting policiesand practices undervalue most, if not all, women work-ers. The purpose of a faculty salary study is to identifyand to propose institutional solutions for systemicbiases in the salaries of women and minorities.'

By contrast, the individual view of the potential forgender and race bias in salaries is that the market tendsto reward human capital fairly. Thus, a year of educa-tion or experience or the attainment of a higher rankwill be equally rewarded in the salaries of women,minorities, and white men. Intervention is rarely neededbecause the market is generally fair. Isolated personalprejudices can exist, however, causing pockets of salarydisparities. The purpose of a salary study under theindividual perspective is to find the few individualswhose salaries have been affected by personal prejudiceand adjust their salaries accordingly. Depending on the

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findings, a secondary objective may be to remove theprejudiced person(s) from hiring and salary assignmentresponsibilities.

Articulating these two different conceptualizations ofthe source of salary bias early in your institution's pro-cess of examining salaries can facilitate discussions aboutthe methods you use and the remedies you recommend.

Fit between perspectives and partiesYou may find, as Ferree and McQuillan (1998) did at theUniversity of Connecticut Health Center, that these per-spectives tend to be associated with the parties involvedin the salary discrimination studies: the faculty and theadministration. Ferree and McQuillan reported that thefaculty members on the health center committee believedthat salary inequity existed on the institutional level, asthe result of gender and race stratification that was his-torical, pervasive, and ongoing. Ferree and McQuillaninterpreted the administration's behavior to be a reflec-tion of their belief that gender- and race-based salaryinequities did not exist, or if they did, that they stemmedfrom the isolated prejudices of a few individuals.

Note that these are not necessarily competing ormutually exclusive perspectives. Holding the view thathistorical and systemic gender or race bias is transferredto salaries through societal and institutional processesdoes not rule out also believing that biased individualscan exacerbate bias in salaries in their particular depart-ments or colleges. Faculty members and administratorscan, and frequently do, hold both perspectives.

There is also national variation in whether theinstitutional-systemic perspective is espoused. In ourexperience, both administrators and faculty members inCanada, New Zealand, and other Commonwealth coun-tries are more likely than their U.S. counterparts to holdthe institutional-systemic view of salary bias. In theUnited States, both faculty members and administratorstend to espouse the individual perspective. For exam-ple, at an East Coast public research university, thewomen faculty had previously won the right to use thewhite-male regression equation to calculate their indi-vidual predicted salaries for comparison with their actu-al salaries. They believed this information empoweredthem individually, despite the fact that the universityanalyses showed salary inequities for women as a classthat were not being addressed.

Fit between perspectives and study resultsIn our experience, if bias is found at the university level,administrators may push for analyses of the nooks andcrannies (colleges, departments) in hopes of making itdisappear or confining it to a few specific subunits. On

60

the other hand, if bias is not found at the universitylevel, women and minority faculty are likely to lobbyfor further analysis of subunits to see if pockets of biasexist.

Overall, however, the tendency in the United Statesconcerning choice of perspective is consistent with theexperience of Ferree and McQuillan: administrators arefar less likely to espouse the institutional-systemic per-spective on bias than are faculty. Like Ferree andMcQuillan, we have experienced many settings inwhich administrators press for further analysis conduct-ed at smaller and smaller institutional subunits (see"Problem 6" in chapter 6).

Despite the administration's affection for the individ-ual perspective, never have we had a brave administra-tor say, "Well, it is gratifying to know that we have noevidence of bias in salaries at the university-wide level,but I suspect we have bias in salaries in the college ofXYZ. Would you please check there?" Such observa-tions seem to come only from the faculty. Frequently,they come from the faculty even if there is substantialevidence of systemic bias at the institutional level.

Pockets of BiasPockets of bias may exist. Determining their effect asdistinct from that of institutional bias is a difficult andsensitive problem.

Institutional-level checksIn the best-case scenario, there is a common apprecia-tion among faculty and administration of the method-ological fit between multiple regression's focus on classdifferences and the logic of the institutional-systemicperspective. A common agreement on this perspectivewould mean that all parties accept the institutional-levelresults. This does not mean that you fail to checkwhether the individual perspective and pockets of biascan explain your findings. Ruling out the presence ofpockets of bias may be accomplished in two ways:through use of interaction terms and through examina-tion of the pattern of the residuals.

As explained in "Improved analysis" in chapter 5,you can check for interactions that indicate that yourresults may be due to pockets of bias rather than sys-temic bias. You may get a clue that findings differ basedon discipline or tenure status by examining the coeffi-cients for these categories and comparing the white-male with the total-population results. If you observesubstantial differences, first check the number of facultyin the suspect categories. Might the differences be dueto one or two aberrant salaries? Are there more thanfive faculty members in the categories involved? Next,

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Diagnosis Dynamics and Treatment Turmoil

rerun the total-population analysis with a race-genderinteraction term (see chapter 5) and observe the specificimpact. For example, you might surmise that averagelower salaries for women arise from salary bias amongnon-tenure-track faculty and does not exist amongtenure-track faculty. To test that possibility, enter intothe analysis an interaction term for non-tenure-trackwomen. If the coefficient for this interaction term is neg-ative and substantial while the coefficient for the femalevariable (which now represents all female faculty exceptthe non-tenure-track women) is much less negative oreven positive, the *salary bias you observe relates pri-marily to non-tenure-track faculty.

The second method of checking for pockets of bias isto examine the pattern of the residuals using the white-male faculty regression equation. Ferree and McQuillan(1998), who recommend this method, note that:

If the average difference between men's andwomen's residuals is explained by some individ-ual women being grossly and unfairly under-paidas the individual model suggests wouldbe the casethere will be a bimodal curve, witha second "hump" near the tail end of the nega-tive residuals. Such a "hump" would represent acluster of women with abnormally low salarieswho pull down the average for the whole group(14).

If you find such an abnormal picture when you plotthe residuals, further analysis may reveal that the facul-ty members in this "hump" are disproportionately in acertain school, discipline, or hiring cohort. In turn, youmay find that this effect relates to a prejudiced adminis-trator or administrative process that has a constrictedimpact. (See "Residuals: The Ungreat Unknown" inchapter 5 for more information on residuals.)

Subunit analysesIf no agreement exists on the institutional-level findingsand pressures exist for subunit analysis, the challengeis to proceed in a methodologically correct way.Multiple-regression statistical analyses are group-levelanalyses of systemic bias. They should not be appliedto the individual level. The general rule of five cases foreach independent variable should be respected. Manycolleges within large universities are large enough tosustain separate regression-model analyses and stillhave five cases (faculty) for each independent variable.However, just having the numbers necessary to analyzesubunits does not, in and of itself, legitimate such anal-yses. Consider the reality of how salaries and salary

increments are assigned at the institution. Do the sub-units actually have substantial input in determiningsalaries? If so, then analyses at the subunit level may beappropriate.

Case StudyThe SUNY-UUP joint faculty-administration committeemet on a regular basis for over a year to decide how bestto adjust for salary bias revealed by multiple-regressionstudies at twenty-nine SUNY institutions. At first, boththe union and the administration assumed that salaryadjustments would be individually determined. Thequestion that began to haunt us was: what level of dataaccuracy was needed before we were justified in givingmoney to one woman and not another, or to one AfricanAmerican man and not another, or to several whitewomen but only one Latino man?

Despite close attention to data accuracy and diligencein data cleaning (see chapter 3)plus a general pride inthe quality of our datawe did not believe our datawere accurate enough to estimate individual-level salarydisparities. If we had to validate the data for every indi-vidual woman and minority man at twenty-nine SUNYinstitutions, we would still be doing the study today.

We began to see the wisdom of an institutional-systemic approach to awards, similar to the one usedin adjusting faculty salaries by the University ofConnecticut at Storrs in 1988. There is the advantagethat errors are assumed to be random, eliminating theneed to validate every piece of data studied. Althoughconsideration of the institutional approach was initial-ly motivated by methodological concerns, the otheradvantages to this approach became apparent, includ-ing the extension of the adjustment to all women,including the superstars; the adjustment of the femalescatter to more closely approximate the male facultyscatter; the fit between multiple-regression class orgroup results and the adjustments of salaries for allthose in the group; and lower total costs.' These advan-tages are discussed more fully in the next section.

We concluded that using group rather than individ-ual disparities provided the best approximation ofwhat the salaries of women and minorities would havebeen in a completely gender- and race-blind society.Thus, we gave all of those in the gender and minoritycategories who had a negative coefficient the sameaward based on the amount of negotiated moneyavailable.

Institutional-Systemic RemedyThe institutional approach assumes that the effect of gen-der and race on salaries is systemic, affecting all those in a

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Figure 7.1

Salaries Before Remedy60

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given gender and race category. In other words, the under-valuing of workers based on gender and race affects the"superstars," the "duds," and the average performers.Why should the highly productive females have actual sal-aries that are lower on average than the highly productivemales? Similarly, why should the substandard women bepaid less, on average, than the substandard men? Gray(1990) states that "discrimination affects the salaries of thebest, the poorest, and the average woman faculty mem-ber"(7). Any remedy should address the entire class.

In fact, an emphasis on group or class differences,rather than individual differences, is a more appropri-ate use of multiple-regression statistics, becausemultiple-regression results, like averages, indicate class,rather than individual, differences (Gray and Scott1980). For example, suppose the regression equationindicates that women faculty members receive $1,200less a year on average than comparable white-male fac-ulty members after controlling for rank, discipline,years of service, and the other predictor variables. Thisdoes not mean that there are no faculty women who arepaid above the average received by comparable men.Neither does it mean that there are no white men paidless than women or minorities. What it means is that itis less likely that white men make less than comparablewomen and minorities and that it is less likely thatwomen and minorities make more than comparablewhite men.

Applying the group approach to salary awards meansthat the distribution of women and minorities' residuals

62

(or the scattergram of their actual and predictedsalaries) will be more similar to that for white men.The highest-paid women and minorities will havesalaries more like the highest-paid white males, andthe lowest-paid women and minorities will havesalaries more like the lowest-paid white males. Figures7.1 and 7.2 show the effects of this approach on aSUNY two-year college.

Figure 7.1 plots the actual salaries (vertical axis)against the regression-predicted salaries (horizontalaxis) for each faculty member. Each rectangle representsa male faculty member's predicted and actual salaries,and each oval represents a female or minority facultymember's predicted and actual salaries. The scatter forthe women and minorities is lower than that for themen, and separate lines representing the general trendof the scatter (the line of "best fit") have been plotted foreach group. Raising the salaries of all those in thewomen and minorities category by the total amount oftheir negative coefficient has the effect of moving thefemale-minority best-fit line up to coincide with themale line (figure 7.2). The scatter around that line willpersist so that relatively equal proportions of the white-male scatter and women and minorities' scatter areabove and below that line.

While the group approach creates equalization acrossgender and race groups, it does not change the distri-bution of salaries within these groups. Most whitemales in the UUP bargaining unit expected the genderand race adjustments and knew that they came out of

4

Diagnosis Dynamics and Treatment Turmoil

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Figure 7.2

Salaries After Remedy

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specially negotiated money that could not be used forany other purpose and would not draw away from annu-al increments or discretionary awards. However, womenand minorities were expecting some corrections in theirsalaries. Awarding increments to some women andminorities but not others would have created a difficultsituation. For the twenty-nine SUNY-WP institutions,awards were based on institutional-level results. If themultiple-regression analyses indicated no bias for a par-ticular race-gender group at a particular college or uni-versity, the individuals in that group did not receive asalary adjustment. When bias was found for women or aminority male group at an institution, each individual inthat group at that institution received the same salaryincrease.' Under the group approach, no women orminority faculty saw others in their same race-gender cat-egory leap ahead of them in salary. The group approachto remedy recognizes the underpaid women and minori-ty stars and confronts the cultural pressures to limit themto salaries that are average or below those of white men.

LongevityThe most senior women and minority faculty membersmay have suffered more bias simply because of thecompounding effect of time.' Gray (1990) recommendsadjusting for seniority either by introducing an across-the-board adjustment with a seniority bonus or by bas-ing each individual's adjustment on the number ofyears at the institution. The seniority bonus approachcould, for example, give a bias increment to all faculty

in an underpaid race-gender category and, in addition,a longevity bonus to those with more then ten years ofservice to the institution. Alternatively, the total remedycould be based on years of service. For example, if theregression results indicate that, on average, each personin a race-gender category is underpaid by $1,000 andthe average time at the institution is ten years, then eachfemale or minority can receive $100 for each year at theinstitution. Thus, a faculty member who has been at theinstitution for five years would receive $500, and some-one who has been there for fifteen years would get$1,500.

A percentage increase is sometimes suggested as away of correcting for the compounding effect of biasover time. The presumption is that the highest-paidindividuals have been at the institution longest andtherefore should be awarded proportionately higherbias corrections. We do not recommend this approach.As multiple-regression studies demonstrate, many fac-tors other than longevity contribute to high pay. A per-son hired last year as a full professor in a prestigiousdiscipline could receive a much higher award than themany women and minorities in disciplines that are lowpaid (Bellas 1994).

Flagging and Other RemediesThe group-award approach just described is popularwith researchers because of its consistency with themultiple-regression method. It is popular with facultyorganizations because of its broad equitable approach to

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Lois liaignere

the problem. But it is not very popular with deans,department heads, and others who have been responsi-ble for the salary-setting process. These administratorsprefer to view gender and race bias as a rare occurrenceand, therefore, to "flag" those women or minoritieswhom the analyses show to be underpaid relative totheir predicted salaries. Gray (1990) notes:

Any suggestion that one use the regressionmodel merely to identify individuals whosesalaries are below what is predicted for themand raise their salaries to the predicted amountmust be resisted; even more invidious is thenotion that these, and only these, cases will beexamined to see whether the low salaries are"justified" (7).

Salary bias identified by multiple regression is by def-inition not individual, but pertains to class or systemicdifferences (Gray and Scott 1980). Accordingly, it is con-troversial to base remedies on the individual-level pre-dicted salaries provided by the multiple regression.Multiple-regression results, like averages, indicate class,rather than individual differences. A class can be anygroup membership such as a rank, discipline, highestdegree, gender, race, or hiring cohortbut not an indi-vidual. Flagging, which uses multiple regression tofocus on individuals and individual corrections, is,therefore, inappropriate.

The most common flagging approach locates all thewomen and minorities whose actual salaries are lowerthan their predicted salaries and raises their salaries tothe predicted levels. In other words, the salaries ofwomen and minorities whose residuals are negative(who are below the white-male line) are brought to theprediction line. Only white males remain below theline. Those white males whose actual salaries arebelow their predicted salaries do not receive anyadjustments and, therefore, end up being paid lessthan the adjusted women and minorities (see figure7.3).

Any remedy that involves only those whose predict-ed salaries are below their actual salaries is misguided.When the regression coefficient for any group or classstudied is negative, everyone in that group is, on aver-age, paid less than everyone in the default group. Forexample, if the default rank is associate professor andthe variable for assistant professor has a negative coef-ficient, this indicates that, on average, all assistant pro-fessors are paid less than associate professors. Toassume that being an assistant professor affects onlythose assistant professors that are paid below the asso-ciate professor line misuses this finding. Similarly, ifbeing in a liberal arts rather than a natural science dis-cipline is shown to, on average, cost a faculty member$400, it is wrong to assume that the only liberal arts fac-ulty members affected are those paid below the naturalscience discipline average.

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Figure 7.3

Below-the-Line Remedy

25 30

NMwir

White MaleOFemales and Minorities

Linear White (Male)

35 40

Predicted Salary(thousands of dollars)

45 50 55 60

7464

Diagnosis Dynamics and Treatment Turmoil

cti

60

55

50

c.n o 45To -8c cc 40

35

30

25

20

Figure 7.4

Below-the-Line Remedy Extended to All

White MaleCD Females and Minorities

Linear White (Male)

25 30 35 40

Predicted Salary(thousands of dollars)

45 50 55 60

Moreover, a number of practical problems arise withthe application of this flagging approach. The mostobvious one is that leaving all of the white males belowthe line while raising the women and minority facultymembers' salaries to the line increases the potential forreverse discrimination allegations. This can lead to asecond problem. Faculty organizations sometimesattempt to raise the salaries of all those below the line tothe line. Such an adjustment aggravates the gender biasin salaries rather than eliminating it (figure 7.4). Raisingsalaries of the many white males below the line lifts theregression line itself, so that a substantial majority of thefemale and minority faculty members are paid belowthat line. This could lead to chasing the linean activitylike chasing your tail.

Another variation on this flagging approach is to"allow" all the women and minorities whose actualsalaries are below their predicted salaries to apply forindividual case reviews. Case reviews can involve pair-ing an individual woman or minority with a compara-ble white male or small group of comparable whitemales to illustrate the need for adjustment (Holmes-Rovner et al. 1994). Case reviews are lengthy processes,necessitating the development of criteria for comparingfaculty members, and focusing attention on the issueand related controversy for an extended period of time.Such comparisons tend to become accusatory, competi-tive, and contentious, perhaps leading to recrimination,defensive re-action, and exacerbation of any race orgender animosity.

Whether or not case reviews involve paired compar-isons, they have the obvious drawback of using thesame decision makers and institutional structures thatcreated the discrepancy in the first place, perhaps evenrequiring self-incrimination. And what happens tomonies that are not awarded? Does the administrativeunit that does not award them retain them? (See Snyder,Hyer, and McLaughlin 1994.)

Case reviews assume that bias is individual, not sys-temic. Under this assumption, no reason exists to conducta multiple-regression analysis. Statistical methods do notadequately address the individual level. Even if they did,the data available for most salary analyses are not ade-quate or appropriate for suggesting remedies for individ-ual cases of salary disparity. Individual faculty salary dis-parities are better explored through qualitative approaches.

If you use multiple-regression analyses and find indica-tions of gender or race bias in faculty salaries, consider aclass-based remedy consistent with that statisticalmethod. Remedies that are distributed equally to all thosein the affected group can be applied easily, efficiently,promptly, and without prolonged attention to the issue.

Remedy approaches that do not include the womenand minorities at the top risk confirming the stereotypethat women and minorities are low performers. Manyhighly successful minorities and women may acquiesceto such an approach because they feel apologetic abouthaving more power, status, and rewards than others intheir gender and race groups. Given that they arealready better off, they may be reluctant to insist on the

65

Lois Haignere

real value of their work and to compare themselves withwhite men. But fairness is more than just bringing up thebottom. When elite women and minorities get paid morefairly relative to white men, they make it easier for allothers in their race-gender group to be more fairly treated.

Toward a More Permanent SolutionWhen members of the AAUP's Committee on the Statusof Women in the Academic Profession first proposed,over twenty years ago, that the average salaries for menand women faculty be published separately, they opti-mistically presumed that "unmasking salary discrimina-tion would be the prelude to eliminating it" (Gray 1988).But the problem persists. Both faculty and administra-tors assume there is less bias in the salaries of morerecent hires. Too often this assumption is false.

In chapter 1 we noted that prejudice is resistant tochange because it is based on "unconscious ideology"a set of beliefs that we accept implicitly, but which weare not aware of because we cannot conceive of alterna-tive interpretations of the world (Top 1991; Bern andBern 1970).

The author of this chapter experienced the resilienceof unconscious ideology directly in explaining a facultysalary-equity study and related salary awards to a facul-ty audience. A particularly unhappy white-male associ-ate professor of physics explained that he and a womanfaculty member had been hired at the same time sixyears earlier with what he admitted were equal creden-tials. They had both been promoted in the same year,four years after hire. He had been paid $1,300 moreannually than she until the gender-equity adjustment.Under the remedy, she would be making $300 morethan he was making. In the six years since their hire, hehad made $7,800 more than she. At $300 a year, itwould take her twenty-six years merely to catch up. Hehad not been bothered when the inequity was in hisfavor, but when the tables turned in a nonstereotypicaldirection, he felt the injustice keenly.

Statistical analyses have little impact on such uncon-scious ideology. Gray notes that "[t]he courts' refusal toaccept well-constructed statistical models as evidence ofdiscrimination is not based on statistics, but on an un-willingness to accept that statistics can prove what thedecision maker does not want to believe" (1993, 154).Confronted with analyses of faculty salaries showingevidence of discrimination, often the very faculty whosestock in trade is to persuade others of the efficacy ofstatistics refuse to believe what is presented to them(Gray 1993).

We hope the information we have provided helps youbecome more proactive in your efforts to identify and, if

66

appropriate, remedy salary and promotion disparities.Attention to the fairness of the many interrelatedaspects of academic life that influence the campusreward system, including recruitment, hiring, promo-tion, tenure, counteroffers, and the enticement of faculty"stars," can help combat unconscious ideology.

Formal procedures that protect employees in generalprotect against the subtle influence of gender and racebias. Salary schedules that stipulate entry-level salariesor attach specified criteria for salary setting deterunconscious prejudice. Any standardization of the pro-cesses used in awarding initial salaries, discretionarysalary awards, research resources, promotions, andother honors can help prevent gender and race bias.

The methods we describe in this guide tend to be usedas one-time fixes for many higher education institutions.They focus attention on the problem for a short time.Although salaries are adjusted at a moment in time tocorrect some of the historical impact of unconscious ide-ology, the subtle drift toward gender and race bias con-tinues. Periodic multiple-regression salary reviews anddiagnostic analyses of rank assignments should be con-ducted, and they should be independent of the salarysetting and rank assignment processes.

We know how difficult it is to reach agreement on theassessment of bias in salaries or rank once, let alonerepeatedly at regular intervals. But a powerful deterrentto the subtle drift of gender and race bias is "the spot-light." Higher education institutions such as AmericanUniversity, the University of Wisconsin-Stout, andNorth Carolina State University have implemented aprocess of annual or other periodic review and adjust-ment. Other institutions set the time period for the nextreview when they finish the current study; theUniversity of Maine System, having just completedstudies of its seven institutions, has scheduled the nextstudy to be in three years.

Of the twelve SUNY institutions used to test themethods for this guide, two (one two-year and one four-year college) showed no substantial gender or race bias,which indicates that salary bias is not inevitable. Webelieve that it is possible for higher education institu-tions to take the steps necessary to eliminate what sys-temic gender and race bias exists in faculty salaries andto maintain equitable salaries. We congratulate thosethat have done so and hope that this manual encouragesothers to achieve gender- and race-neutral facultysalaries.

Notes1. As indicated in chapter 1, the research described in thisguidebook does not address difference in pay that is related to

7 6

Diagnosis Dynamics and Treatment Turmoil

the underpayment of disciplines where women and minoritiespredominate. Discipline is one of the control variables.Therefore, comparisons are constrained by the regressionmodeling to those within discipline.

2. Snyder, Hyer, and McLaughlin (1994) suggest a variant ofthis approach as an alternative to conducting regression analy-ses on very small subsets. Once you have examined bias at theinstitutional level, you can use the predicted salaries and com-pare the average white-male and female or minority residualswithin rank and discipline subsets. This approach could revealthe "humps" Ferree and McQuillan (1998) describe, if theresiduals are calculated using the white-male equation andnot the total-population equation.

3. Toutkoushian (1994a) notes that the across-the-boardapproach to salary adjustments is likely to be less expensivethan individual adjustments because of restrictions on lower-ing salaries in the remedy process. For example, if there arefour faculty women of whom three are underpaid by $1,000and one is overpaid by $1,000, the average underpayment is$3,000 - $1,000 /4 = $500. To give each of four faculty women$500 costs $2,000. If the actual salary discrepancy were paid toeach individual with a negative residual, the cost would be$3,000.

4. To address concerns about very low outliers, we agreed thatthose whose residuals were more than one-and-a-half stan-dard deviations below the mean would be submitted to eachinstitution for special discretionary award consideration.

5. Just prior to the SUNY-UUP salary-equity awards, somelongevity corrections had been made. As a result, the genderand race awards did not address longevity.

6. The researchers involved in two studies, VirginiaCommonwealth University and the University of Hawaii atManoa, recommended the group-award approach. In bothcases, administrators chose instead to proceed with a "flag-ging" approach.

7 7 67

APPENDIX A

Multiple Regression andGender- and Race-Equity in Salaries

By Lois Haignere

This appendix provides an introduction to theinterpretation of regression statistics for salary-equity studies. Recognizing that it will be read by

an audience with a wide range of mathematical knowl-edge, we have attempted to make it understandable tothose who are not familiar with statistical techniques.

To begin with a simple example, assume that we areinterested in finding out how some variables relate tobody weight. These variables are shoe size, hours ofexercise each week, eye color, fast-food meals con-sumed, height, and make of automobile. If we usedmultiple regression to relate these characteristics tobody-weight data, we would expect some to be morestrongly associated with body weight than others. Wewould probably find that make of automobile and eyecolor had no relationship to body weight. The amountof exercise each week might be negatively related tobody weightas exercise goes up, body weight goesdown. Height, shoe size, and fast-food meals might bepositively related to body weightas they go up, bodyweight goes up. Among these positively related vari-

ables, we would probably find that height is morestrongly related than shoe size and fast-food meals.

The particular strength of multiple regression is that itcan isolate the effect of one of these variables while con-trolling for all of the others. For example, it can controlstatistically for height, shoe size, and fast-food mealswhile examining the impact of hours of exercise eachweek. Conceptually, we can compare a group of peopleof exactly the same height, wearing the same size shoes,and eating the same number of fast-food meals eachweek, differing only in their amount of exercise.

Instead of body weight, we are interested in explain-ing variations in faculty salaries. In particular, we wantto estimate the effect of variables like gender and racewhile controlling for other important salary-relatedvariables, like years of service and discipline. Toexplain how multiple regression works, we begin byconsidering how just one variable, say, years of service,explains differences in salaries. If we plotted the yearsof service against salaries, we would probably see ascatter plot similar to figure A.1. Even a casual glance at

Figure A.1

Salary by Years of Service60

55

50'Fs

Z0 45coaias -0cr) c 40

co:

o 35t I

t30

25 + t$.

0 5

1

10

$t I

$t 1

I I I

15 20 25

Years of Service

I I

30 35

7669

Lois Haignere

this figure indicates that salary increases as years of ser-vice rise. Note, however, that the relationship is not per-fect; every increase in years of service does not result inan equal jump in salary. If the relationship were perfect,all points would fall on a straight line.

To describe this relationship statistically, we couldprovide an equation that would estimate how large adifference in salary we would expect, on average, forindividuals who differ by one year in their years of ser-vice. This is done by fitting these points with the line of"best fit" (figure A.2).

"Best fit" is a statistical criterion, indicating that theline is drawn to minimize its distance from the pointsscattered around it) In other words, the line is as closeto all points as a straight line can be. The slope of thisline indicates the predicted change in salary for eachyear of service. For example, if we draw a straight lineup from five years of service on the horizontal axis offigure A.2 until we reach the line of best fit and thendraw a line over to the vertical axis, we will find the aver-age predicted salary for faculty members with five yearsof service.

We do not have to have a graph or line of best fit infront of us to be able to predict the salary of those withfive years of service. Regression analysis provides uswith a formula representing the straight line on figureA.2. This line can be described by just two pieces ofinformation: (1) the intercept, that is, the place the linestarts on the vertical axis; and (2) the slope of the line(called the regression coefficient), which is the average

70

increase in salary for a one-unit (year) increase in lengthof service.

This formula is: predicted salary = intercept point +slope of the line x years of service. It is the same as theformula we learned for a straight line in basic algebra: Y= a + bX, where Y is the predicted salary, a is the inter-cept value, b is the slope of the line, and X is years ofservice.' Thus, for any number of years of service, wecan easily arrive at the predicted salary.

Assume, for example, that the regression formula tellsus that the starting point of the regression line (theintercept or a) is $29,000, and the slope of the regressionline is $800. We can figure out that a faculty memberwith five years of service is predicted to have a salaryof: Y = $29,000 + ($800 x 5 years of service) = $33,000.This example is a simple two-variable linear regression.Salary is the dependent variable and years of service is apredictor or independent variable.

Since we want to know about the effects of manyvariables on salary, we use multiple regression.Fortunately, the equation for multiple regression is astraightforward extension of the two-variable equa-tion. Suppose we are looking at just two predictor vari-ables, years of service and years in rank. The multiple-regression procedure might tell us, for example, thatwith the introduction of this new variable, our inter-cept has changed to $31,000, the unstandardizedregression coefficient (the slope of the line) for years ofservice has changed to $700, and the unstandardizedregression coefficient for years in rank is $800. For a

7 9

Appendix A

faculty member with five years of service, two of whichhave been in his or her current rank, the predictedsalary (Y) would be: Y = $31,000 + ($700 x 5 years of ser-vice) + ($800 x 2 years in rank) = $36,100. But what hap-pens when we try to include variables such as discipline,which is not a quantity? How can this become a part ofour calculation?

Dummy VariablesThe two independent or predictor variables we havethus far used in the example, years in rank and years ofservice, are continuous variables. That is, they take on aseries of values, equal distances apart; each additionalyear of service or year in rank is equivalent to any otheryear of service or year in rank. Such variables can beentered into regression analyses in their current form.But many of the independent variables commonly usedin studies of salary equity are not measured in equalintervals; that is, they do not have numeric value.Special steps must be taken to include them in themultiple-regression analysis.

Discipline, gender, race, and rank are called categori-cal variables; they represent categories rather thanquantities. Some categorical variables (discipline, gen-der, and race, for example) cannot be ordered; others(like rank) have an order, but the differences betweenlevels are not necessarily equal. For example, we do notknow if the value difference between the ranks ofinstructor and assistant professor is the same as thevalue difference between the ranks of associate profes-sor and full professor, or whether the rank of full pro-fessor is worth twice as much as assistant professor andfour times as much as instructor. Similarly, we have nobasis for deciding that being in the business and man-agement discipline is worth twice as much as being inthe education discipline, but only half as much as beingin the computer and information sciences discipline.Regression analysis can actually tell us these relation-ships if we transform these variables by making theminto what are called dummy variables.

Dummy coding is a way of quantifying variables thatare basically qualitative or categorical in nature. Forgroup membership variables (race, sex, rank, and thelike) you need to convert each category within the vari-able into a separate variable. Each of these new dummyvariables can have only two values: 0 or 1. For example,for the variable female, all women are coded 1, and allothers are coded 0; for the variable assistant professor,we assign the value of 1 to those who are assistant pro-fessors and the value of 0 to all others. The transforma-tion to dummy variables, therefore, involves an increasein the number of variables. Where there was originally

one categorical variable called current rank, there arenow five dummy variables, one for each rank category.Where there was originally one gender variable, thereare now twoone for male, coded 1 and 0; and one forfemale, coded 1 and 0.

Of course, saying someone is female (female = 1) isthe same as saying she is not male (male = 0); we do notneed both categories. When entering a group member-ship variable into the regression analysis, one of thedummy categories is omitted. This is because you con-vey all of the information contained in the codes of theoriginal variable with one less than the number of cate-gories. If there are five categories of rank, anyone who iscoded as zero in four categories must be in the fifth. Theselection of the particular category to be omitted fromthe regression analysis does not affect the analysis, butit is simplest to consider the omitted category to be thelogical reference. Thus for pay-equity studies it makessense, for example, to choose white males as the refer-ence group, omitting male as a gender category andwhite as a race. Similarly, it may pay to choose a well-understood rank category like associate professor as theomitted reference category, rather than lecturer, whichis a rank whose use varies across institutions.

The estimate for the omitted category is representedby the intercept. For example, if the category male isomitted for gender, the category associate professor isomitted for rank, and the category social sciences isomitted for discipline, the salary at the intercept will bethe estimate for the average salary of male associateprofessors in social sciences with zero years of serviceand zero years in rank. To calculate the average salaryfor any other group, the regression coefficient for thatgroup is added to the intercept value. (In the case of anegative regression coefficient, the sum will be less thanthe intercept, because adding a negative amount to anumber results in subtraction, thereby reducing it.)

How can the dummy variables be part of regressionequations?' Our dummy variables each have only one oftwo values: 0 or 1. These values must be multiplied by aregression coefficient, a number we derive signifyingthe effect of that dummy variable on predicted salary. Ifwe find that being female has an average effect onsalary of -$900, then -$900 is the regression coefficientfor female. In effect, being female (1) adds to the equa-tion (1 x -$900) or -$900. This coefficient has no effect onthe reference category male, since the intercept alreadyrepresents the salary for those in the default categories.

Suppose we include the dummy variables for genderand discipline and leave out the reference categories ofmale and social sciences. Say that our multiple-regression equation indicates an intercept of $33,000

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Lois Haignere

Table A.1

Predicted Salaries of Male and Female Faculty in Three Disciplines

Male in businessIntercept$33,000

Years Service(3 x $700)

Female in businessIntercept Years Service$33,000 + (3 x $700)

Female in social scienceIntercept Years Service$33,000 (3 x $700)

Male in fine artsIntercept$33,000

Years Service(3 x $700)

Years Rank(3 x $900)

Years Rank(3 x $900)

Years Rank(3 x $900)

Years Rank(3 x $900)

Business Male Predicted+ $2,500 0 = $40,300

Business Female Predicted$2,500 -$900 = $39,400

Soc. Science Female Predicted+ $2,500 + -$900 = $36,900

Fine Arts-$400 +

Male Predicted0 = $37,400

and these regression coefficients: years of service = $700;years in rank = $900; fine arts = -$400; business = $2,500;female = -$900. Using this intercept and those coeffi-cients, Table A.1 estimates the salaries of male andfemale faculty members with three years of service andthree years in rank in the disciplines of business, socialscience, and fine arts.

Remember that the categories of social science andmale are the defaults and, thus, the intercept representsthe salary for faculty members in these categories. Thisis why nothing is added or subtracted for these cate-gories in the formula. You can see by these examplesthat the parameter estimate (or unstandardized coeffi-cient) for the dummy variable female is a measure ofhow much on average it costs a faculty member to be awoman, assuming that all the other variables in theequation are held constant. Similarly, dummy variablesfor race, such as African American and Latino, can indi-cate the average effect of each race category.

Validity of Regression EquationIt is important to know how to judge the validity of dif-ferent regression equations. Returning to the body-weight example, we could run a regression equationwith variables like eye color and make of automobilethat do not strongly relate to the dependent variable. Theresult would be a fancy equation that would not tell usmuch. Multiple regression provides an estimate of howwell the set of independent or predictor variables (eyecolor or shoe size) accounts for the variation in thedependent variable (individual body weight). This mea-sure is called the adjusted R (R-square). An adjusted R

72

of 0.75 indicates that 75 percent of the variation in salaryis accounted for by the predictor variables in the equa-tion; an adjusted R of 0.55 indicates that 55 percent ofthe variation is accounted for by the variables.

Another way of conceptualizing this is in terms of thescatter of points around the "best fit" line in figure A.2.The smaller the scatter of observed points around theline represented by the regression equation,,the betterthe prediction and the closer the adjusted R is to 1. Ifthere is no association between the predictor variablesand the dependent variable (that is, the scatter is ran-dom and does not tend to form a line) the adjusted R =0. In the social sciences, an adjusted R below 0.3 is gen-erally thought to indicate little or no association. Thosein the range of 0.4 to 0.6 are considered to indicate mod-erate association. Those above 0.7 are considered toshow strong association, indicating that most of thevariations in the dependent variable have been account-ed for by the independent or predictor variables.

Interpretation of ResultsTable A.2 is an example of typical computer outputfrom a multiple-regression analysis of faculty salariesfor an institution we call Proxy College. At the top ofthat illustration, the adjusted R results are reported as0.8211. This means that 82.11 percent of the variation insalary is accounted for by the variables in the equation.The remaining 17.89 percent could be due to randomfactors, measurement error, or variables left out of theequation. An adjusted R of this magnitude is an indica-tion that the variables in the equation explain most ofthe variation in salaries.

Appendix A

Table A.2

Sample Computer Output for Proxy College:Regression Analysis of Faculty Salaries

Variable DF Sum°

ParameterEstimate

StandardError

T for HO:

Parameter=0 Prob > T

INTERCEPT 1 335 29495 994.62906029 29.654 0.0001

YR_RANK 1 2927 544.348571 42.44607444 12.824 0.0001

YR_SERV 1 4988 336.390498 48.57062401 6.926 0.0001

ASST 1 81 -5447.273440 634.67422069 -8.583 0.0001FULL 1 134 5951.380714 455.91364220 13.054 0.0001

MASTERS 1 101 -539.921096 808.87423663 4.005 0.0001BACHELORS 1 4 -1076.643425 1641.2392210 -0.656 0.5123

AGIRFARC 1 11 5032.979425 1053.0875729 4.779 0.0001ARMIN 1 9 3988.706165 1135.4294293 3.513 0.0005BUSINESS 1 9 6457.295117 1170.5822575 5.516 0.0001BIOLOGY 1 14 4456.221675 967.48669527 4.606 0.0001AREASTDI 1 13 4976.437719 1004.8530098 4.952 0.0001COMUNCTN 1 8 441.642358 1159.3391086 0.381 0.7035COMPUINF 1 10 2922.576103 1067.8918658 2.737 0.0066HIUCATIN 1 8 1422.662763 1155.0865960 1.232 0.2191HIGNERIN 1 15 2393.906709 936.39183011 2.557 0.0111HNEARTS 1 6 2380.802276 1340.5263086 1.776 0.0768FORGNLAN 1 3 3548.019256 1724.3069450 2.058 0.0405HEALTPRF 1 5 1738.377402 1395.4345988 1.246 0.2138HONIECNMY 1 5 1588.998793 1376.3579156 1.154 0.2492LAW 1 5 1356.105647 1378.8903794 0.983 0.3262LETTERS 1 5 4060.422238 1467.0322010 2.768 0.0060UBRARY 1 8 791.285924 1178.9245073 0.671 0.5026MATH 1 14 473.654141 947.47812117 0.500 0.6175PHYSICS 1 6 568.258532 1281.6642459 0.443 0.6578PSYCLOGY 1 8 1243.279501 1146.2883723 1.085 0.2790PUBSERVC 1 9 1476.943558 1106.7881700 1.334 0.1831THEOLGY 1 17 466.892901 908.79433574 0.514 0.6078

FEMALE 1 117 -1016.832795 389.18698941 -2.613 0.0694

Note: Dependent variable: salary. Dummy variable defaults: male, social sciences, Ph.D., associate professor.a. SAS output usually includes this column elsewhere with other simple statistics. We have transplanted it into this chart so that it isbeside the parameter estimate (unstandardized regression coefficient column).

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Lois Haignere

To illustrate the common appearance of multiple-regression computer output, table A.2 includes columnstitled Standard Error, T for HO, and Prob > T eventhough (you will be happy to note) these three columnscan be ignored by most faculty salary analyses. They areimportant for inferential statistics, which make infer-ences about a population based on a sample. Facultysalary studies are typically not based on samples. Mostinclude the entire population of faculty at a given insti-tution, so interpretation of inferential statistics is notneeded or meaningful. (See the discussion of "Problem5" in chapter 6.)

The left-hand column in table A.2 identifies the inde-pendent (predictor) variables. The next column, DF, indi-cates the degrees of freedom. Each variable has one degreeof freedom associated with it. The next column, Sum, is thesum of the variable for all cases in the equation.' Fordummy variables, the sum tells the number of cases in thatcategory. We see that there are 81 assistant professors and134 full professors included in the equation.

The next column is headed Parameter Estimate. Thespecific type of parameter estimate shown in this col-umn is the unstandardized regression coefficient thatwe have been describing. A single unit change in thevariable results in a change in predicted salary that isshown by the parameter estimate. As previously indi-cated, when dummy variables are used in a regressionequation, one category for each group-membershipvariable must be omitted from the equation. In tableA.2, the omitted variables are listed in the table note. Inthis case, they consist of male for gender, social sciencefor discipline, Ph.D. for educational attainment, andassociate professor for current rank. With these omittedcategories, the intercept, which is listed in the first row,would represent the salary for a male associate profes-sor in a social science discipline whose highest degree isa Ph.D. This also explains why these variables are notfound in the variable list of the first column.

We can look down this column to the regression coef-ficient (labeled Parameter Estimate in table A.2) forYr_rank, and see that it is 544.348571. This means that ifthe individual's years in rank are greater than zero, wewould multiply those years in rank by 544.348571 andadd that amount to the intercept to get a more accurateestimate of his or her salary. If the individual is not anassociate professor, but an assistant, we would add-5,447 (the unstandardized regression coefficient forassistant professor) to the individual's salary to improveour estimate. (The addition of a negative number actual-ly amounts to subtraction.) The unstandardized regres-sion coefficient for the variable female shows us that,even when controlling for all other factors in the equa-

74

tion, women at Proxy College are paid an average of$1,017 less than men. Again, this is indicated by the neg-ative unstandardized regression coefficient.

To see if you understand this output, calculate the pre-dicted salary for a full professor with a Ph.D., three yearsin rank, and ten years in service in the discipline of busi-ness. You should get a predicted salary of $46,895 if thisfaculty member is a male and $45,878 if the person is afemale (rounding to the nearest whole number).

Notes1. The line of "best fit" also creates an average residual of zero.In other words, the average difference between the actual andpredicted scores is zero.

2. Another way to describe the intercept is the value of Y(salary) when the value of X (years of service) is zero. Thus,with our current example, it is what the average faculty mem-ber is paid if he or she has no years of service.

3. We have included only two dummy variables to keep theexample simple. In an actual regression analysis of salary,other dummy variables such as current rank and highestdegree would probably also be included.

4. SAS output usually includes this column elsewhere withother simple statistics. We have transplanted it into this chartso that it is beside the parameter estimate (unstandardizedregression coefficient) column.

6 °

APPENDIX B

The Twelve SUNY Data SetsBy Lois Haignere

In selecting the twelve SUNY institutions on whichwe tested the methods explained in this guide, ourfirst criterion was attaining the broadest possible cross

section of different-sized data sets within each institu-tional type. A second consideration was the accuracy ofthe data and the ease of correcting any belatedly discov-ered data errors. The four selected two-year collegesincluded both the largest (244 full-time faculty members)and the smallest (99). The four selected four-year collegesranged in size from 421 to 117 faculty members, and thefour university centers, from 811 to 477. This variety infaculty size and institutional type has enabled us toobserve the effects of the different statistical approacheson a range of institutional types and sizes.

As indicated in chapters 1 and 2, the AAUP publishesits Annual Report on the Economic Status of theProfession in the MarchAprilissue of its bimonthly maga-zine, Academe. According to thedescriptive categories used inthese reports, the four SUNYuniversity centers are "doctor-al-level institutions," character-ized by significant doctoral-level education, granting aminimum of thirty doctoral-level degrees. Although two ofthe SUNY universities includehealth science centers, the fac-ulty at these centers were notincluded in these analyses.

Three of the four colleges are"comprehensive institutions,"characterized by diverse post-baccalaureate programs, grant-ing a minimum of thirty post-baccalaureate degrees. Thefourth college is a "general bac-calaureate institution," charac-terized by a primary emphasison undergraduate bachelor'sdegree education. The fourtwo-year colleges are classifiedas "two-year institutions with

academic rank," characterized by conferring at least 75percent of their degrees below the bachelor's-degreelevel. The SUNY two-year institutions are technical col-leges, which resemble community colleges in that thefaculty's main responsibility is teaching. Therefore,salary determinants at the two-year colleges more close-ly resemble those at community colleges than those atinstitutions with strong research missions.

Table B.1 displays the gender and race composition ofthe twelve faculty data sets. Clearly, white males are thepredominant race-gender category at every institution.As a result, and because they are presumed not to expe-rience bias, white males form the baseline comparisongroup for assessing salary equity. Testing for race andgender bias requires comparisons, and the appropriatecomparison is the white-male reference category.

Table B.1

Faculty Composition by Race and Gender at TwelveState University of New York Institutions

Universities

AlbanyBinghamtonBuffaloStony Brook

Colleges

BuffaloGeneseoOswegoPurchase

Two-Year Inst.

AlfredCantonCobleskillFarmingdale

TotalFaculty

634477811639

421233311117

17599

132244

WhiteMale Female

AfricanAmerican

Male FemaleLatino

Male FemaleAsian

Male Female

430 122 7 10 15 10 31 9323 95 10 5 11 2 29 2560 124 25 6 7 3 79 7447 97 15 5 6 5 54 10

286 95 10 6 5 4 11 4154 63 1 3 1 1 8 2211 71 6 4 4 1 12 264 41 2 1 2 0 5 2

148 23 0 0 0 0 4 072 26 0 0 0 0 1 088 34 2 2 1 1 3 1

147 75 6 3 3 3 6 1

8475

Appendix C

Salary-Equity Contract LanguageBy Donna Euben

Contract language addressing salary equity varies agreat deal from contract to contract. While onecontract may contain a detailed article establishing

a joint faculty-administration salary-equity committee,another contract may simply include a new salary sched-ule that does not explicitly mention salary equity but thatincorporates equitable salary rates. Some collective bar-gaining agreements include no salary-equity provisions,because such efforts are included in a memorandum ofunderstanding, which is a separate side agreement. Con-tract clauses covering the following areas may be designedto help achieve salary equity: the makeup of, and proce-dures for, faculty-administration salary-equity commit-tees; the amount of money available; the establishment ofminimum salary floors; and the grievance procedure.

Regardless of the final language negotiated, yoursalary-equity contract provision should clearly establishthat no professor's pay will be downgraded as a resultof a salary-equity adjustment program. For example, the1989-92 collective bargaining contract of the AAUPchapter at St. John's University stated that the informa-tion gathered for salary adjustments "shall be used sole-ly for the purpose of determining the needs for upwardsalary adjustments. In no event shall the salaries of anyfaculty members be lowered as a result of these proce-dures, nor shall the foregoing procedures be used forany purposes other than salary adjustments."

The specific contract language that you bring to thetable will depend on your union's salary-equity policy,as well as the particular circumstances in your universi-ty or college. Some or all of the following suggestionsmay apply to your situation.

Joint Faculty-Administration CommitteesIf you decide to bargain for a salary-equity study, themost important contract language is a clause that estab-lishes the faculty union's role in this process, generallythrough a joint union-administration committee. Thelanguage should specify the committee's membership,selection mechanism, goals, the scope of the commit-tee's work, the process the committee will use to reachdecisions, the timetable for the committee's work, and adispute-resolution procedure.

Often helpful in such joint committee discussions issalary data from the institution. The AAUP's annualsalary survey, published in the MarchApril issue of theAAUP's bimonthly publication, Academe, provides awealth of information on faculty salaries by institution,including wage differentials based on gender, whichmay be helpful to you in negotiations. For example, the1995-98 collective bargaining agreement of theUniversity of Cincinnati's AAUP chapter provided:

Equity Study. In order to assure that theUniversity has an equitable salary and rankstructure, the parties to the contract herebyestablish a joint committee to study these issues.The committee will be composed of four (4)individuals: two (2) selected by theAdministration and two (2) selected by theAAUP. The Committee shall be named no laterthan the beginning of Fall Quarter 1993. TheOffice of Institutional Research should becharged with the responsibility to assist in thisproject; the report from the Salary EquityCommittee details a comprehensive model forsuch a study and should be considered theguide for this study. The final report and rec-ommendations from the Committee will be sub-mitted no later than June 1,1994, to the partiesto the contract.

The United University Professions (UUP)StateUniversity of New York (SUNY) collective bargainingagreement (1985-88) provided as follows:

A joint SUNY-UUP committee consisting ofthree members appointed by the Chancellorand three members appointed by the Presidentof UUP shall be established to review perceivedsalary disparities, including, but not limited to,retention and recruitment problems and salarydisparities by title based on comparisons withinor outside the University. The Committee's firstpriority shall be to investigate, consider andreview instances where the salary of any

8 577

Donna Euben

employee with ten or more years of Universityservice is below the average salary for suchemployee's rank. Joint recommendations to cor-rect demonstrated salary disparities shall bemade by the committee to the Director of theGovernor's Office of Employee Relations.

MoneyAnother stepeither before or after the completion of asalary-equity studyis to negotiate contract languagethat sets aside a specific amount of money and delin-eates the controlling formula. The LTUP-SUNY agree-ment established a "disparity fund":

The State agrees to make every effort to addressdemonstrated salary disparities which mayexist within the unit. To this end, the State shallapportion an amount of One Million($1,000,000) dollars in the second year of thisAgreement and Two Million ($2,000,000) dollarsin the third year of this Agreement . . . to beused to correct demonstrated salary disparities.. .. The unexpended portion of any year'sapportionment shall be carried over into thesucceeding year and added to the apportion-ment for the succeeding year. These funds maynot be used for across-the-board increases on aUniversity-wide basis.

The salary-equity provision in the 1993-96 collectivebargaining agreement of the Eastern MichiganUniversity's AAUP chapter established a percentageamount:

Salary Differential Pool. EMU-AAUP and theUniversity recognize and are concerned that onoccasion salary differentials may be createdamong faculty in departments owing to externalmarket conditions. In order to address theseconcerns, an amount equal to seven-tenths(7/10) of one percent (0.7 percent) of Facultybase salaries, calculated as of February 1, 1994,shall be set aside and shall be distributedamong faculty immediately following the1994-95 salary adjustment . . . in accordancewith the formula developed by the Universityand EMU-AAUP. Additionally, an amountequal to five tenths of one percent (0.5 percent)of Faculty base salaries, calculated as ofFebruary 1, 1995, shall be set aside and shall bedistributed among faculty immediately follow-ing the 1995-96 salary adjustment .. . in accor-

78

dance with the formula developed by theAssociation and the University.

Minimum-Salary ScalesCollective bargaining language that establishesminimum-salary scales often helps to mitigate salarydisparities by limiting the salary gap (at least among thelowest paid faculty in each rank) that often emergesbetween male and female faculty. For example, the1995-97 collective bargaining contract of the ClevelandState University's AAUP chapter included the followingprovision:

Minimum salary. Effective retroactively toSeptember 19, 1994, the following minimumsalaries will be implemented: (1) Instructor-$28,000, (2) Assistant Professor-$34,000, (3)Associate Professor-$42,000, (4) Professor-$52,000.

Other helpful collective bargaining language ensuresthat existing faculty are brought up to these minimums.For example, the 1996-98 contract of Kent StateUniversity's AAUP chapter provided:

Salaries and Promotion: Academic Years 1996-97through 1997-98: . . . Salary Floors-BeginningAcademic Year 1996-97. As a means of assuringappropriate entry-level pay at both academicranks, the Employer will establish salary mini-ma on a University-wide basis. The minimumannual contract salaries for Faculty members atthe professional academic ranks of Instructorand Assistant Professor .. . shall be as follows:Assistant Professor (with terminal degree)$37,500 (nine months), $45,833 (twelve months).Instructor (nonterminal degree) $31,000 (ninemonths), $37,888 (twelve months). The salariesof all current Faculty will be brought up tothese minima. No one's salary or rank will bereduced.

Similarly, the recent UUP -SUNY collective bargainingagreement (1995-99) provided for such salary mini-mums and that not only a new hire but lamn incumbentpromoted on or after the effective dates ... shall receivenot less than the minimum basic annual salary for therank or grade to which that incumbent has beenpromoted."

In addition, such minimums can be set for new facul-ty positions, which provide the union with the opportu-nity to ensure that equity is established at the outset.

86

Appendix C

The contract may spell out provisions for obtainingunion agreement with the creation of new positions andthe assignment of these positions to salary ranges.

Grievance ProceduresTo the extent the law allows, salary disparities based onsex, race, or national origin, and so on should be subjectto the grievance and arbitration procedures in a unioncontract. While it is difficult to recommend languagethat would be adaptable to all contracts becausegrievance procedures vary, the following points applyin many situations.

Any claims that arise under a fair-employment clausethat prohibits discrimination on the basis of sex, forexample, should be grievable and arbitrable, and shouldbe broad enough to include dealing with salaryinequities. In addition, the grievant should not be pre-cluded from seeking other available external remedies.The current law is unsettled in this area, and it is impor-tant to confer with a lawyer who practices in your juris-diction to determine any legal restrictions regarding theinterplay between your contract and antidiscriminationlaws.

A contract provision should require the employer tofurnish payroll and other information, including after-salary adjustments and the source or type of adjust-ment, to the union in order to bargain or to administerexisting contracts without barring disclosure of theinformation to the membership. (Decisions of theNational Labor Relations Board entitle private-sectorunions to this information. In the public sector, theinformation is available through bargaining laws and"freedom of information" laws.) For example, the1989-92 collective bargaining agreement of the St.John's University AAUP chapter provided: "TheAdministration shall provide the AAUP-FA with a com-plete list of all salaries of continuing faculty members inthe affected discipline after the adjustments have beenmade, identifying the adjustments made."

In the end, the ultimate language to which you agreeis specific to your local or chapter and the higher educa-tion institution. The above suggestions are provided tofoster discussion about the most effective ways for yourfaculty organization to address salary-equity issues incollective bargaining.

8779

Appendix D

U.S. Laws on Gender-Based Wage DiscriminationBy Donna Euben

The purpose of this guidebook is to encouragefaculty and administration to work together indeveloping and implementing salary-equity

studies and recommendations. Nevertheless, salary-equity studies are sometimes undertaken for, or usedin, litigation in which professors challenge salaries setby administrations as discriminatory. The applicationof federal laws to salary equity in the academy canraise a myriad of complex legal issues. This appendixbriefly reviews the federal laws that address gender-based salary inequity on higher education campuses.There are four legal bases for challenging such dispar-ities under federal law in higher education: the EqualPay Act, Title VII of the Civil Rights Act, Title IX ofthe Education Amendments, and Executive Order11246.'

Equal Pay ActThe Equal Pay Act of 1963 (EPA), which is part of theFair Labor Standards Act (FLSA), 29 U.S.C. Sec. 206(d),provides:

[N]o employer [who is covered by the FLSA]shall discriminate . . . between employees on thebasis of sex by paying wages to employees insuch establishment a rate less than the rate atwhich he pays wages to employees of the oppo-site sex in such establishment for equal work onjobs the performance of which requires equalskill, effort, and responsibility, and which areperformed under similar working conditions.

However, the EPA allows salary differences whensuch differences are based on: (a) a seniority system; (b)a merit system; (c) a system that measures earnings byquantity or quality of production; or (d) a differentialbased on any other factor other than sex.

Congress passed the law to fight the "ancient but out-moded belief that a man, because of his role in society,should be paid more than a woman" and to ensure that"'equal work will be rewarded by equal wages"'(Corning Glass Workers v. Brennan, 417 U.S. 188 [1974]).In EPA cases, the issues are whether the jobs in whichan alleged pay disparity exist are "substantially simi-

lar," and whether any of the four exceptions mentionedabove apply. The EPA is enforced by the EqualEmployment Opportunity Commission (EEOC). (See D.Green, "Application of the Equal Pay Act to HigherEducation," 8 Journal of College and University Law 203[1981-82].)

Title VII of Civil Rights ActTitle VII of the Civil Rights Act, 42 U.S.C. Sec. 2000e etseq., prohibits discrimination based on race, color, reli-gion, sex, or national origin in employment, includinghiring, promotion, and dismissal. It provides, in rele-vant part:

It shall be an unlawful employment practicefor an employer(1) to fail or refuse to hire or to discharge anyindividual, or otherwise to discriminate againstany individual with respect to his compensa-tion, terms, conditions, or privileges of employ-ment, because of such individual's race, color,religion, sex, or national origin; or(2) to limit, segregate, or classify his employeesor applicants for employment in any way whichwould deprive or tend to deprive any individu-al of employment opportunities or otherwiseadversely affect his status as an employee,because of such individual's race, color, reli-gion, sex, or national origin.

Wage discrimination based on gender constitutessex discrimination under Title VII. In 1972 Congressamended the law to apply to all public and privateeducational institutions, including colleges and uni-versities. Generally, Title VII cases, unlike those aris-ing under the EPA, require proof of intent: "UnderTitle VII, in all but a few cases, the burden of proofremains with the plaintiff at all times to show discrim-inatory intent. In contrast, 'the Equal Pay Act creates atype of strict liability in that no intent to discriminateneeds to be shown"' (Fallon v. Illinois, 882 F.2d 1206,1213 [7th Cir. 1989]). Title VII complaints are filedwith the EEOC or the state human rights commissioncounterpart.

88

81

Donna Euben

Title IXTitle IX of the Education Amendments of 1972, 20 U.S.C.Sec. 1681 et seq., prohibits sex discrimination, includingin employment, in all education programs or activitiesreceiving or benefiting from federal financial assistance.(See North Haven Board of Education v. Bell, 456 U.S. 512[1982].) In so doing, it also offers protections to womenwho work at educational institutions that receive feder-al funds. Title IX is administered by the Office for CivilRights of the Department of Education. (See AAUWLegal Advocacy Fund, A License for Bias: SexDiscrimination, Schools, and Title IX [2000].)

Executive OrdersExecutive Order 11246, as amended by Executive Order11375, prohibits discrimination "because of race, color,religion, sex, or national origin," and mandates affirma-tive action for minorities and women. The order appliesto federal government contractors and subcontractors,including colleges and universities. Such contractoragreements must include an equal opportunity clause,and contractors must file compliance reports with thefederal contracting agency. Some state and local govern-ment contractors are exempt from coverage. However,"educational institutions and medical facilities" areexcluded from that exemption. The executive order isadministered by the Office of Federal ContractCompliance Programs of the Department of Labor. (SeeAnnotation, "Right to Maintain Private EmploymentDiscrimination Action Under Executive Order 11246, AsAmended, Prohibiting Employment Discrimination byGovernment Contractors and Subcontractors," 31American Law Reports Federal 108 [2000].)

Note1. For a more thorough examination of the legal issuesinvolved in salary-equity litigation in higher education, seeEuben 2001.

82 89

APPENDIX E

Activist Strategies When All Else FailsBy Maita Levine

If you find that you can not gain the cooperation ofthe administration in designing the study in a validway or addressing any salary inequities that may be

found, you may find the list below helpful.

Invite all faculty members, especially women, to ameeting to discuss the study.

Use campus grievance procedures.Request meetings with individual members of the

administration and the board of trustees to discuss solu-tions to the problem.

Bring the issues to the bargaining table if you are ona campus engaged in collective bargaining.

Obtain the names and addresses of alumni from theuniversity development office and mail copies of yourreport or grievance to them.

File a complaint and ask for an investigation byyour regional office of the U.S. Department of Labor,Office of Contract Compliance.

Publicize the results of the study as widely as possi-ble, both on campus and in the community.

These activities assume an increasingly adversarialrelationship. Since studying and correcting salaryinequities involves reordering existing priorities, someof the more extreme strategies listed may be required.

90 83

APPENDIX F

Categorical ModelingBy Lois Haignere and Bonnie Eisenberg

Selecting an appropriate statistical approach isimportant. We chose to use as our categorical mod-eling method the most generalized logistic regres-

sion model, based on maximum likelihood tables, asopposed to (a) a logistic regression for an ordinalresponse variable, which satisfies the assumption ofproportional odds; (b) a logistic regression for adjacentlevels of an ordinal response variable; or (c) a discrimi-nant analysis.

The logistic regression for ordinal response variables,which satisfies the assumption of proportional odds,was not used because in ten of our twelve data sets, thelevels of the response variable (current rank) were notparallel with regard to predictor variable effects; that is,proportional odds could not be assumed. That wouldmean, for instance, that having previous experience or aPh.D. has the same predictive value for full professorsas it does for assistant professors. We could have usedthe logistic regression if we had included interactionterms, but that would have produced too many predic-tor variables in the model. To discover if all currentranks at your school are affected in the same way by thepredictor variables, you can perform a score test for theproportional odds assumption.

A logistic regression for adjacent levels of an ordinalresponse variable did not work with our data, since thestatistical software that we used allowed only for theweighted least squares method of estimation with thistype of regression. This form of estimation is more sen-sitive to very small data pools than the maximum likeli-hood tables method. Even a faculty of more than eighthundred, when broken down by current rank and thenfurther subdivided according to each of the predictorvariables, produced very small data pools. So we chosethe method least sensitive to small numbers.

When used for studying potential gender or race bias,discriminant analysis produces results that are more dif-ficult to interpret than does the method chosen. Ratherthan generating an odds ratio for women and men foreach pair of adjacent ranks, discriminant analysisrequires two separate analyses to produce interpretableresults, one for men and one for women. These analysesreport the percentage found above, at, and below thepredicted ranks. After these analyses are done, you

must still make the comparison of these percentages formen and women. Thus, the results are not easily inter-preted, requiring much manipulation before any conclu-sions can be made. In addition, discriminant analysisdoes not work with categorical predictor variables suchas gender or race, although it can be used if these vari-ables are translated into dummy variables.

The software that we used, SAS CATMOD, led to twocomplexities worth noting. First, each rank step requireda separate model to produce results that were easilyinterpreted. Since the last level of the dependent orresponse variable was the one to which all others arecompared, we needed to run a separate analysis for eachpair of adjacent ranks. The first model would compareall ranks to assistant professors in order to analyze thepromotional step from instructor to assistant professor;the second model would compare all ranks to associateprofessors to analyze the step from assistant to associateprofessor, and so on. Although there was an SAS optionto analyze adjacent ranks in one model, this option usedthe weighted least squares method of estimation, whichwill not work on the very small pools of data found incurrent rank analyses.

The second complexity worth noting was that theresults were in the form of the natural log of the oddsratios, not the odds ratios directly. Therefore, we had toadd programming to create the inverse natural log ofthe estimate produced for each predictor variable beforethe odds ratios could be easily interpreted.

DataTo analyze gender bias in current rank, you must haveenough men and women in all of the rank levels. If youhave ranks that lack either men or women (zero cells),then you cannot use categorical modeling to investigategender bias for these ranks.

To identify the zero cells in your data, produce a fre-quency table like table 4.1 that shows men, women,whites, and minorities in each current rank. If you havefaculty members in each category (no zero cells), thenyou can perform categorical modeling that will provideyou with information about bias for every promotionalstep. If some current ranks lack women or minorities, orwhite males for that matter, then you need to determine

9185

Lois Haignere and Bonnie Eisenberg

whether your zero cells are critical ones that precludeusing categorical modeling.

If you are analyzing both gender and race bias, thetwo must be examined separately for zero cells. As table4.1 shows, it is possible to have critical zero cells forminorities that block race analyses but still have enoughwomen to allow gender analyses.

The distribution of women faculty in table 4.1 alsoillustrates that zero cells will eliminate only some of thepromotional steps from a study. The absence of femalelecturers stops the model from computing gender biasfrom lecturer to instructor. But there are women in theinstructor, assistant, associate, and full professor currentranks, so three pairwise comparisons are possible: (1)instructor to assistant professor; (2) assistant to associateprofessor; and (3) associate to full professor.

If there are zero cells, but not in every pairwise com-parison, you will need to decide whether categoricalmodeling will provide enough insight to be worthwhile.For example, if the only step categorical modeling canassess is from instructor to assistant professor, you maydecide that this information is not valuable enough towarrant running a categorical model.

Overall Model StatisticIt is valuable to know whether the predictor variableschosen for your categorical model are any good at pre-dicting the response variable (the dependent variable).In a current rank analysis, this translates into: do thecontrol or predictor variables truly influence currentrank at your institution? If the control variables do nothave substantial influence on rank assignments at yourschool, then any bias suggested by the findings can beminimized by the argument that the logistic regressionmodel cannot accurately predict rank with the variableinformation available to it. The overall model statisticR2L (R-square sub-L) provides an indication of how wellthe predictor variables are predicting rank, so that youcan have some measure of confidence in your results.

A categorical model analysis of current rank withoutany predictor variables shows the total amount of vari-ability found in rank. This measure, called Do (D-Naught), is the last iteration (or final estimate) of the -2log likelihood found in the maximum likelihood analy-sis table. The amount of variability remaining after thepredictor variables are included in the model is calledthe Dm (D-M, which stands for model). Dm is the last iter-ation of the -2 log likelihood produced for the modelthat includes the predictors. Gm is simply the differencebetween Do and Dm, and represents the amount of vari-ability accounted for by the predictor variables. Finally,the R L (the proportion of variability accounted for by

86

the predictor variables) is calculated by dividing Do (thetotal amount of variability) by G, (the variabilityaccounted for by the predictor variables).

For categorical models, R2L values in the middle rangeindicate the most reliable results. A value for R2L of 0.8 isquestionable because it is too close to perfect. At theother extreme, R2L values below 0.2 indicate that thevariance accounted for is very little.

92

APPENDIX G

Redundancy ProblemsBy Lois Haignere and Bonnie Eisenberg

Statistical modeling tries to determine mathemati-cally how much of the dependent variable (currentrank or salary) differences are attributable to each

predictor or independent variable. When two predictorvariables overlap or measure the same underlyingdimension, the results may be unreliable because theprocedure cannot reliably determine which of the twopredictor variables should get the credit for explainingcertain current rank or salary differences. This problemis called redundancy or multicollinearity.

Redundancy is relative. There may be total redundan-cy, as when the same information is labeled differently;age and time since birth date would be completelyredundant. Accordingly, one of the variables has to bedropped. There may be partial redundancy, as with thetwo variables time since degree at hire and experienceprior to hire. If we use both of these variables in analy-ses, we test carefully to see if the redundancy betweenthem could make the categorical modeling results unre-liable. The redundancy between these two variables wasnot a problem at any of the twelve schools studied, duein part to the fact that some people acquire previousexperience before they receive their highest degree, andsome people do not get their degrees until after they arehired.

There is, however, a source of redundancy that wefrequently find has to be addressed. Recall that to con-trol for curvilinearity a quadratic term variable is usedfor each time variable in the analysis. To do this yousquare the variable. Not surprisingly, there is redundan-cy between each variable and its squared term, betweentime at the institution and (time at the institution)2, forexample. Initially, we tried dealing with this problem bydropping one of the two redundant variables. It isaccepted practice to drop the quadratic term if it is notstatistically significant. However, to determine whetheror not the quadratic is significant or, alternatively,which variable is less important and, therefore, shouldbe the one dropped, requires running the analysis twice,once to determine relative importance so as to decidewhich variable to drop and a second time to get theresults.

We find it easier to just "center" these variables.Centering a variable is simple, and the redundancy is

sufficiently reduced so that dropping a time variable orits quadratic term is no longer necessary. Just subtractthe mean for that variable from each of the measures ofthat variable. For example, if the mean or average num-ber of years a person has been at the institution is 5.4,then 5.4 is subtracted from each faculty member's yearsat the institution. The effect is that those with fewer thanthe average number of years at the institution (for exam-ple, 4) will have a negative score (4 5.4 = -1.4) andthose with more than the average (say, 7 years) willhave a positive score (7 5.4 = 1.6). The mean for thiscentered variable is zero (if there are no roundingerrors). The quadratic or squared term is recalculatedbased on the newly centered variable.

At the twelve SUNY campuses we studied, centeringeliminated all but one redundancy problem betweentime-related variables and their quadratic terms.

93 87

APPENDIX H

Promotion and Salary Inequities BetweenMen and Women FacultyBy Robert Johnson and Dorothy Kovacevich

For nearly a century now, studies have documenteddisparities in salary and rank between the menand women who teach in our nation's colleges and

universities. Laws forbidding discrimination in salaryor conditions of employment date back to Title VII(1972) of the Civil Rights Act of 1964 and the Equal PayAct of 1963, yet the effects of discriminatory practicescontinue to trouble most institutions of higher learningin the United States. In 1990 the American Associationof University Professors' Committee on Women andMinorities reported that most campuses were far fromachieving pay equity, especially for women facultymembers with many years of service. At the end of the1990s, institutional discrimination on the basis of sexremained a primary source of salary inequity forwomen in the workforce. Evidence shows that womenare hired and promoted less often and at slower ratesthan men (Johnson and Herring 1989). The combinedeffects of the market's devaluation of sex-integratedoccupations and institutional discrimination by sex areoften compounded when differences between academicdisciplines are used to measure legitimate (nondiscrimi-natory) market factors. This problem is widely recog-nized by researchers who attempt to model salaryinequities by sex (Be llas 1994).

Academic Rank As a Measure of ProductivityOne attempt to resolve the problem of measuring pro-ductivity uses academic rank as an indicator of totalproductivity, on the assumption that people who attainhigher ranks are more productive in research, teaching,and service than those who do not. Rank, it is argued,represents factorsthe quality of a professor's research,teaching, and servicethat go unmeasured in othermodels of salary inequity. The idea is that once youintroduce rank and the sex difference in salary disap-pears, then there is no inequity. This notion has obviousflaws. Teaching, research, and service are not rewardedequally across ranks, nor across colleges or campuses.Some campuses emphasize their teaching mission overresearch. Others place equal stress on teaching andresearch, while yet others focus primarily on research.

Few campuses or colleges emphasize service to thesame degree as research or teaching. Rewards for teach-ing, research, and service can also vary across ranks. Atthe assistant professor level, for example, research pro-ductivity often carries more weight than teaching or ser-vice. On the other hand, teaching may become moreimportant at higher ranks at the same institution.

A related problem is that rank is a minimum thresh-old measure of productivity, not a continuous measure.It cannot account for differences in levels of productivi-ty that might distinguish the faculty member who meetsthe minimum criteria for promotion from the professorwho far exceeds that performance threshold. Moreover,rank cannot account for increasing expectations ofscholarly performance as the thresholds change for eachnew cohort of faculty. And rank most certainly cannotaccount for the variations in productivity that occurafter promotion to full professorship. For a further dis-cussion of the use (or misuse) of rank as a measure ofproductivity in regression models that predict salaries,see chapter 4.

Academic Rank As a Reflection of StatusUsing rank to judge individual productivity has obvi-ous flawsyet promotion, rank, and tenure remainimportant predictors of salary. If they do not measureproductivity, what accounts for their effects on salary?The simple answers are often overlooked. Promotion isa status transition, and rank and tenure representachieved status. Status itself, regardless of differences inproductivity, is something valued and rewarded in oursociety. We confer status on people we value highly (orwho have attributes we esteem), and we withhold statusfrom individuals we value less highly (or who haveattributes we do not esteem). Thinking about promo-tion and rank in terms of status is more suitable thanconceiving of rank as a measure of productivity. In asociety that values men over women, the status of rankwill be conferred more often on men than women, andwithheld more often from women than men. Such sexbias is a strong argument against using a status attain-ment variable as a measure of productivity. Doing so

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Robert Johnson and Dorothy Kovacevich

becomes particularly troublesome when the evaluatorsof women seeking to attain status are men, especially ifthese men rely on traditional sex-biased values in theirevaluations.

Conceptual and Statistical ModelsSome studies of salary inequity, assuming that the pro-motion process is probably not free of bias, haveattempted to quantify the level of discrimination in theprocess. A study by Behling et al. (1994) applied amultinomial-ordered probit model to rank, which pre-dicts the probability of a given faculty member being ina given rank. Using the model as described by Maddala(1992), the study concluded that the variable of ranktherefore contained significant sex bias.

Other studies (Raymond, Sesnowitz, and Williams1990) have attempted to estimate the conditional probabil-ities of attaining a given rank at a given time, makingadjustments for those who do not meet minimum require-ments (faculty who have fewer than five years in rank, forexample). The adjustments simply restrict the sample toindividuals who have met the minimum criteria.

Unfortunately, neither approach considers the timingof the promotion or allows for "early promotion," some-thing believed to be more common among male facultymembers than among females. An alternative to bothapproaches, which does adjust for the timing of the pro-motion, is the proportional hazard linear regressionmodel. The "Data" and "Findings" sections of thisappendix describe how the model was used to analyzepromotion patterns at Kent State University. Beforetouching on the Kent State study, however, it is neces-sary to explain the hazard rate, which is the dependentvariable in the model. The hazard rate can be thought ofsimply as the likelihood of an event happening at anygiven time. For example, how likely is it that, after tenyears, a female faculty member will be promoted to thenext rank? That likelihood is the hazard rate.

The hazard rate is usually examined in the context ofdescriptive tables known as life or survival tables. Thehazard rate is depicted by the expression h(t), which isthe risk of an event (the hazard) occurring at time t, orthe probability of an event occurring at time t in an at-risk population. The hazard rate is formally defined bythe following equation, where G is a number of individ-uals from the population j at any given time, t is thetime, At is the change in time, (t + At) is a time later thant, and to is the time at which all members of j were atrisk (when G=j) (Tuma and Hannan 1984).

hj(t I t 0)a. lim G j(t I t0)-G j(t +At I to)

At 10 Gj(t I t0)At

90

The equation reads "the hazard rate in a population jat time t, given to , is defined as the limit as the changein t goes to zero of the ratio of (those in G at t, given to ,minus those in G at t plus the change in t, given to) to(those in G at t multiplied by the change in t)." If we letAt (the change in time) get smaller and smaller and takethe limit of the function above, we have a formula for thehazard rate. This hazard function gives the instantaneousprobability of an event occurring at a specific time t.

Consider, for example, the proportion of faculty mem-bers who have not been promoted by time t, but whowill be promoted between t and (t + At). This proportionis the number in the group G at t who are promotedbetween t and (t + At), divided by the number of facultymembers eligible for promotion at time t. In the modelsexamined in this chapter, the event used for the hazardrate is promotion in rank. It will be calculated separatelyfor men and women to compare the probability of pro-motion over the course of a twenty-year career. The haz-ard rate is a useful indicator not only of the probabilityof promotion, but also of the timing of promotion. Foreven though men and women may have the same prob-ability of occupying each rank, they may be promoted atdifferent times in their careers.

When 50 percent of a group under study has experi-enced an event, the median survival year has beenreached. It is based on another useful indicator of sur-vival analysis, the cumulative proportion surviving(known as the survival function) at any given time. Forthe purposes of this chapter, the surviving proportion ismade up of faculty members who were not promoted.The survival function depends on the hazard rate, andcan be roughly thought of as its inverse function,although neither the survival function nor the hazardrate is ever negative. That is, as a hazard rate increaseswith time, the survival function exhibits a faster decline,although it will not increase as the hazard rate decreas-es. The survival function remains constant if the hazardrate is zero.

Among faculty members, there are several normativeexpectations regarding the survival function and hazardrates for promotion to associate and full professor.Promotion to associate professor is expected to occur atthe end of the tenure process, which usually takes placefive or six years after service to the university begins.Some faculty members receive credit for earlier careeractivity (postdoctoral studies or tenure-track service toanother university, for example), while others may bepromoted before five years for extraordinary scholarlyperformance. Similarly, when scholarly performance islimited, tenure may occur, but promotion may bedelayed for several years. Nonetheless, based on the

9J

Appendix H

principle of "up or out," most faculty members are pro-moted to associate professor at the time they receivetenure. Two patterns in the hazard rate for promotion toassociate professor are therefore expected: (1) peak haz-ard rates should occur five or six years into college oruniversity service, and (2) most promotions shouldoccur earlier rather than later over the course of atwenty-year career.

Promotion to full professor is also a normative expe-rience, which often follows a five-year period spent asan associate professor, a period commonly referred toas "time in rank." Promotions to full professorships donot, however, occur at a substantial rate until afterabout ten years of service, including an initial five-yearperiod, promotion to an associate professorship, andfive additional years at the rank of associate professor.

Moreover, it is not expected that all faculty memberswill attain the rank of full professor. Even over thecourse of twenty years of service to the university,many faculty members will not perform enough schol-arly activity to merit such a promotion. Two additionalpatterns are therefore expected: (1) peak hazard rates ofpromotion to full professor should begin after a mini-mum of ten years of service, and (2) there should be amuch smaller cumulative proportion of promotions tofull professorships compared with promotions to associ-ate professorships.

Hazard rates can also be specified as the dependentvariable to be estimated in general linear models of pro-portional hazards. The regression estimates obtained inthe "Data" section of this chapter are defined by the Cox(1972) proportional hazards linear regression model.Independent variables are used to predict the hazardrates. The model is represented in the equation:

h(t)=e a+Ebixi

In the data described in the following section, regres-sions of the hazard rate for promotion to associate pro-fessor are performed among all faculty who were hiredat the assistant professor rank. Regressions of the pro-motion rate for promotion to the full professor rank areperformed among all faculty members who were hiredat the assistant professor rank and later promoted tothe rank of associate professor. In each model, one vari-able is sex. If the estimate for sex is negative and signif-icant, it will mean that females are less likely than mento be promoted at any given time.

DataThe Office of the Associate Vice President for Academicand Student Affairs at Kent State University provided

the data in this section to the Kent State Universitychapter of the American Association of UniversityProfessors under the provisions of the faculty collectivebargaining agreement. The database contains informa-tion on each faculty member in the collective bargainingunit for the Kent campus and for seven regional cam-puses of Kent State University. Full-time administrators,including those who hold faculty rank (for example,department heads), are excluded from the analysis,which is based on 833 full-time, tenure-track facultywhose main responsibilities are teaching and research.There are 636 faculty members on the Kent campus (449men and 187 women) and 197 faculty members on theseven regional campuses (130 men and 67 women).With regard to rank, there are 18 instructors (6 men and12 women), 326 assistant professors (181 men and 145women), 287 associate professors (212 men and 75women), and 202 full professors (180 men and 22women).

The information on each faculty member provided bythe administration included date of birth, sex, race,salary, rank, years in rank, year hired, department, thecalendar years of promotion to each rank, year tenured,year of highest degree, and highest degree. These arethe variables used in the analyses described above todetermine the existence and magnitude of sex inequities.

FindingsTable H.1 shows the hazard rates and cumulative pro-portion of female and male faculty members not pro-moted to associate professor in each of the twenty yearsfollowing receipt of the highest degree.

The analysis was conducted only for faculty membershired at the assistant professor or instructor level.Faculty members hired at the associate or full professorlevel were excluded, because they were promoted else-where or negotiated a rank at time of hire and weretherefore not fully subject to Kent State's promotionmechanism. The median survival time among the 464men eligible for promotion to associate professor was9.55 years, while the median survival time among the229 women eligible for the same promotion was 16.93years. The 7.38-year gap between men and women intime spent in a lower rank means that the women in thesample had a lower probability of promotion in each ofthe ten years after attainment of the highest degree. Ontop of that, the men continued to get promoted to asso-ciate professor at high rates even after the normativefive- to six-year probationary period, while the rate ofpromotion among the women dropped off drasticallyafter the sixth year. In other words, the men continuedto receive promotions even when they failed to follow

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Robert Johnson and Dorothy Kovacevich

Table H.1

Hazard Rate and Cumulative ProportionNot Promoted to Associate Professor, by

Sex and Year Since Highest Degree

Year SinceHighest Degree

Hazard Rate forPromotion

Female Male

CumulativeProportionSurviving°

Female Male

1 .01 .01 .99 .992 .00 .03 .98 .968 .02 .04 .97 .924 .02 .06 .95 .875 .09 .10 .87 .796 .08 .14 .80 .687 .06 .10 .75 .628 .03 .15 .73 .539 .05 .12 .69 .47

10 .10 .09 .62 .4311 .02 .12 62 .3812 .05 .10 .58 .3413 .02 .04 .57 .3314 .08 .03 .52 .3215 .03 .05 .51 .3016 .03 .03 .50 .2917 .04 .06 .48 .2818 .00 .04 .48 .2719 .00 .04 .48 .2620 .06 .02 .46 .25

a. The cumulative proportion surviving is the proportion offaculty members who have not been promoted in each yearsince receiving their highest degree.

the normative pattern for time spent on probation,whereas the women seemed marked if they were notpromoted "on time." The repercussion of not being pro-moted is important for salary, because an associate pro-fessor earns on average $10,615 more than an assistantprofessor.

The same discrepant patterns of promotion betweenmen and women showed up for faculty members eligi-ble for promotion to full professor (see table H.2). Butfor both the men and the women in this group, themedian survival time for promotion was over twentyyears, suggesting that fewer than half of all academicscan expect to receive full professorships in their firsttwenty years of service. Nonetheless, among the actualproportion surviving in the Kent State sample aftermore than twenty years, men still fared better thanwomen: only 54 percent of the men remained in thelower ranks, while 74 percent of the women did. This is

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Table H.2

Hazard Rate and Cumulative ProportionNot Promoted to Full Professor, by Sex

and Year Since Highest Degree

Year SinceHighest Degree

Hazard Rate forPromotion

Female Male

CumulativeProportionSurviving°

Female Male

8 .01 .01 .99 .987 .00 .01 .99 .978 .00 .02 .99 .95

.00 .03 .99 .9310 .01 .03 .98 .9011 .02 .06 .96 .8512 .03 .04 .93 .8218 .01 .02 .92 .8014 .01 .05 .91 .7615 .02 .05 .89 .7216 .02 .03 .88 .6917 .04 .03 .85 .6718 .04 .02 .81 .6619 .03 .04 .79 .6420 .03 .02 .77 .62

a. The cumulative proportion surviving is the proportion offaculty members who have not been promoted in each yearsince receiving their highest degree.

important for salary, because a full professor earns onaverage $26,224 more than an assistant professor and$15,609 more than an associate professor.

The Cox (1972) regression model predicting probabili-ty of promotion to associate and full professor at eachtime interval since receiving the highest degree includesthe variables sex, whether or not the faculty memberhas earned a Ph.D. degree (as opposed to anotherdegree such as a master's), whether or not the facultymember is on the Kent campus, and the number ofyears of service to Kent State University. The results asreported showed that the coefficient for sex in bothequations was negative and significant at p<.05 (one-tailed test). This meant that women were less likelyoverall than men to be promoted to either the rank ofassociate or full professor. The exponential value for thecoefficients are the relative odds ratio for promotion ofwomen compared to men. For the associate professorlevel, this value is .70, indicating that women are only70 percent as likely as men to be promoted in any givenyear. For the full professor level, the value of the expo-nent or the coefficient is .66, indicating that women are

9 7

Appendix H

only 66 percent as likely to be promoted in any givenyear since their highest degree.

ConclusionThe Kent State analysis revealed that female facultymembers at the university were promoted later and at alower rate than their similarly situated male colleagues.Discrimination against female faculty members proba-bly accounted for most of these promotion inequities.The prevalence of discrimination can be detected infailure to promote or to promote on time, and its mostserious consequence is individual salary inequities inthe $10,000 range.

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APPENDIX I

Locating OutliersBy Lois Haignere and Yangjing Lin

The practice of dropping outliers is predicated onthe assumption that they distort the real picture.As indicated in chapter 6, sometimes outliers get

dropped in salary-equity studies when they do not dis-tort the picture but simply are the highest and lowestcases in the picture.

There are a number of diagnostic measures that canbe used to detect outliers, but three are of particularinterest for salary equity studies. They are:

the studentized residuals, which locate dependentvariable deviant cases;

the hat matrix diagonal element, which locates pre-dictor (or independent) variable deviant cases; and

Cook's Distance (CD), which locates cases that aredeviant relative to both dependent and independentvariables and substantially affect the parameter estimatesor distort the results.

The following is a brief discussion of each of thesethree measures.'

Studentized ResidualThe studentized residual is a measure that identifies anoutlier in the dependent variable. It is created asfollows:

A regression model is run without one individual'sinformation.

The results of this regression are used to create apredicted salary for the individual who was left out ofthe regression.

The difference between the actual salary and thepredicted salary (the salary residual) for that individualis calculated.

This residual is then standardized by dividing it byits standard error. The resulting value is the studentizedresidual for that individual.

This measure determines observations that haveunusually high or low dependent variable data (salary).The suggested cutoff value to identify outliers rangesfrom the absolute value (negative or positive) of two tothe absolute value of three (Stevens 1984). Larson (1994)

recommends using a table based on the number ofmodel parameters and the sample size (incorporated inan SAS macro program) to determine this cutoff value.Based on this macro program, the cutoff values for ourtwelve SUNY schools for the studentized residual weregenerally greater than three, and relatively few of thefaculty in these analyses exceeded the cutoff value, thatis, were found to be outliers. If you observe individualcases that are outliers based on the studentized residualvalues, remember that this does not mean that theobservation in question substantially affects the param-eter estimates or distorts the results (Stevens 1984).

Hat Matrix Diagonal ElementThe hat matrix diagonal element is a measure that iden-tifies an outlier in predictor (or independent) variables.The cutoff value for the hat diagonal element dependson the number of predictor variables (p) in a regressionmodel and the number of cases (n) in the study. For adata set that has more than ten predictor variables andmore than fifty cases, it is suggested that 2p In be used.For example, if there are eleven predictor variables andsixty cases, then the cutoff value would be 2 x 11 /60 =0.4. Any value that is greater than the number derivedfrom this formula is considered an outlier. Like the stu-dentized residual value, a large hat diagonal elementdoes not mean that the observation identified substan-tially affects the parameter estimates or distorts theresults (Stevens 1984).

Cook's DistanceCook's Distance (CD) is a measure indicating the com-bined effects of the dependent variable, as well as theindependent variables, on the change of the regressionparameter estimates that would occur if a given obser-vation were dropped from the regression model.Outliers identified by this method substantially affectthe parameter estimates and may distort the results.High CD values are more likely to be found in smallrather than large data sets.

The cutoff value for CD is about one (Cook andWeisberg 1982, 118). In our experience, those cases that

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Lois Haignere and Yangjing Lin

have a substantially higher CD value than the rest of thepopulation can also potentially have significant effectson the parameter estimates even though the CD value isless than one. A case in point is a white female facultymember at a two-year college. Her CD value is 0.52,which is about ten times higher than the other people ather school (the average CD value for the analysis of thisschool is 0.05). Dropping this highly paid woman fromthe regression analysis substantially increases the biasindicated for white females.

Comparison of the Three Outlier MeasuresIn our experience, using either the studentized residualor the hat diagonal element alone can be misleadingbecause neither necessarily identifies cases that affectthe parameter estimates. If the estimates are not affect-ed, then the case is not distorting the results and neednot be eliminated. At the twelve SUNY schools, wefound that the percentage of cases reaching the cutoffvalue for the hat diagonal element (about 10 percent)was higher than for the studentized residual (about 5percent). By contrast, at all twelve SUNY schools therewas only one case that was found to exceed the CD cut-off value. This means there was only one outlier thathad excessive influence on the parameter estimates.

Using the studentized residual or the hat diagonalvalue alone to flag and drop outliers is a questionableprocedure. By the very nature of the studentized residu-al statistic, positive and negative outliers are identified.In salary-equity studies, most of the high-paid outliersare white males, while most of the low-paid outliers arefemales or minorities.

Observations flagged by Cook's Distance should bescanned for data errors. A case in point is an individualfrom one of the SUNY two-year colleges who was iden-tified as an outlier by a CD of 1.66. We carefully exam-ined his information regarding salary, current rank,highest degree, and years in current rank. After check-ing all the possible information, we found that this indi-vidual had seventeen years in his current rank as a fullprofessor instead of two years, as was recorded in ourdata. He had been a dean, as well as a full professor, forfifteen years. He stepped down from the deanship butcontinued to be a full professor. The two years in cur-rent rank referred to the time after he left the dean'sposition. Adjusting his years in current rank droppedhis CD value to 0.08, indicating that he is not an outlier.

Dropping the deviant cases flagged by Cook'sDistance (greater than 1.0) may be appropriate oncetheir data have been carefully confirmed as accurate.These are cases that are very different from the generalpopulation being studied and excessively influence the

96

parameter estimates. Nonetheless, remember that whilestatistical methods can be used to detect outliers, drop-ping them is as much a political decision as a method-ological one. The practice of dropping outliers is predi-cated on the assumption that they distort the real pic-ture. Don't drop them unless they do. (See chapters 5and 6 for additional discussion.)

Note1. For a more technical discussion of using influence statistics, seeStevens 1984; Chatterjee and Hadi 1988; Belsley, Kuh, and Welsch1980.

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Glossary'

Adjusted R2A measure of how much variability in the dependentvariable is accounted for by the predictor (indepen-dent) variables in a regression analysis. As the adjust-ed le gets closer to 1.0, the predictor variables accountfor more of that variability. The term is referred to as"adjusted" because it accounts for the number of pre-dictors. (For a more in-depth discussion of this topic,see appendix A.)

Anti logSee Log Odds.

Categorical ModelingA statistical procedure used to analyze the relation-ship between predictor variables and a categoricalvariable. It is a generalized logistic regression modelthat uses maximum likelihood tables to estimate theserelationships.

Categorical VariableA variable that classifies subjects into a limited num-ber of categories. Even if we assign numbers to eachcategory or level, the categorical variable does notbecome continuous because the intervals between lev-els are not equal. Rank provides a good example.Even if we assign lecturer = 1, instructor = 2, assistantprofessor = 3, associate professor = 4, and full profes-sor = 5, we do not know if the difference betweenbeing an instructor (rank = 2) and an assistant profes-sor (rank = 3) is the same as the difference betweenbeing an associate professor (rank = 4) and a full pro-fessor (rank = 5), or whether an associate professor(rank = 4) is worth twice as much as an instructor(rank = 2) and four times as much as a lecturer(rank = 1).

CellNumber of Individuals by Race in Each Rank

Race Lecturer Instructor Assistant Associate Full

Black 3 5 7 3 4

Asian 2 4 2 8 5

Hispanic 1 0 0 2 1

White 25 63 572 641 250

Each piece of information found within a table ormatrix is called a cell. In the matrix (table) in this

example, each number represents a cell. The bolded 3is the cell that identifies the number of black lecturersin this institution. All zeros in the table identify cate-gories that have no individuals in them and are called"zero cells." Hispanic instructors and Hispanic assis-tant professors both constitute zero cells.

Censored CasesCensored cases are used in event history analyses.Cases that are censored are ones that contain incom-plete or missing information. Typically, the infor-mation is missing or incomplete because the indi-vidual fails to experience the event during the timeperiod in which the analysis occurs. For example, ifthe event we are studying is promotion from therank of associate professor to full professor duringthe time period 1990-97 and the individual has notbeen promoted during this time, this individualcase becomes censored. By censoring the data, thisindividual contributes seven person-years to thedatabase, even though she or he has not experi-enced a promotion.

Cluster AnalysesAny of several multivariate procedures designed todetermine whether cases are similar enough to fallinto groups or clusters.

Coefficient (Parameter Estimate)The regression coefficient, which is also calledparameter estimate, is a number that indicates howan independent variable affects the dependentvariablefor example, how years of experience orgender or race affect salary. The coefficient alsorepresents the slope of the line for the independentvariable relative to the dependent variable. Anunstandardized regression coefficient in an analysisof salary can be interpreted in dollar equivalents. Ifthe coefficient for years of experience is 200, on aver-age, each year of experience increases salaries by$200. See appendix A for a detailed explanation ofhow coefficients are multiplied by variables inregression equations to calculate predicted salaries.In studies of the effect of gender and race on salaries,the coefficients for the gender and race variables arethe results, or findings. For an explanation of thestandardized coefficient and its common misuse, see"Problem 1" in chapter 6.

1Uii97

Glossary

Continuous VariableA variable that is numeric, with equal intervalsbetween levels of the variable. Salary is an example ofa continuous variable. For salary, we know that eachadditional dollar of salary is the same as all other dol-lars. The interval between one level of salary and thenext level is equal no matter what level is beingreviewed. The difference between $1 and $2 is thesame as the difference between $40,000 and $40,001.

Cox RegressionA logistic regression procedure that reconstructs indi-vidual records to person-years.

Critical Zero CellsEmpty cells that preclude categorical modeling as ananalytical tool. If gender bias in the awarding of aca-demic ranks is being examined, critical zero cellsoccur when every other rank lacks females. If racebias is being examined, then critical zero cells arefound when every other rank lacks minorities.

CurvilinearityA relationship between two variables that, when plot-ted on a graph, forms a curve rather than a straightline or linear relationship.

Default CategoryThe group that is not represented by a value of 1 inany of the dummy variables. For example, if you havea dummy variable for female (female = 1, male = 0),then the default category is male. As a result, theregression coefficient for the female variable in asalary-regression analysis represents what femalesare paid compared to males. In an analysis where allof the race-gender groups are represented by dummyvariables, then white males are the default group, andthe coefficients represent what each minority-gendergroup is paid compared to white males.

Dependent VariablesThe focus of an analysis whose values are predictedby or "depend" on the independent or predictor vari-ables (Vogt 1993). Changes in the independent vari-ables are thought to affect the dependent variable. Inan analysis of whether salary allocation is biased bygender, the dependent variable is salary.

Dummy VariableA variable that is used to represent the different lev-els of a categorical variable. A dummy variable has avalue of either 0 or 1. The number of dummy

98

variables needed to fully represent a categorical vari-able is the number of levels of that variable minusone. For example, for a variable with two levels, suchas gender, you will need one dummy variable,female, which you can code 0 for males and 1 forfemales. Because anyone who is not female is male,you do not need a variable for male. If the variablehas three levels, you will need two dummy variables,and so on. See appendix A for a further discussion ofthe use of dummy variables.

Event History AnalysesMethods for studying the movement over time ofsubjects through successive states or conditions. Thegoal of event history analyses is to study changesfrom one state to the next, such as from associate tofull professor. Event history analyses are a usefuladjunct to pay studies for diagnosing gender or racebias in the promotion process.

Exponential ValueThe exponential value of a coefficient (or of a number)is the power (or exponent) to which the base of natu-ral logarithms, e, is raised. For example, if the coeffi-cient is equal to c, then the exponential value is ec,where e=2.718. When the coefficient (or number) isnegative the exponential of this number yields anodds ratio, for example, ell= e022= 0.803.

Independent (Predictor) VariableA variable that is used to predict changes in a depen-dent variable, based on a change in its own value.Some possible independent (predictor) variables thatmay affect the dependent variable salary are gender,race, years of experience, educational level, anddiscipline.

Interaction TermA term that describes the effect of one independent(predictor) variable on the dependent variable acrosslevels of a second independent variable. For example,if males are paid $200 for each year of previous expe-rience, but females are paid $100, then there is aninteraction between gender and years of previousexperience. The interaction term is the product of thetwo independent variables.

Log OddsAn odds ratio that is based on the logarithm or theexponent of a base number indicating the power towhich that number must be raised to produce anothernumber. For example, the log of 100 is 2 because 102

Glossary

(10 x 10) equals 100, and the log of 1,000 is 3 because103 (10 x 10 x 10) equals 1,000. The antilog turns therelationship around. For example, antilog 2 = 100 and3 = 1,000.

Logistic RegressionA type of regression analysis used when thedependent variable is categorical and scored 0, 1.It is commonly used to predict whether or not anevent (such as promotion or business failure) willhappen.

Multicollinearity (Redundancy)The condition that exists when one predictor variableis highly correlated with another predictor variable orgroup of variables in the analysis. In general, correla-tions above 0.80 are suspect, and correlations above0.90 are red flags. These high correlations mean thatthe variables overlap so much that it is difficult, if notimpossible, to determine their separate effects on thedependent variable. Also called redundancy.

Normal DistributionA distribution of scores that when graphed produce asymmetrical, bell-shaped curve, centered around themean (average). Statistics are often tested usingnormal distributions.

OutlierA case in the data that has extreme values on one ormore variables in the analysis.

Parameter Estimate (Coefficient)A number that indicates how an independent variableaffects the dependent variablefor example, howyears of experience or gender or race affects salary. Inmultiple-regression analyses, this measure is alsocalled the coefficient. See Coefficient for moreinformation.

Predictor VariableUsed interchangeably with Independent Variable. SeeIndependent Variable.

Quadratic TermA variable that has been squared (multiplied byitself). It is used to solve the problem of curvilinearityin statistical models that rely on linear relationshipsbetween predictor and dependent variables. Time-related variables are often thought to have curvilinearattributes, and are frequently included in models inboth the linear form and the quadratic form.

Redundancy: See Multicollinearity.

Response VariableThe dependent variable in categorical modeling. In anattempt to predict academic rank based on othercareer characteristics, rank is the response variable.

SASA statistical analysis software package that is com-monly used by social scientists.

ScatterThe distribution of scores above and below a regres-sion line. A large amount of scatter means that theregression model is not very good at predicting scoreson the dependent variable. In this case, the additionof other independent variables may reduce the scatterand improve the predictive power of the model.

ScattergramA pattern of points that indicates the relationshipbetween two variables. Each point represents whereone unit of the analysisfor example, a faculty mem-beris on the two variables. For the purposes ofstudying salary, we frequently put salaries on the ver-tical axis and another variable, like years of experi-ence, on the horizontal axis so that the scatter repre-sents the relationship between salary and the othervariable. (See appendix A, figures A.1 and A.2.) Themore the points tend to form a straight line, thestronger the relationship. Also called "scatter dia-gram" and "scatter plot."

Statistical PowerThe probability of being able to say that one variableaffects another. If the effect of one variable on anotheris very small, then more power is needed to detect theeffect, just as you would need a higher power micro-scope to see a virus than you would need to see anant. Aspects of the data set, such as the number ofvariables, variance, and sample size, affect power.

Statistical SignificanceA judgment criterion based on the probability that asample comes from a specific population. The num-ber can range between 0 and 1; a low number for sta-tistical significance indicates that the data are unlikelyto be ascribable to chance. The alpha level, which isusually set at either 0.05 or 0.01, is the point at whichwe reject the null hypothesis that our sample camefrom the same population that we are comparing it to;that is, it is the point at which we consider our results

10399

Glossary

to be statistically significant. (See also "Problem 5" inchapter 6.)

Tainted VariableIn bias studies, a variable that is likely to have dis-crimination embedded in it and thus mask or sup-press the gender or race effects. In research vernacu-lar, such variables are called confounding or sup-pressing variables because they obscure or concealcausal relationships between other variables.

Time-Dependent CovarlateA variable whose value can change over time. Forexample, highest degree is commonly a time-dependent covariate, since individuals in the databasewho are hired with a master's degrees commonlysubsequently receive Ph.D. degrees. Time-dependentcovariates are used in event history analyses. Specialprogramming is needed to assure that time-dependent covariates are properly recognized by thestatistical software.

Zero CellAny cell of a matrix that contains no observations. Insome analyses, for example categorical modeling, azero cell can curtail the analyses or cause misinterpre-tations of the results.

Note1. Some of the definitions in this glossary are borrowed fromthe Dictionary of Statistics and Methodology by W. P. Vogt (1993).

100

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