W. W. CHARTERS, JR.With a Foreword by Richard A. Schmuck

HYPOTHESES SCIENTIFIC

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®Clearinghouse on Educational ManagementCollege of EducationUniversity of Oregon

VARIABLESONUNDERSTANDING

R E S E A R C H

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Design: LeeAnn August

International Standard Book Number: 0-86552-115-8Library of Congress Catalog Card Number: 91-77518ERIC/CEM Accession Number: EA 023 510

Printed in the United States of America, 1992ERIC Clearinghouse on Educational ManagementUniversity of Oregon, Eugene, OR 97403

Prior to publication, this manuscript was submitted for critical reviewand determination of professional competence. The publication has metsuch standards. The publication was prepared with funding from theOffice of Educational Research and Improvement, U.S. Department ofEducation, under contract no. OERI-R 188062004. The opinions ex-pressed in this report do not necessarily reflect the positions or policiesof the Department of Education.

No federal funds were used in the printing of this publication.

The University of Oregon is an equal opportunity, affirmative actioninstitution committed to cultural diversity.

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MISSION OF ERIC AND THE CLEARINGHOUSE

The Educational Resources Information Center (ERIC) is a national information system operated by theU.S. Department of Education. ERIC serves the educational community by disseminating research resultsand other resource information that can be used in developing more effective educational programs.

The ERIC Clearinghouse on Educational Management, one of several such units in the system, wasestablished at the University of Oregon in 1966. The Clearinghouse and its companion units processresearch reports and journal articles for announcement in ERIC’s index and abstract bulletins.

Research reports are announced in Resources in Education (RIE), available in many libraries and by sub-scription from the United States Government Printing Office, Washington, D.C. 20402.

Most of the documents listed in RIE can be purchased through the ERIC Document Reproduction Service,operated by Cincinnati Bell Information Systems.

Journal articles are announced in Current Index to Journals in Education. CIJE is also available in manylibraries and can be ordered from Oryx Press, 2214 North Central at Encanto, Phoenix, Arizona 85004.Semiannual cumulations can be ordered separately.

Besides processing documents and journal articles, the Clearinghouse prepares bibliographies, literaturereviews, monographs, and other interpretive research studies on topics in its educational area.

CLEARINGHOUSE NATIONAL ADVISORY BOARD

Jim Bencivenga, Education Editor, The Christian Science MonitorGordon Cawelti, Executive Director, Association for Supervision and Curriculum DevelopmentTimothy J. Dyer, Executive Director, National Association of Secondary School PrincipalsPatrick Forsyth, Executive Director, University Council for Educational AdministrationJoyce G. McCray, Executive Director, Council for American Private EducationRichard D. Miller, Executive Director, American Association of School AdministratorsSamuel Sava, Executive Director, National Association of Elementary School PrincipalsThomas Shannon, Executive Director, National School Boards AssociationDon I. Tharpe, Executive Director, Association of School Business Officials InternationalGene Wilhoit, Executive Director, National Association of State Boards of Education

ADMINISTRATIVE STAFF

Philip K. Piele, Professor and DirectorKeith A. Acheson, Associate DirectorStuart C. Smith, Director of Publications

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P R E F A C E

again. All will benefit from Sandy’s wise,witty, and lucid discourse on the “distinctionsand rules and procedures for unraveling vari-ables, examining relationships between them,and analyzing hypotheses.” And for those ofhis students, colleagues, and friends whoseprofessional lives were enriched by Sandy,this work will stand as a lasting reminder ofthe remarkable gifts of this brilliant teacherand distinguished scholar.

On Understanding Variables and Hypoth-eses is destined to do for scientific researchwhat Elements of Style did for writing.

Philip K. PieleProfessor and Director

The opportunity to publish this instruc-tional manual occurred quite by chance inearly October 1991 when Sandy left a type-written copy on my desk with a handwrittennote telling me that he was tired of answeringrequests for copies and asking if I wouldconsider “putting it in ERIC.” Realizing atonce that this was the material that Sandy hadused for so many years in his policy researchcourse at Oregon, I immediately called himand suggested that instead of merely puttingthe work in the ERIC database, he shouldallow the Clearinghouse to publish it. Fortu-nately for us, and for those who will now havean opportunity to read this classic work, Sandyagreed.

For anyone doing empirical research to-day—be they graduate student, beginningacademic, or established scholar—this manualshould be read and reread again, again, and

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C O N T E N T S

FOREWORD ..................................................................................... vii

1. TO START WITH ........................................................................ 1What’s Ahead ........................................................................................... 1Equipment You Will Need ..................................................................... 2

2. THE ESSENCE OF VARIABLES .................................................... 3

Discourse on What a Variable Is ............................................................ 3The Mode of Variation ............................................................................ 5Analyzing Variables in Empirical Studies ........................................... 8Some Potential Problems in Unravelling Variables .......................... 10How Variables Are Used in Empirical Studies ................................. 14Concluding Note .................................................................................... 15

3. RELATIONSHIPS BETWEEN VARIABLES ....................... 17

The General Idea .................................................................................... 17Examining Simple Relationships ......................................................... 18Sorting Out the Variables in a Study .................................................. 21Turning It Around: Assessing the Mode of Variation from the Data Analyses ....................................................................... 24

4. ANATOMY OF THE HYPOTHESIS ................................... 25

Finding and Dissecting Hypotheses ................................................... 26Specifying Expected Relationships ..................................................... 27The Unit of Analysis .............................................................................. 32The Invisible Ceteris Paribus.................................................................. 34A Note on the Null Hypothesis ........................................................... 34Hypotheses Involving Three or More Variables ............................... 36

5. PATHOLOGY OF THE HYPOTHESIS .............................. 39

Malformations of the Variable ............................................................. 40Abnormalities in Specifications of Relationships .............................. 42

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For thirty years Sandy Charters el-egantly lectured about research methods tohundreds of doctoral aspirants in educationalpolicy and management at Washington Uni-versity and the University of Oregon. Withemotional warmth and intellectual precision,he was determined to contribute to his stu-dents’ understanding of scientific research,and to their belief in the relevance of positiv-ist reasoning to educational administration.

Today there are hundreds of Oregongraduates worldwide who were profoundlyaffected by his intelligent grace in the class-room. When those alumni reread this tinybook, they will be transported back inmemory to when they sat with Charters in aEugene classroom. They will think: at lastwe have printed in a single binding the read-ing that Charters distributed during his finetwo-quarter course on policy research meth-ods. Readers who never heard Charters lec-ture, moreover, will find his systematic andlogical dissection of variables and hypoth-eses insightful and practical. This book hascome at the right time.

What Charters contributes here is justwhat is needed today to correct a currentbias and tilt in favor of qualitative methods.In the face of a paradigm shift in policy re-search in which qualitative methods are be-ing exalted and quantitative methods are be-ing undervalued, Charters’s treatise on clear

F O R E W O R D

conceptual definitions and precise opera-tional hypotheses will play a pivotal role, Ihope, in reintegrating the best of both thequalitative and the quantitative traditions. Iurge students who wish to carry out casestudies or ethnographic descriptions to pre-pare a concrete research plan by heeding self-consciously Charters’s advice to defineclearly and precisely the variables understudy.

Born a few days before Christmas sev-enty years ago, W.W. Charters, Jr. was raisedwith books near his crib in an intellectualhome under the shadow of Ohio State Uni-versity (OSU). His father was director of theBureau of Educational Research; his motherwas a professor of adult education. The onlyson in a four-child family, Charters’s sistersall distinguished themselves with advancedgraduate degrees, each in a field of humanservice. Sandy, a nickname he would neveroutgrow, attended the experimental labora-tory school at OSU in Columbus, received aB.A. with honors in sociology from DePauwUniversity, studied summers with L.L.Thurstone, Herbert Blumer, and Carl Rogersat the University of Chicago, and in 1952received a Ph.D. in social psychology fromthe University of Michigan, the same doc-toral program from which Philip Runkel andI also graduated in 1959 and 1962, respec-tively.

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Among his professional positions, Char-ters worked in the Bureau of EducationalResearch at the University of Illinois, along-side Cronbach, Gage, and others, carryingout research on the social organization ofthe school, and he explored alternative waysof understanding educational issues withCallahan, DeCharms, and L. Smith at Wash-ington University in St. Louis. In 1966, hemoved to the Center for the Advanced Studyof Educational Administration at Oregon. Bythe time he retired in 1987, Charters had pro-duced ten books or monographs and overfifty articles or chapters. Most distinctiveamong his books were two volumes of read-ings in the social psychology of educationthat he coedited with Nate Gage and MattMiles, respectively. On Understanding Vari-ables and Hypotheses in Scientific Research is,however, his most personally distinctiveproduct.

Nevertheless, it is a mistake to overem-phasize the importance of his publications,for it was Sandy Charters, the professor, whowill be remembered more vividly by his stu-dents and colleagues. He sparkled andglowed as he probed students for their ideasabout variables and their speculations abouthypotheses. By probing the meaning of hisstudents’ variables and hypotheses, he prod-ded them to achieve clarity and precision intheir research plans. He tactfully persuadedand painstakingly helped students to relateconceptual definitions logically to operationaldefinitions. As one student told me, “Insteadof giving me answers, Charters helps me toask the right questions of myself.” Other stu-dents characterized Charters as challenging,curious, helpful, insightful, masterful, me-ticulous, and forever questioning. His stu-dents saw him as a “graceful master” of theSocratic method of teaching.

The Sandy Charters I most respectedhad a passion for conceptualizing social-psy-

chological relationships. He labored dili-gently at defining networks of relationshipsbetween roles and at analyzing how people’slocations in a network of communicative re-lationships constituted the fundamental re-ality of bureaucratic structures. He believedthat individual cognitions and feelings growout of interpersonal relationships and thathuman beings are simultaneously social andindividual. He understood that the social re-alities that exist between us are part and par-cel of the cognitive and emotional realitieswithin us.

During his retirement party at my homeover four years ago, I honored him as one ofthe top ten social psychologists of educationever. I said that Sandy, still a brilliant youngman in my mind, reminded me of RobertFrost’s youthful swinger of birches. For inmy dreams, I could imagine a golden-hairedSandy keeping “his poise to the top branches,climbing carefully with the same pains youuse to fill a cup up to the brim, and evenabove the brim.” In my mind’s eye, I couldsee Sandy leaping out in space and “throughthe air to the ground” returning securely toearth. I could see that because I believe thatSandy Charters, the master teacher, tookgreat pains to fill the cups of his studentsand that he always maintained contact withthe ground, even as he filled their cups tothe brim. I trust that you, too, will see thosevery special qualities of Sandy Charters inthis gem of a book.

Richard A. SchmuckProfessor of EducationalPolicy and Management

University of Oregon

January 1992

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THE HYPOTHESIS IS A KEYcomponent of research in the behavioral (andother) sciences. It is the device scientists useto translate questions, theories, or proposedexplanations into a form amenable to empiri-cal research. In addition, a set of hypotheseslaid out at the beginning of a study is aninvaluable guide in directing the researcherthrough the intricacies of collecting and ana-lyzing data.

Exactly what are hypotheses? Oddlyenough, textbooks and other sources on re-search methods do not tell you much abouthypotheses, and what they do say may evenbe a bit misleading. The authors seem toassume that you already know what theyare. The same thing is true of variables, whichare the constituent parts of hypotheses. Theterm is used over and over again by research-ers, but you would have to look long andhard to discover what it means. This manualwill let you in on the secrets.

The manual is written for novices in re-search. It introduces distinctions and rulesand procedures for unraveling variables, ex-amining relationships between them, andanalyzing hypotheses. The purpose of thedefinitions and procedures is purely instruc-tional. Once you have mastered them, theywill become second nature and you will nolonger need to go through the fol-de-rol Iinsist on at first. They will have served theirpurpose. You should be in a better position tounderstand the empirical research you readand to plan studies of your own devising.

WHAT’S AHEAD

The hypothesis, in its elementary form,consists of two variables and a specificationof the relationship that one expects to holdbetween them. The variables are like twoatoms bonded to create a particular kind ofmolecule. There is a good bit more to it thanthis, of course, but the analogy suggests that

TO STARTWITH

C H A P T E R 1

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it will be useful to learn about the atoms andthe bonding glue (relationships) before con-sidering the molecule. In fact, two-thirds ofthe task of understanding the hypothesis willbe accomplished once you have a good graspon the nature of variables. Chapter 2 intro-duces you to their essence.

In chapter 3, I venture into the subject ofrelationships between variables. Early on,the chapter deals with the three ways of look-ing at the relationship between a pair of vari-ables, depending on their “modes of varia-tion” (chapter 2). Contemporary research,though, rarely deals with just two variables.More likely there is a whole closet full ofthem. It is crucial that you have a way ofputting them in order, of recognizing howthey stand with respect to one another, andgenerally making sense of their variety, so thechapter introduces you to some terms thatallow you to sort through them.

Chapter 4 gets into the anatomy of thehypothesis itself. Much of what you need toknow will already have been covered inchapters 2 and 3, but here the focus is onwriting an elementary hypothesis in properform. Beyond this, several key notions re-lated to the hypothesis will be introduced,including the idea of the “null hypothesis”and where it fits in research and a consider-ation of hypotheses beyond the elementaryvariety.

The last chapter takes up some of themore common diseases and pathologicalforms of hypotheses. My main interest intelling you about the hypothesis is in preven-tive medicine. I hope that, when all is said anddone, you will be able to construct healthy,viable hypotheses of maximum utility in yourown research. A malformed hypothesis in thebody of a study is often fatal.

EQUIPMENT YOU WILLNEED

The tools you will need for studying vari-ables and hypotheses are simple—paper andpencil, specimens on which to work, and adissection table. (A white lab coat is optional.)I have provided a number of preserved speci-mens of variables and hypotheses at variousplaces in the manual on which you are en-couraged to exercise your dissection skills.Appropriate locations for finding clinicalspecimens are studies published in such re-search journals as:

American Educational Research JournalAdministrative Science QuarterlyEducational Administration QuarterlyEducational Evaluation and Policy

AnalysisJournal of Educational ResearchJournal of Experimental EducationSociology of Education

There are numerous other scholarly jour-nals that publish original research, and youwould do well to get acquainted with those inyour own field of interest. Avoid the popularprofessional journals in education, though;while they might report summaries of re-search, they are not good sources of originalstudies. They rarely say enough about theresearch to provide dissectable specimens.

You might also try your hand at abstractsof research studies, like Dissertation Abstracts(a prime source for pathological hypotheses),Educational Administration Abstracts, Psycho-logical Abstracts, and the like. Some giveenough detail to permit a provisional dissec-tion of the variables and hypotheses of astudy, and they furnish the reference to theoriginal source if you need to clear up ambi-guities.

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C H A P T E R 2

THE ESSENCE OFVARIABLES

THIS CHAPTER TELLS YOU SOMEimportant things to know about variables.You will learn:

• What a variable is

• That variables have two basically dif-ferent “modes of variation”: kind anddegree

• That there are two special cases ofmodes of variation: the present-ab-sent mode and ordered categories

• What format to use in describing vari-ables completely and unambiguously

• What puzzling situations you arelikely to confront as you try to iden-tify variables in the field and howbest to resolve them

DISCOURSE ON WHAT AVARIABLE IS

To explain variables, it is necessary to usethree general terms: objects, properties of ob-jects, and values of a property.

OBJECTS AND THEIR PROPERTIES

Objects are the things one does researchon. They are often people (sixth-grade stu-dents, school board members, female ath-letes), but they can be school districts, nations,small groups, newspaper editorials, or spe-cific events (bond elections, employment ofprincipals).

We intuitively distinguish between thingsand properties of things in our everydaylives—between an object like “hat” and aproperty that hats might have, like “color”or “size.” This idea is embedded in the dif-ference between a noun and an adjective.We talk about a “large hat,” implicitly dis-

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tinguishing it from other hats that are ordi-nary or small.

Objects that we see around us have anunlimited number of properties, or attributes,according to which they can be described.These properties enable us to talk about waysobjects are alike and ways they are different.

Empirical research is concerned with theway objects differ from one another (or theway a given object differs from one time to thenext). A property that allows us to make thisdistinction between the objects of study iscalled a variable. Consider the following prop-erties, or attributes, that would allow us todifferentiate between school principals:

Gender

Height

Rate of speaking

Whether or not afflicted with ulcers

Amount of knowledge about school law

Number of previous administrativepositions

Eye color

Level of self-esteem

The list could be continued indefinitely,but the point is that each of these propertiescould be used as a variable in a study of schoolprincipals.

VALUES OF A PROPERTY

A property (or a variable) always impliesan associated set of values—at least two—thatset objects apart from one another. For in-stance, size (of a hat) implies a range of valuesfrom 6 7/8 or smaller to 7 3/4 or larger. Gender(of a principal) implies two values, male andfemale. Ulcer affliction might imply two, af-

flicted and not afflicted. Eye color may entailfour or five values or more, depending onhow finely one wished to discriminate be-tween principals. Height entails a continuousarray of values, usually denoted in feet, inches,and fractions of an inch or perhaps in centime-ters, while number of previous administra-tive positions implies a set of discrete valuesthat might run from 0 to 10 or so.

When used as a variable, the values asso-ciated with the property must be exhaustiveand they must be mutually exclusive. A placefor everything and everything in its place. Anexhaustive set of values means that one mustbe able to assign some value to all objectsunder consideration (even if that means pro-viding a value called “information missing”).

Mutually exclusive means that each ob-ject can be assigned only one of the set ofvalues. A hat cannot be both 6 7/8 and 7 3/4 at thesame time.

(Researchers sometimes run into prob-lems as they try to follow these rules in creat-ing classification systems. What do you doabout a principal who has one gray eye andone green eye? Answer: establish anothervalue, “mixed.”)

VARIABLES VS. CONSTANTS

When all is said and done, a variable issimply a property (and its associated values)according to which objects of study are ex-pected to differ.

We also use properties and their values togroup objects into classes whose members arealike in certain ways. This is useful in definingwhat (or who) the objects of an investigationare. Thus, a researcher might limit a study tofemale school principals, using the principals’gender as a criterion for selecting subjects. In

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such a study, gender would be a constant, nota variable. Everyone would be alike with re-spect to the property. Another researchermight select school principals without regardto gender but use gender as one of the vari-ables for investigation. In short, the sameproperty may be used as a variable in onestudy and as a defining attribute, hence aconstant, in another. What is and is not avariable depends on the study.

In the context of a particular study, a“variable” with only one value is not a vari-able at all.

VARIABLES AND THE MEASUREMENTOF VARIABLES

Sometimes the properties in which re-searchers are interested can be measured sim-ply and directly. A principal’s gender nor-mally can be ascertained with little difficulty,by observation in a face-to-face situation or byasking respondents to check the appropriatebox on a questionnaire. The same is true forheight and eye color.

Other properties of interest, though, arenot immediately accessible to the senses andrequire a more elaborate (and potentially fal-lible) measurement process. Properties re-mote from the plane of immediate observa-tion commonly are called constructs. “Amountof knowledge of school law” is a fairly ab-stract property, as is “level of self-esteem,”and certainly neither can be determined by aquick glance. Rather, one has to assemblepieces of information from which an infer-ence can be drawn about the principal’s legalknowledge, perhaps using a set of pointedquestions designed to reveal it.

By listening to, or seeing, the principal’sresponses, the measurement procedure con-verts an otherwise hidden property into ob-

THE ESSENCE OF VARIABLES

servable form. But it has its price. A constructand the pieces of information from whichinferences are made regarding an object’sstanding on it are not in one-to-one corre-spondence. A principal’s score on a 15-itemtest is only a rough approximation, at best, ofhis or her “amount of knowledge of schoollaw.” Considerable slippage can occur be-tween the conceptual meaning of a variableand the procedures used in trying to measureit, an issue researchers address under therubric “validity of a measure.”

When researchers attempt to specify whatthey mean by a property and its variations,they are providing what is called a conceptual,or constitutive, definition of the variable. Whenthey describe the procedures used to measurethe property, they are furnishing an opera-tional definition of it.

The two are not the same, and it behoovesthe novice researcher not to mistake the latterfor the former.

THE MODE OF VARIATION

There are two fundamental ways in whichobjects can differ from one another: in kindand in degree. Which of the two modes ofvariation is at stake in the variables of a studyhas wide ramifications for the conduct of re-search, ranging from the phrasing of hypoth-eses through measurement procedures to themanner of analyzing data and reporting re-sults. It is imperative that you recognize thedifference between the two.

VARIATION IN KIND

The set of values associated with varia-tions in kind are like pigeon-holes, arrangedin no particular order. Each pigeon-hole has a

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name or brief description of what gets stuffedinto it. They do not fall along any continuumor underlying dimension. In fact, if you wereto make a list of the values, you could putthem in any order you chose. (But see mycomments on “ordered categories” on page10.) Following are illustrations of variationsin kind, listing first the property and then thevalues that might be implied.

Leadership style: autocratic, democratic,laissez-faire

Personality disorder: schizophrenic,manic-depressive, paranoic

Marital status: single, married, separated,divorced, widowed

Region of country: Northeast, Midwest,South, Far West

Opinion regarding school closure: favor,oppose, indifferent

Orientation to profession: place-bound,career-bound

College graduate: graduate, not a gradu-ate

As the illustrations indicate, the propertymay involve several values or only two. Butthere always must be at least two.

It should also be clear, if you go backthrough the list, that the name of the propertyalone doesn’t often give you a sure clue as towhat the values are going to be. A propertylike “gender” does give a clue (at least amonghumans), since one is either male or female. Aproperty such as “leadership style,” however,is equivocal. There are a number of alterna-tive systems for classifying leadership styles(nomothetic, ideographic, transactional, forexample, or power-augmentive vs. power re-ductive), and unless the values were spelledout one would not know which set was in-

volved. The same is true for the other illustra-tions in the list. There are other ways of cat-egorizing marital status, region of the coun-try, and so forth.

The lesson is that, when dealing with avariation in kind, it is essential that you ex-plicitly enumerate the implicated values.

VARIATION IN DEGREE

Variables whose mode of variation is indegree imply an array of values that are or-dered along a continuum or dimension. Thevalues are actual numerical values indicatinghow far along the dimension an object lies;they are not just names of categories. Here aresome illustrations:

Level of job satisfaction

School size

Length of membership on school board

Annual salary

Aggressiveness

Extent of centralization of decisionmaking

Intelligence quotient

Pupil-teacher ratio

For the most part, the properties ratherclearly point to the fact that they involve aquantitative measure, at least as I havenamed them. Some contain clue-words, suchas “level,” “length,” “extent,” “quotient,” “ra-tio,” and “amount.” Others, like school sizeor annual salary, conventionally imply anarray of numerical values (number of pu-pils, dollar amounts) and are readily recog-nized as variations in degree.

On the other hand, the variable name maynot obviously indicate a variation in degree ormay not make plain the underlying dimen-

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THE ESSENCE OF VARIABLES

properties in question are “ulcers,” “collegegraduate,” “teacher aide,” “drug administra-tion,” “adoption of modern math,” and “men-tion of school issues,” and they are eitherpresent or absent for a member of the class ofobjects under study.

My point in discussing present-absentvariations is that you may not recognize themas variables when you encounter them. Thevariable may be given the name of the prop-erty that is present, leaving it to your intuitionto realize that the second value of the variableis the property’s absence.

Putting this in the form I used earlier, theproperty and its values would look like this,with the implied value in parentheses:

Ulcers: ulcers, (no ulcers)

College graduate: graduate, (not a gradu-ate)

Teacher aide: teacher aide, (no teacheraide)

Textbooks in research methods often re-fer to variables in this way, mainly because itmakes the illustrations simpler, but variablesin the present-absent mode, with their unspo-ken “absent” value, harbor trouble.

They might be mistaken for constants—aspecification of the objects of study—ratherthan variables. For another thing, it is notalways clear what the absent state is. Arecollege graduates to be contrasted with col-lege students who have not yet graduated,with technical-school graduates, with otheradults who never finished college, or withwhom? The absent condition, in this way,may be a “waste-basket category” containinga great mix of objects that do not happen tomeet a particular criterion for inclusion in the“present” state.

sion along which the values are arranged.Thus, had I named the third illustration above“school board membership,” you would notknow for sure that it represented a variationin degree. Here’s another example. “Teachercommunication with colleagues” might referto the number of colleagues with whom ateacher talks on a daily basis, ranging, say,from 0 to 15, or it could refer to the reportedfrequency of the teacher’s conversations withcolleagues, expressed perhaps on a weeklybasis and ranging from 0 to 15 to 20 times aweek. Either would reflect a variation in de-gree, but the variable’s dimension is ratherdifferent in the two cases, and the variablename alone would not indicate which was atstake.

Another issue associated with variationsin degree concerns the meaning to be at-tached to small and large numerical values,or scores. Which direction do the operation-ally derived scores run? Ordinarily, big num-bers mean that the objects of study have a lotof the property in question, but this is notalways the case. (More on this shortly.)

PRESENT-ABSENT: A SPECIAL CASE OFKIND

You will sometimes encounter variablesin which the property is either present orabsent. I have included some of these in thepreceding illustrations of variations in kind.A principal is or is not afflicted with ulcers. Acommunity citizen is or is not a college gradu-ate. Other examples: a classroom does or doesnot have a teacher aide assigned to it, a subjectin a medical study is or is not administered anexperimental drug, an elementary school hasor has not adopted modern math, a newspa-per editorial does or does not deal with schoolissues. All are instances of a mode of variationin kind consisting of just two values. The

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The lesson is as before: when dealing witha variation in kind, including one in thepresent-absent mode, explicitly enumeratethe values; don’t leave them to intuition.

ORDERED CATEGORIES: A HYBRIDVARIETY

“Ordered categories” is an in-betweenmode of variation that might be used as avariation in kind or as a variation in degree ina given study. (It might even be used bothways.)

Ordered categories are unlike variationsin kind discussed above in that the values ofthe property do, in fact, fall in a logical order.Even though the variable may be treated as avariation in kind in the analysis section of astudy, each category reflects “more” of someproperty than the next category. The set ofcategories is arrayed along a distinct dimen-sion and, in this way, looks more like a varia-tion in degree than in kind.

For example, the values of a variablecalled “social-class membership” [of schoolpatrons] might be labelled (a) “working,”(b) “middle,” (c) “upper-middle,” and (d)“elite,” obviously reflecting increasing lev-els of social status. Two more examples. Thevalues associated with a variable called“principal’s efforts in backing teachers” mayhave categories named (a) “poor,” (b) “av-erage,” (c) “good,” and (d) “outstanding.”They clearly fall along a continuum. Teacher“homework assignment practice” may con-sist of these categories: (a) “never assignshomework,” (b) “occasionally,” (c) “fre-quently,” or (d) “always assigns homework.”Again, the values reflect varying frequen-cies of assignment.

Should you regard these as variations inkind or in degree? It all hinges on how the

data are handled in the study. If the values aremaintained as discrete categories in the analy-sis and report of findings, regard the variableas varying in kind. Note, though, that theinvestigator may choose to give numericalvalues to the categories and literally treat thevariable as a variation in degree. He or shemight assign a score of 1 to the “working-class” category, 2 to the “middle-class” cat-egory, 3 to the “upper-middle” category, and4 to the “elite” category and proceed to calcu-late mean social status scores for subgroups ofschool patrons. (Calculation of a mean for avariable should tip you off immediately thatits mode of variation is not in kind; see thefollowing chapter.)

ANALYZING VARIABLES INEMPIRICAL STUDIES

To understand variables, you need to readresearch articles in your field. Single out thekey variables of a study and analyze each oneseparately. (You may discover that this prac-tice helps you understand better the studyitself.)

Virtually every study you encounter willhave a good many variables in it—maybeonly 4 or 5 but perhaps 20 or more. Thevariables normally are not of equal standing;later I will have more to say about how vari-ables stand with respect to one another. Fornow, though, it is enough to single out forpurposes of analysis the ones that are centralin the study.

DESCRIBING A VARIABLE COMPLETELY

Variables can be slippery, slinky, and sly,but they have to be unravelled if you are to seehow they work in research. Just giving them

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THE ESSENCE OF VARIABLES

cific categories, or values, that areinvolved. Give them alphabeticalletters (and, for purposes of clar-ity, list them directly under oneanother).

b. If you declare the mode of varia-tion as degree, indicate clearly theunderlying dimension or con-tinuum. Also indicate the direc-tion the numerical values run. It isusually sufficient to say somethinglike “low to high X” or “little tomuch X,” where X is a brief char-acterization of the dimension.

Care in naming the property mayforestall the need for extendedelaboration. Sometimes you face atrade-off between using a short,convenient name for the variableand extending its description inthe elaboration or squeezing allthe information into the name it-self and minimizing the elabora-tion.

To be systematic about it, lay all this outon a dissection table. Use a separate form,such as shown in table 1, for each variable youanalyze.

names doesn’t tell you much about them. Afull description of a variable used in a studyusually requires you to examine words theauthor employs to say what the variablemeans and to inspect how it was actuallymeasured or manipulated and used in dataanalysis.

There are three sections of a researchreport where you should look to do theunravelling. Opening sections of the reportoften include discussions of the key vari-ables, what they mean, how they have beenused in other studies, and the like. (If you arelucky, the author may provide carefully de-veloped formal definitions.) You will need tolook in the section on “Method” to find howthe variable was measured in the context ofthe study. The tables contained in the “Re-sults” section may turn out to furnish the bestinformation about the nature of the variable.(Read the next chapter of this treatise con-cerning Relationships between Variables toget help in knowing what to look for in thetables.)

A variable is fully unravelled when youdo the following four things:

1. Name the property, or attribute, atstake. This is equivalent to namingthe variable itself. What is the prop-erty that differentiates one object (per-son, event, etc.) from another?

2. Indicate the objects to which the prop-erty attaches.

3. Declare its mode of variation. Youhave two choices: kind or degree.

4. Elaborate on the mode of variation.(This does not mean giving details ofhow the variable was measured.)

a. If you declare the mode of varia-tion as kind, then list all the spe-

Your description of the variable shouldstand on its own feet when you are done. If

Table 1. Dissection Table for Variables

Objects: [To whom or what does theproperty apply?]

Property: [Name of the property.]

Mode of Variation: [Kind or degree?]

Elaboration: [List the categories ordescribe the dimension.]

10

precise, and there are many intricacies andtechnicalities that might escape you until youhave gained some practice. I will mention afew things here that seem to make life hard fornovices as they get into the business of analyz-ing variables of a study.

The first two have to do with singling outvariables. Obviously, you must be able to spotone in order to analyze it, and it is not alwayseasy to decide where one ends and anotherbegins.

1. VARIABLE VERSUS A CLASS OFVARIABLES

An author reporting a study containing anumber of variables may classify them underseveral headings: variables relating to “stu-dent motivation,” those relating to “student-teacher interaction,” those concerning “schoolcharacteristics,” and so forth. A common mis-take is to think that the name for a class ofvariables is itself a variable.

Also, merely because a group of variablesis measured with the same “instrument” doesnot mean that a single variable is at hand. TheLeader Behavior Description Questionnaireis a case in point. The LBDQ XII, as it is called,is a 100-item form that is designed to measure12 distinct dimensions of a leader’s behavior,such as Tolerance of Uncertainty, Persuasive-ness, Initiation of Structure, Production Em-phasis, Superior Orientation, and so forth.Each of the dimensions represents a separatevariable whose mode of variation is in degree.

This instrument does not offer an overallmeasure of “leader behavior” that varies alonga diagnosible dimension. (See the next prob-lem, below.)

A good way to figure out what the distinctvariables of a study are is to examine the

you were to show it to others unfamiliar withthe study, they should be able to understandit.

Incidentally, use your common sense atthis point to designate the objects of study.When we get to chapter 4, particularly thediscussion of the “unit of analysis” in a study(a closely related topic), you will discover thatespecially troublesome problems wiggle outof the woodwork.

In table 2, I give two illustrations of thedissection table at work.

SOME POTENTIALPROBLEMS INUNRAVELLING VARIABLES

The task of spotting and analyzing vari-ables in empirical studies is not terribly diffi-cult when you get the hang of it, but you arebound to run into problems and oddities.Authors of research pieces are not always

Table 2. Two Examples of the VariableDissection Table at Work

Object: Public schoolsuperintendents

Property: Orientation to thesuperintendency

Mode of Variation: Kind

Elaboration: a. Place boundb. Career bound

Object: Elementary schoolteachers

Property: Sense of work autonomy

Mode of Variation: Degree

Elaboration: Low to high feeling ofclassroom autonomy

11

similarly: satisfaction with supervision, withsalary and wages, with colleague relations,with work facilities, etc., as well as “generalsatisfaction” (a sum of the other varieties).Authors of research articles sometimes feelimpelled to analyze and report all scores andsubscores within their grasp. When do youstop counting and unravelling variables un-der such circumstances? Let common sensebe your guide.

3. “CHANGE,” “IMPROVEMENT,” AND“GAIN”

Now and then you will find allusions to avariable such as “attitude change “ or “im-provement in performance” or “achievementgain.”

To avoid trouble, treat the variable as“attitude,” not “attitude change,” or “perfor-mance,” not “improvement in performance.”

Why? Ordinarily, words like change, im-provement, and gain involve situations inwhich a variable has been measured at twopoints in time; scores on the variable at Time2 are subtracted from scores at Time 1 toyield a numerical value indicating theamount of change (positive or negative) inthe property between the two times. Thus,one property (variable) is measured twice.There are occasional exceptions when“change” literally means change, but you arenormally better off analyzing the variable asthough it had been measured just once anddropping any reference to “change.”

4. INVENTING NAMES FOR VARIABLES

When you name the property, or variable,you should remain as faithful as possible tothe words the author uses in the researchreport. It does not always happen, though,

THE ESSENCE OF VARIABLES

tables presenting the study results. What dothey suggest the author considered the vari-ables to be? Even if the author is muddy in hisor her exposition in the text, the tables oftentell the tale.

2. SCORES, SUBSCORES, AND ITEMS

Whereas the preceding situation mightinduce you to count too few variables in astudy, a reverse situation may lead you tocount too many. The measure of a variable isoften constructed from a number of separateitems or indicators to yield a single score, andit would be incorrect to declare each of theitems to be a variable. Attitude and personal-ity scales and academic achievement tests areclassic examples; scores are summed fromalternative responses to a number of items.An index of a family’s “socioeconomic status”might be formed by combining in a certainway measures of the occupation, the educa-tional attainment, and the income of thebreadwinner(s). Here there is one variable,not three. “Satisfaction with services” in astudy of the clients of a placement officemight be calculated from the numerical dif-ference between ratings of the amount of helpthe client expected and the amount of help heor she received. “Expected help” and “re-ceived help” would not be separate variablesin the study, unless they were also used inde-pendently of the “satisfaction” variable.

As long as a single score or index is de-rived and used as such in data analyses, treatit as a single variable. Again, examination ofthe tables can help.

Matters can get a bit complicated, though.Achievement tests based on multiple itemsoften yield subscores as well as overall scores.Job satisfaction measures may be calculated

12

that the author furnishes a nice, tidy name fora variable, and it may be up to you to inventone. This occurs most often for variables thatvary in kind. The author may list a set ofspecific values but not give a generic name tothe property.

For example, a researcher might report astudy comparing, say, teaching styles in: (a)secretarial schools, (b) nursing programs incommunity colleges, and (c) civics courses inCatholic secondary schools, obviously a varia-tion in kind. But kind of what? How do youname the general property of which the threeare particular values, especially if the authordoes not suggest one? The best you could doin your analysis is to give the variable aninnocuous name, like “type of setting,” andrely on the list of categories to describe itsmeaning. (Make a mental note to avoid theauthor’s mistake in your own research.)

5. OBJECTS OF STUDY ARE NOTVARIABLES

A variable is a property that attaches to theobjects of study and provides a basis for dis-tinguishing between them. An occasional er-ror of novices is to believe they have named avariable when they have only named the ob-jects. If academic deans of large Americanuniversities were the objects of investigation,it would be incorrect to name a variable“deans.” The variable(s), rather, would besome property or properties used in the studywith regard to which the deans differ, forexample, their frequency of interaction withfaculty members (in degree) or the disciplin-ary field from which they stemmed (in kind).

6. THE CONVERSION OF VARIATION INDEGREE TO VARIATION IN KIND

A variable with all the earmarks of avariation in degree may actually be treated

in the analysis as a variation in kind. “Schoolsize” might be a case in point. Although theresearcher may have in hand the student en-rollments for a set of schools—values rang-ing from 50 to 1,000, for instance—he or shemay decide to use some convenient cutoffpoints to classify them as “small,” “medium,”and “large” for purposes of data analysis. Apotential variation in degree is reduced toone in kind (i.e., ordered categories).

Respondent age might seem, on the sur-face, to be a variation in degree, but to facili-tate responses on a questionnaire the re-searcher might have asked respondents tocheck the age-range within which they fall(20-24, 25-29, 30-34, etc.). Again, this is a varia-tion in kind rather than degree.

In general, it is always possible to reducea variable measured in degree to a variation inkind, but you can’t go the other direction. Avariable measured as a set of categories can-not be elevated to a variation in degree.

7. COLLAPSING THE CATEGORIES OF AVARIATION IN KIND

A rather common practice in dealing withvariables in kind is to combine, or “collapse,”categories in the course of data analysis. Thefive-year age categories in the preceding illus-tration could readily be collapsed into ten-year categories or, even further, into just twovalues.

Consider another illustration. In a mea-sure of occupational values, respondents areasked to select one of ten things that theyregard as the most important criterion of “anideal job or occupation”—things such as “pro-vide a chance to earn a good deal of money,”“provide an opportunity to be helpful to oth-ers,” “enable me to look forward to a securefuture,” and “permit me to be creative and

13

THE ESSENCE OF VARIABLES

original.” For purpose of analysis, the tencategories are collapsed to four: people-ori-ented values, extrinsic rewards, self-expres-sion, and other values.

When you dissect such a variable, do so inlight of the categories actually used in theanalysis, not those that potentially could havebeen used.

8. WHEN SMALLER NUMBERS MEAN ABIGGER QUANTITY

At some point in the measurement pro-cess, the researcher assigns numerical valuesor scores to variables that vary in degree. Heor she usually arranges that the larger quan-tities or levels of the property in question berepresented by bigger numbers and thatsmaller quantities or lower levels be repre-sented by smaller numbers. For some vari-ables the numerical values and the “direc-tion” of the variable have a natural correspon-dence. For “school size,” larger enrollmentsmean greater size, and for “salary level,” moredollars mean higher salaries.

Things do not always work out this nicely,though. In the game of golf, for instance,better golfers are the ones with lower scores,and faster runners are the ones who cover adistance in shorter times. So it is in measuringvariables. “Amount of knowledge aboutschool law” conceivably could be measuredas the number of wrong answers on a 40-itemtest, with the result that low numbers mean alot of knowledge and big numbers mean littleknowledge. Employees’ feelings of “alien-ation from work” may be measured so thatthe larger the score, the less the alienation.

The lesson: watch out! As you analyzevariables that vary in degree, double check tomake sure the numbers run in the directionone would expect them to from the name of

the variable. If they don’t, either rename thevariable or make the underlying dimensionclear in your elaboration of the mode of varia-tion.

9. BI-POLAR VARIABLES

Some variations in degree are consid-ered as ranging between a high level of oneextreme to a high level of another extreme,with the extremes regarded as direct oppo-sites of each other. Distinct names are givento each extreme value, or “pole,” of the di-mension. An illustration will give you theidea. The Pupil Control Ideology scale (orPCI) is designed to measure teacher viewsregarding the classroom control of pupilsalong a continuum ranging from highly “hu-manistic” views to highly “custodial” viewsof control. Inventors of the scale stipulatethat “custodial” views are to be regarded asthe opposite of “humanistic” views. Scoringinstructions for the instrument provide nu-merical values ranging from 20 to 100, withlarger numbers indicating greater“custodialness” and smaller numbers indi-cating greater “humanisticness.” Teacherscan be located anywhere between the twopoles.

Such a variable poses several hazards.You might mistake the variable as varying inkind (the two kinds being “humanistic” or“custodial”). You might think there are twovariables at stake (degree of “humanisticness”and degree of “custodialness”). What do youname the variable in order to properly de-scribe the dimension? (In this instance, thedimension usually is called “custodialness ofview” because, according to the scoring pro-cedures, larger numbers represent higher lev-els of custodialism.) Since the assignment ofnumerical values, or scores, to a bi-polar di-

14

mension is arbitrary, you need to be espe-cially alert to the particular direction the scoresrun.

HOW VARIABLES ARE USEDIN EMPIRICAL STUDIES

Almost no study you read will be limitedto just one variable. More likely you will findthat researchers collect data on four or five orten (and sometimes many more) variables ina given study. What in the world do you dowith them? It depends, of course, on theinvestigator’s point of doing the study in thefirst place. The purposes behind research canbe of many sorts, but it is possible to separateempirical studies into two major piles by con-sidering whether the researcher’s interest is inthe variables in their own right—in reportinghow the objects of study stand on them one ata time—or whether the concern is with causalrelationships between the variables.

The hypothesis, the main subject of thistreatise, is a prediction about relationshipsbetween variables. Hence, our attention willbe confined in succeeding chapters to studiesin the second pile, where the intent of researchis to develop or test hypotheses and whererelationships assume center stage. (Differentnames are attached to this form of research,and no common agreement exists. I tend tofavor “verificational studies.”) Before mov-ing on, it may be useful to look briefly atstudies in the first pile.

A study’s intent may be simply to de-scribe a population with respect to one ormore variables. Cause-effect relations are nei-ther hypothesized nor examined. Investiga-tions of this variety go under such names asdescriptive surveys (or just plain surveys),status studies, polls, or censuses; “descriptive

studies ” is a sufficiently general designation.The number of variables measured in thepopulation (or a sample of the population)may be vary large, or the measurement maybe directed toward just a few variables, per-haps only one. Examples are legion.

• A study may seek to establish clientsatisfaction with several aspects of a univer-sity placement office for purposes of identify-ing the services needing improvement. Eachaspect on which clients are queried regardingtheir level of satisfaction represents a vari-able.

• A research team may measure the in-cidence of sex-bias in a sampling of a schooldistrict’s American history textbooks, usingseveral different indicators of bias. One indi-cator (or variable), for instance, could be theratio of female to male figures referenced inthe textbook—the smaller the ratio, the greaterthe bias.

• A study may seek to describe the trendin dropout rates of a state university’s fresh-man class over a five-year period.

• A public opinion poll may measurecitizen views on a number of current issues orvoting preferences in several line-ups of po-tential political candidates.

• The business manager of a commu-nity college may use a standard checklist torate the adequacy of physical facilities in theclassroom buildings on campus. The check-list may provide a scheme for calculating anoverall score for each building as well assubscores for separate categories (space,lighting, climate control, and so forth).

The list of illustrations could go on and onand on. They share the characteristic that thevariables measured in the studies are impor-

15

THE ESSENCE OF VARIABLES

Descriptive information is enormouslyimportant to policy makers and others in allsectors of modern society, as witnessed bythe vast resources devoted to its collection.The information runs the gamut from thedecennial census of the population, throughthe Dow-Jones averages, to statistics on base-ball player performance and the GuinessBook of Records.

Serious descriptive research is equally asdemanding of disciplined inquiry asverificational studies, and the requisite meth-odological tools are similar in the two. De-scriptive studies, though, place a premium onthe accuracy and relevance of measurementand on the techniques of population sam-pling; knowledge of elaborate statistical pro-cedures and of the ins and outs of researchdesign have less bearing. The researcher whoundertakes a descriptive study must, aboveall, be clear about his or her purposes, mean-ing particularly how the information is to beused.

CONCLUDING NOTE

There is more to know about variables. Inparticular, there are a number of adjectivesattached to the word variable that designate avariable’s function in a study. I’ll talk aboutindependent and dependent variables, con-trol variables, intervening variables, and thelike in the next chapter. For now, though, youhave enough tools in your kit to begin disas-sembling the variables in empirical studiesand to understand what makes them tick.Take it from me, a strong grasp of the natureof variables is a foundation for virtually everytopic in research methods. It is up to you tohone your skills in spotting and unravellingthem.

tant in their own right—they are free-stand-ing, so to speak—and that the researchers orinvestigating agencies exhibit little interest inestablishing relationships between the vari-ables, and certainly not causal relationships.The business manager, for instance, is unin-terested in testing if buildings with more ad-equate space tend also to be buildings withmore adequate lighting.

Ordinarily, it is fairly easy to figure outfrom its flow whether a study is of the de-scriptive or verificational sort. The mannerin which the data are presented, in the tablesor in the text, can help to nail this decisiondown. Two things can cloud the matter a bit,though. For one thing, true verificationalstudies often contain tables or other infor-mation describing in some detail the sampleon which the study was conducted, espe-cially in an early part of the report. The heartof the study, however, is in a later part whererelationships are displayed.

For another thing, reports of descriptivestudies may contain tabulations for specialgroupings or subpopulations of the objects ofstudy. Such tables are formally equivalent tothe examination of relationships. For instance,the incidence of sex bias may be reportedseparately for texts of different publishers, orcandidate preferences may be reported bygeographical region. The university’s drop-out rate may be tabulated separately accord-ing to whether or not the freshmen were in-state or out-of-state students. The purpose ofthe cross-tabulations is not so much to exam-ine relationships among variables (and cer-tainly not to test causal relations) as it is toprovide more detailed descriptions of thepopulation.

17

STUDIES THAT BRING EMPIRICALevidence to bear on hypotheses do so byexamining relationships between variables.It is useful to understand how this is done,and the present chapter offers initial guid-ance in a topic that can quickly get obscure.Also, such studies often deal with quite a fewvariables at a time. Trying to dope out whatthey are for and how they enter into theinspection of relationships can be a difficulttask without a scheme for sorting throughthem. In the chapter, I will:

• Explain the three basic ways of examin-ing relationships between two variables. Theone that is applicable depends on the modesof variation of the two variables.

• Introduce you to a bunch of terms thathelp to classify variables and to see theirstanding with respect to one another.

THE GENERAL IDEA

A relationship between two variablesmeans that, for some set of objects of inter-est, their standing with respect to one vari-able tends to correspond with their standingon the second. In the American adult popu-lation, for instance, age tends to be related toeconomic conservatism. Specifically, personswho are older on the age variable tend tohave higher values on the conservatism vari-able (assuming the conservatism values runfrom low to high). The number of cigarettessmoked daily is related to the likelihood ofcontracting lung cancer. Exposure to TV vio-lence (vs. no exposure) is said to be relatedto aggressive behavior among children.

Association, covariation, and concomitantvariation have the same meaning as relation-ship. So does the term correlation (although it

RELATIONSHIPS BETWEENVARIABLES

C H A P T E R 3

18

also has a technical meaning used to describea particular kind of relationship, as notedshortly).

A relationship is always between just twovariables. It is impossible to examine the rela-tionship of three variables, except by doing ita pair at a time.

Two things must be true in order to exam-ine the relationship between variables in astudy. First, each object under investigationmust have been measured or otherwise as-signed a value on both variables. And second,there must be some variation among the ob-jects on each variable. If all the objects havethe same value on one or both variables, thevariable becomes a constant insofar as thestudy is concerned, and the relationship can-not be determined.

HOLDING OTHER VARIABLESCONSTANT

A good bit of the business in contempo-rary research is devoted to the examinationof relationships between pairs of variableswhile “controlling for,” or “holding con-stant,” one or more other variables. Riddinga study of extraneous conditions that couldaffect results in unwanted ways is a perpetualconcern in conducting research, and it comesunder discussion at various places in a courseon research methods. Care in choosing ob-jects of study in the first place, in arrangingparallel conditions of investigation, and inusing standard data-taking methods areamong the considerations.

An important and very common proce-dure is the use of “statistical controls” duringdata analysis, through techniques known asmultivariate analysis . Their use adds complex-

ity to the task of examining relationships andunderstanding what is going on in a study,and eventually you will need to know aboutthem. For now, though, we will limit ourattention to simple (or bivariate) relationshipsbetween variables.

EXAMINING RELATIONSHIPS VERSUSTESTING SIGNIFICANCE

Two branches of that hairy subject knownas statistics get interwoven in the inspectionof relationships between variables. Thebranches are descriptive and inferential statis-tics. The descriptive branch involves littlemore than counting things, calculating per-centages, and figuring means (averages). Themost complicated thing you run into is thecalculation of a correlation coefficient. Gen-erally speaking, it is possible to comprehendthe notion of relationships without gettinginto the other branch, though in practice thetwo are intertwined.

Inferential statistics concerns the ques-tion of whether the difference in percentagesor means that you figure, or the numericalsize of the correlation coefficient you com-pute, is greater than could be expected bychance. This is where statistics begins to getdeep, and I will barely touch on the matterhere.

EXAMINING SIMPLERELATIONSHIPS

Although the technical trappings of in-ferential statistics may disguise the fact, thereare only three basic ways of examining the

19

RELATIONSHIPS BETWEEN VARIABLES

Table 4: A Sample Percentage Table

Gender For Against Undecided Total

Male 27% 54 19 l00%Female 40% 46 14 l00%

Both 35% 48 16 l00%

relationship between a pair of variables. Thethree depend on the modes of variation ofthe implicated variables.

CASE 1: BOTH VARIABLES IN KIND

Procedure: compare percentages in a per-centage table.

A percentage table actually is derived fromanother table—a cross-tabulation or, techni-cally, a “contingency table.” Contingency tableis a fancy name for an everyday sort of tablewith which you are familiar. It is constructedby counting the number of objects in the cat-egories of one variable that fall in the catego-ries of the second. For instance, if one of thevariables were gender (male, female) and theother were opinion regarding the school bud-get (for, against, undecided), the contingencytable would contain the number of malesfound to be for, against, and undecided andthe number of females who are for, against,and undecided. Entries in the cells of a contin-gency table are simply counts of the cases, astable 3 illustrates.

Table 3: A Sample Contingency Table

Gender For Against Undecided Total

Male 30 61 22 113Female 81 92 28 201

Total 111 153 50 314

It is not always easy to see relationships ina contingency table merely by looking at thenumbers, especially if the numbers are largeand the totals are unevenly divided, as in thepresent case.

For this reason, the numbers typically areconverted into percentages. Table 4 shows thesame information expressed as the percent-ages of males and the percentages of femalesin the three opinion categories. (The only trickypart of the procedure is in deciding whetherto base the percentages on the row totals, as inthe present case, or the column totals; eitherway will work, but one way may make rela-tionships easier to see than the other.)

A relationship exists when the percent-ages are not the same between the rows (if thepercentages are calculated in that direction).The relationship in this example suggests thatmales are more likely to be against the schoolbudget or undecided than females, who aremore likely to be for it.

CASE 2: ONE VARIABLE IN KIND ANDONE IN DEGREE

Procedure: compare the means in a tableof means.

When a variable is measured in degree, itis possible to compute a mean (average) forthe objects measured on it. A table of meanssimply shows the averages for the objects ineach of the several categories of the kindvariable. If one were interested in the relation-ship between favorability toward the schoolbudget and gender and if favorability hadbeen measured on a scale from 1 to 10, for

20

Although there are other varieties, thecorrelation coefficient usually calculated isthe “Pearson product-moment correlation.”In fact, it is the one so often used that, unlessexplicitly stated otherwise, you can take it forgranted that a correlation coefficient is theproduct-moment correlation.

Its calculation begins by copying down,in two columns, the pair of values for eachcase. (Call the values of the age variable Xand those for the favorability variable Y forthe time being.) So if you have 314 cases,then 314 values of X should be paired with314 values of Y.

Make three more columns: one for thesquare of each X value, one for the square ofeach Y value, and the last for the “cross-product,” or X times Y. Now get out youradding machine (or abacus, if you prefer) andadd up the columns. You should end with fivesums: of the X s and Y s (SX and SY), of theirsquares (QX and QY), and of the cross-prod-ucts (XY). Along with the number of cases (N),you are ready to plug them into a formula.

The formula:

r = N X Y - S X S Y

(N Q X - S X2) (N Q Y - S Y2)

All of this is work when you have a lot ofcases. Some hand calculators do most, if notall, the arithmetic for you; you need onlypunch in the pairs of values, and the squaring,multiplying, and adding is done automati-cally—maybe even the results of the formula.Still, it isn’t easy.

A correlation coefficient:

r = -.23

There it is. The data have been reducedfrom a table to just a number. Now there’s no

x x

x

x

x

√

Table 5: A Sample Table of Means

Gender (N) Mean FavorabilityMale (113) 4.87Female (201) 6.50

Both (314) 5.91

Note: The N’s in parentheses indicate the number ofcases on which the means are calculated.

example, one would construct a table show-ing the mean favorability of the males and themean favorability of the females. The out-come is demonstrated in table 5.

A relationship exists when the objects inthe categories of the kind variable have differ-ent means on the degree variable. Here therelationship is such that females have higherfavorability values, on the average, than males.

CASE 3: BOTH VARIABLES IN DEGREE

Procedure: calculate a correlation coeffi-cient and contemplate it.

For instance, one might calculate the cor-relation between respondent age andfavorability toward the budget (measured indegree).

Thanks to the mysteries of algebra, it ispossible to come up with a number, with apotential range from -1.00 to +1.00, that de-scribes the relationship (negative or positive)between two variables measured in degree. Apositive coefficient indicates that the largerthe objects’ values on one variable, the largertheir values are likely to be on the other vari-able (a direct relationship). A negative coeffi-cient indicates that the larger the values are onone variable, the lower their values are likelyto be on the other (an inverse relationship). Acoefficient of zero means that no relationshipexists between the variables.

21

RELATIONSHIPS BETWEEN VARIABLES

need to compare three pairs of percentages ora couple of means. One number says it all: theolder the respondent, the less favorable he orshe is likely to be toward the school budget.

A scattergram provides a visual represen-tation of the relationship between variables indegree. It is constructed by drawing a hori-zontal axis for values of one variable and avertical axis for values of the other and plot-ting where each object of the study is located.It reveals a good bit about the relationshipthat you can’t see by staring at a number.

SORTING OUT THEVARIABLES IN A STUDY

A majority of the published studies youread go beyond the report of simple bivariaterelationships to examine relationships be-tween two variables, holding constant one ormore other variables in the process. As I saidearlier, this increases the study’s complexityand adds to the difficulty of doping out whatis going on in it. An introductory course instatistics offers considerable help, but a sec-ond course often is necessary to get a firmgrasp on a study’s analysis procedures. (Oc-casionally, even that is not enough.) But don’tfret too much. There are ways of bringingorder out of apparent disorder and, at least,enabling you to discern when the statisticalanalyses are truly beyond your current levelof understanding.

A big help, in studies involving a numberof variables and their relationships, is to havea way of sorting out the variables in terms oftheir standing with respect to one another.The following paragraphs provide some termsthat aid in the sorting process and lay a foun-

dation for considering how multivariate rela-tionships are examined.

INDEPENDENT AND DEPENDENTVARIABLES

The point behind many, if not most, em-pirical studies in behavioral research is toferret out causal relationships. What accountsfor teacher burnout? What are the variousconditions that affect voter turnout in schooldistrict budget elections? How do you explainthe decline in Scholastic Aptitude Test scoresover the recent decades? What are the effectsof TV viewing on children’s acceptance of sexstereotypes? Does team teaching lead to allthe good things its advocates claim for it?Why do private schools produce greater aca-demic achievement among youngsters thanpublic schools, if indeed they do? Our privateand professional worlds are full of questionsof this order, questions that entail our think-ing about the causes or the consequences ofthings. One of the principal purposes of re-search is to check out tentative answers tothem.

This being the case, we are furnished withan important basis for distinguishing amongsets of variables in research. In studies con-cerned with causal relationships, there will beone or more independent variables and one ormore dependent variables. Dependent vari-ables are those regarded by the researcher as“effects,” “consequences,” or “outcomes”—the variation that the researcher wants to ex-plain. Independent variables, then, are the ten-tative “causes,” “determinants,” or “predic-tors”—the factors the researcher proposes asexplanations.

A reasonably standard means of depict-ing a causal relationship between two vari-ables (or, better, what a researcher proposes

22

ers as causal and which he or she considersas effects. Some researchers are reluctant tolay out the causal priority of their variablesfor you, despite the fact that an order is im-plicit in the study report, so you may haveto read between the lines to find it. Oneplace they often tip their hands is at the endof the report where they talk about the im-plications of the study.

In any event, order begins to emerge asyou inspect the several variables of study andsort them by whether they are to be regardedas independent or dependent.

CONTROL VARIABLES

In one form of empirical research, theinvestigator’s attention is fixed on the causalrelationship between a particular pair of vari-ables, such as the effect of information over-load on the stress level of administrators orthe effect of voter turnout on the passage ofschool budget levies, and the basic questionhe or she wants to answer is whether or notthe relationship stands up when other vari-ables known to affect stress levels or passageof budget levies are controlled. In research ofthis form, the investigator may choose tomeasure the other variables and then holdthem constant in the course of statistical analysis.

A control variable is a variable believedto be causally related to the dependent vari-able and whose effect on it, if not counter-acted, might be mistaken for the effect ofthe independent variable. It is usually fea-sible to identify the control variables of astudy and to separate them from the pri-mary independent and dependent variables.You may find that relationships between thecontrol variables and the dependent vari-

as a causal relationship) makes use of a one-headed arrow pointing from the independentvariable(s) to the dependent variable(s):

X ———> Y

And, ordinarily in a diagram, the “direc-tion” of causality is shown as flowing fromleft to right. Independent variables are on theleft, dependent variables on the right. Two-headed arrows commonly are used to repre-sent relationships of a noncausal nature be-tween a pair of variables.

Be aware that the distinction between in-dependent and dependent variables is notinherent in the variables themselves but de-pends on the study. Thus, the principal’s lead-ership style may be used as the dependentvariable in one study (affected by, say, theyears of administrative experience) and as theindependent variable in another (affecting,say, the organizational commitment of teach-ers).

Also be clear that, when a relationship isestablished between pairs of variables in astudy, nothing in the tables nor the correla-tion coefficient tells you which is cause andwhich is effect. (This is captured in the oldsaw, “correlation does not prove causation.”)It is quite possible that an observed relation-ship is due to the common association of thetwo variables with a third, outside variablenot taken into account. Under some circum-stances, depending on the research designemployed in a study, it may be equally plau-sible to argue that causation runs in the oppo-site direction. Notions of cause and effect areimputed to the variables by the researcher.They are matters of inference and logic, not ofempirical determination.

As you read studies, usually you can fig-ure out which variables the author consid-

23

RELATIONSHIPS BETWEEN VARIABLES

able or among the control variables them-selves are presented in tables of the studyreport, but these are not of central interest.Rather, the action lies in the tables showingthe relationship of independent and depen-dent variables with the control variables heldconstant.

INTERVENING VARIABLES

In certain studies, a third variable comesinto play not as a control variable but as anintervening variable. In general, an interven-ing variable is offered as an explanation ofhow an independent variable comes to haveits effect on a dependent variable. It implies achain of causal relationships:

X ———> IV ———> Y

Variation in X leads to variation in IV,which, in turn, leads to variation in Y. That is,the known (or discovered) effect of X on Y ispresumed to operate through the interveningvariable; X does not affect Y directly. Forinstance, a researcher interested in under-standing why the presence of a teacher ’s aide(X) enhances the academic performance ofstudents (Y) may propose “amount of indi-vidualized instruction” as an interveningvariable (IV). The argument would run thatthe presence (versus absence) of a classroomaide increases the amount of individualizedinstruction received by students and that it isthe individualized instruction that enhancesstudent performance, not the presence of anaide per se. (That the aide is not expected toaffect performance directly is indicated bythe fact that there is no causal arrow betweenX and Y.)

Empirical support for the argument canbe obtained by observing that the original

relationship between X and Y disappears whenIV is held constant in statistical analysis.

CAUSAL MODELS

The idea of causal chains in the precedingdiscussion can be extended to include morevariables, longer chains, and a more elaborateset of relationships hypothesized among thevariables. The set of variables and relation-ships is commonly called a “causal model,”“path model,” or “structural equation model.”A perusal of research journals in the last fiveto ten years, especially in sociology, politicalscience, or economics, is bound to uncover anumber of illustrations.

Sorting variables by their designations asindependent, dependent, control, or interven-ing does not work in elaborate causal models.A given variable may be all four in differentfacets of data analysis. Normally the variablesare clearly displayed in a diagram so thereader can keep track of their standing withregard to one another. However, rather so-phisticated statistical procedures are requiredto test whether or not the observed relation-ships conform to the hypothesized model,and the novice researcher should not be dis-concerted by the difficulty of figuring outwhat is going on.

MODERATOR VARIABLES

Every so often you will hear reference tothe term moderator variable. It takes part inwhat is called a “contingent” or “conditionalrelationship” or, more generally, an “inter-active effect.” (See the last section of chapter4 for more about contingent relationships.)A moderator variable is one that is said toalter (or moderate) the relationship betweenan independent (X) and a dependent (Y) vari-able. More specifically, the relationship be-

24

turned around to unravel the nature of thevariables employed in a study. After lookingat a study’s title and glancing through itsabstract to get an idea of the key variables, Ioften turn directly to the tables in the “Re-sults” section. While the following clues arenot infallible, they work a lot of the time.

1. If the important tables consist of per-centages, you can be reasonably surethat all variables are measured in kind.

2. If the important tables are tables ofmeans, you have a good inkling thatthe dependent variable is measured indegree and that the independent vari-ables, or most of them, vary in kind.

3. When the central tables show correla-tion coefficients, you can pretty wellfigure that all of the variables are mea-sured in degree. (However, there isslippage here; a correlation coefficientcan legitimately be calculated betweenan X variable in kind and a Y variablein degree if the X variable has just twovalues.)

In making your inspection, try to singleout the important tables—the ones that es-tablish the relationships between the keyvariables. An article for a research journalmay contain a half-dozen or more tables, onlyone or two of which actually examine rela-tionships. The others may present prelimi-nary information, such as characteristics ofthe subjects of study, details of the measuresof particular variables, and so forth. Don’tbe shocked if you find the tables in utterdisarray; not all researchers know what theyare doing.

tween X and Y will be different, dependingon the value of the moderator variable (W).Under certain values of W an X-Y relation-ship will appear, but under other values ofW there would be no relationship betweenX and Y, or even an opposite relationship.

An example will help. One popular theoryof job redesign in business management pro-poses that an increase in the “skill variety”provided by a job will increase the “job satis-faction” of workers, but only for workers whohave a strong “growth need.” If a worker haslittle “growth need,” enhancing the job’s skillvariety will have no effect on his or her satis-faction level. “Growth need strength” is themoderator variable here (W). In effect, thetheory says that there will be a direct relation-ship between the extent of a job’s skill variety(X) and worker satisfaction (Y) when the valueof W is high but no relationship between Xand Y when the value of W is low.

Statistical analyses to detect the operationof moderator variables follow the same pro-cedures, for the most part, as those employedin holding third variables constant. The dif-ference lies in what one looks for in a percent-age table or a table of means. When the X, Y,and W variables are all in degree, though, aslightly more intricate correlational proce-dure is required. (From the standpoint ofsignificance tests, the researcher looks for astatistically significant interaction in the analy-sis.)

TURNING IT AROUND:ASSESSING THE MODE OFVARIATION FROM THEDATA ANALYSES

The discussion of how one examines rela-tionships between variables often can be

25

ANATOMY OF THEHYPOTHESIS

C H A P T E R 4

• How to locate and dissect hypothesesin published studies. (A specially designeddissection table is available for use.)

• How to specify the relationship ex-pected between two variables (there are twoways, depending on whether both variablesare in degree or whether one is in kind).

• What the “unit of analysis” is and thetricky problems it creates.

• Why ceteris paribus always dangles atthe end of a causal hypothesis, even if itdoesn’t appear in print.

• What the “null hypothesis” is (a pre-diction that two variables will not be relatedbeyond chance) and where it belongs in re-search (when a test of statistical significanceis about to be run).

• What kinds of hypotheses implicatemore than two variables at once.

THIS CHAPTER IS ABOUT THEhypothesis, also known as the “conceptual,”“substantive,” or “working hypothesis.” It isthe researcher’s prediction about, or expec-tation of, a relationship between variables.The “null hypothesis,” which you may haveheard about in a statistics course, is some-thing else again, as I’ll talk about later.

In its elementary form, the hypothesisconsists of two variables and a specificationof the relationship (normally a causal rela-tionship) that is expected to hold betweenthem. Attached to the end of every hypoth-esis is the phrase ceteris paribus, which is theLatin for “other things being equal.” A morecomplex (nonelementary) form of the hy-pothesis implicates three variables. Since itis becoming more and more popular in re-search, I will discuss it at the end of the chap-ter. So, count on hearing about:

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FINDING AND DISSECTINGHYPOTHESES

Hypotheses set forth early in a researchproject are wonderful guides for the investi-gator. Among other things, they point to thekey terms that require conceptual definitions,provide the occasion to consider and select anappropriate research design, indicate the needfor collecting data and constructing measuresrelevant to each of the variables, and direct theresearcher through the business of collatingand analyzing data so that he or she does notget lost in a maze of incidental or inconse-quential issues.

FINDING HYPOTHESES

In published reports of studies, the hy-potheses normally appear in the opening sec-tions along with the line of reasoning thatgave rise to them.

They represent the end product of theresearcher’s “conceptualization” of the prob-lem under investigation. (They may even belisted and numbered.) And the author mayallude to them again in the “Discussion” sec-tion of the report.

In perhaps one-half to three-quarters ofthe studies you read, though, depending onyour field of interest, you won’t find any hy-potheses stated explicitly. Then it is up to youto reconstruct them. How? Read the reportcarefully for what the author says was thepoint of the study. The author’s discussion ofthe findings or phrasing of the study conclu-sions may reveal what he or she had in mind.Pick out the key variables and inspect thepresentation of results, including the tables, tosee the relationships that were examined. Tryto figure out which variables the researcherregarded as causal, which ones as effects, and

which ones, if any, were used as control vari-ables. Once you have put all this together, it isentirely possible that you won’t be able to tellwhat expectations the researcher had aboutthe way the relationships would come out.He or she may just have been “looking.”

But if there are any implicit hypotheseslurking around in the research, the chancesare good that you can uncover them and statethem with a fair degree of fidelity.

A word of warning. If hypotheses arestated in the research report, don’t count onthem being in the proper form. Only a mi-nuscule fraction of researchers have read thismanual or one like it, and you are bound tofind plenty of pathological specimens. Thenext chapter will help you spot them.

DISSECTING HYPOTHESES

Anatomically speaking, the hypothesisconsists of three parts: two variables and anunequivocal statement of the relationship ex-pected between them. By now you shouldhave a rough understanding, at least, of thenature of variables, including their two basicmodes of variation, how you describe themfully, and the distinction between indepen-dent and dependent variables.

Thus, the tools you need for dissectinghypotheses into their components are mostlyin your hands.

The steps in dissecting a particular hy-potheses are these:

1. Identify the two variables and sortthem into independent (X) and de-pendent (Y).

2. Describe each variable separately, fol-lowing the procedures outlined inchapter 2 (pages 8-10). When the

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diction (ideally based on a priori reasoning),even though, at the same time, the researcherregards it as a tentative prediction.

In general, sentences that state hypoth-eses come in two varieties, depending onwhether the mode of variation of the inde-pendent variable is in kind or in degree. Theillustrations below represent one of each va-riety.

You might wonder why there isn’t a thirdvariety suited to situations where both vari-ables are in kind, since the previous chaptermade a big deal out of examining relation-ships of that sort. As we’ll see shortly, in suchsituations a dependent variable in kind hasto be jiggled around to make it sound like avariation in degree before a hypothesis canbe phrased succinctly.

Following are illustrations of the word-ing of hypotheses, the first where the inde-pendent variable varies in kind and the sec-ond where it varies in degree.

H-1. Academic achievement will begreater among pupils taught byautocratic teachers than amongpupils taught by permissiveteachers, cet. parib.

H-2. The greater the size of a commu-nity college’s instructional fac-ulty, the greater the centraliza-tion of decision making with re-gard to course offerings, cet. parib.

Consider the structure of the two sen-tences. H-l is a comparative statement: thesentence compares the values on the depen-dent variable, “academic achievement,” ex-pected between the two categories of theindependent variable, which we might call“teaching style.” The categories are “auto-

ANATOMY OF THE HYPOTHESIS

mode of variation is in kind, list thecategories and label them Xa, Xb, Xc,etc., or Ya, Yb, etc.

3. Specify unambiguously the relation-ship expected between the two vari-ables.

4. Note the unit of analysis implied oractually used.

Use the dissection table provided belowfor each hypothesis you take apart. In the nexttwo sections I will explain steps 3 and 4.

Table 6. Dissection Table for Hypotheses

Hypothesis #:

X Variable Y Variable

Variable Name:

Mode of Variation:

Elaboration:

Specification ofRelationship:

Unit of Analysis:

SPECIFYING EXPECTEDRELATIONSHIPS

A hypothesis must specify precisely andunequivocally how variation among the ob-jects under study with respect to the indepen-dent variable is expected to relate to theirvariation on the dependent variable. The pre-diction cannot dilly-dally around or leaveanything to the reader’s imagination. It is notsufficient to say that two variables are ex-pected to be related; the hypothesis must de-scribe exactly how they are expected to relate.A working hypothesis makes a definite pre-

28

equality signs. A > B means A is greater thanB, while A < B means A is less than B. A=Bmeans what it looks like. The third alterna-tive is a further shortcut. Since you have al-ready labelled “academic achievement” as Y(I hope) in sorting the variables for the up-per portion of the dissection table, just makethe substitution and save yourself ink. Thesymbol “Y:” stands for the phrase, “with re-spect to academic achievement.”

Incidentally, these ways of symbolizingrelationships are purely my own invention. Ifyou were to express a hypothesis using all thisshorthand and took it down the hall to thelocal expert in research methodology, he orshe would have no idea of what it meant. Thesole purpose of it is to help you keep yourideas in order.

Consider a hypothesis in which the inde-pendent variable consists of three categories:

H-3. College students will developgreater critical thinking skills inself-directed study groups than ininstructor-led recitation sections,while students in lecture sectionswill develop the least critical think-ing skill, cet. parib.

If we acknowledge “critical thinkingskills” as the Y variable (in degree) and labelthe categories of the X variable as Xa “self-directed study groups,” Xb “instructor-ledrecitation sections,” and Xc “lecture sections,”then the expected relationship expressed inthe hypothesis can be concisely written as Y:Xa > Xb > Xc. Table 7 shows how this hy-pothesis appears when stretched out on thedissection table.

Suppose the reasoning regarding the wayinstructor-student interaction in the teaching

cratic teachers” and “permissive teachers,”and they represent a variation in kind. Thetipoff phrase in sentences of this variety is“greater than” something or “less than” some-thing.

The sentence in H-2 does not compare onecategory against another. Rather, it states thatthe values of one variable, “centralization ofdecision making,” will be greater as the val-ues of the other variable, “faculty size,” aregreater. In this case the independent variableis in degree. Here the tipoff is the structure,“the greater” one thing, “the greater” theother or “the greater” one thing, “the lesser”the other.

That’s the heart of the matter. Next, somemechanics of specifying the relationships.

INDEPENDENT VARIABLE IN KIND(DEPENDENT IN DEGREE)

What would you write down in the dis-section table after “Relationship:” for H-l?You could simply rewrite the entire sentencethat states the hypothesis, but that would be awaste of time and wouldn’t help in layingbare the anatomy of the hypothesis. Here arethree successively more economical ways ofdoing the same thing. They assume you havefollowed instructions and have given labelsof Xa and Xb to the two categories of theindependent variable, “teaching style.”

Relationship: Academic achievementwill be greater for Xa thanfor Xb.

Relationship: With respect to academicachievement, Xa > Xb.

Relationship: Y: Xa > Xb.

The second and third alternatives makeuse of the mathematical convention of in-

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ANATOMY OF THE HYPOTHESIS

Table 7. Dissection of H-3

Hypothesis #: H-3

X Variable Y Variable

Variable Name: Instructional interaction Critical thinking skill

Mode of Variation: Kind Degree

Elaboration: Xa self-directed study group Lo to hi skill level

Xb instructor-led recitation

Xc lecture section

Specification ofRelationship: Y: Xa > Xb > Xc

Unit of Analysis: College student

situation is thought to affect the developmentof thinking skills had led to a different predic-tion:

H-4: College students will developgreater critical thinking skills ininstructor-led recitation sectionsthan in self-directed study groupsor in lecture sections.

(I’m going to omit the cet. parib. qualifica-tion in the remainder of the specimens. Re-member that it is always there. More will besaid about this qualifying phrase on page 36.)

In this version no prediction is made be-tween self-directed study groups and the lec-ture condition but only that the instructor-ledrecitation condition will be superior to both.This would express the prediction exactly:

Relationship: Y: Xa < Xb > Xc

The symbolization, like the hypothesis,says nothing about the Xa-Xc comparison.

It may now be more apparent why I in-sisted that you list and label all the relevantvalues, or categories, associated with vari-

ables whose mode of variation is kind. It isimportant to do so even if there are just twocategories. It permits you to specify relation-ships with precision.

INDEPENDENT (AND DEPENDENT)VARIABLES IN DEGREE

Specifying relationships when both theindependent and dependent variables are indegree is reasonably simple. You declare iteither a “direct” or an “inverse” relationship.(This corresponds to a “positive” or “nega-tive” correlation in statistical language.)

A direct relationship predicts that thegreater the value of X, the greater will be thevalue of Y. (This is synonymous with sayingthe lesser the value of X, the lesser will be thevalue of Y.) An inverse relationship predictsthat the greater the value of X, the lesser thevalue of Y (which automatically implies thelesser the X, the greater the Y). Here are somealternative phrasings:

Direct: The larger the X, the larger the Y.As X decreases, Y decreases.The more the X, the more the Y.

30

Inverse: The larger the X, the smaller the Y.As X increases, Y decreases.The less the X, the more the Y.

To illustrate, one of the following speci-mens predicts a direct relationship, while theother predicts an inverse relationship.

H-5. The more supportive a supervisoris to a teacher, the more support-ive the teacher will be to his/herpupils.

H-6. The larger the school’s faculty, thefewer intimate friends a teacherwill have among his or her col-leagues.

Placing these hypotheses on the dissec-tion tables, you will first identify the vari-ables, declare them in degree, and elaborateon “degree of what?” Then you need onlyproclaim “direct” for H-5 and “inverse” for H-6 in specifying the relationship. For Heaven’ssake, don’t allude to any categories, like Xa orXb, because they don’t exist when the vari-ables are in degree.

All this is pretty straightforward. How-ever, troubles can come in two ways. Whethera relationship is direct or inverse depends onthe name you or an author uses for the vari-ables. Consider this specimen:

H-7 The greater a citizen’s sense ofpowerlessness in political affairs,the stronger will be his or her op-position to school-district budgetreferenda.

It expresses a direct relationship. It be-comes an inverse relationship, though,merely by rewording one of the variables,by changing “sense of powerlessness” to

“sense of power” or by changing “opposi-tion to” to “support for.” For instance:

H-8. The greater a citizen’s sense ofpower in political affairs, theweaker will be his or her opposi-tion to school-district budget ref-erenda.

It’s the same idea, but the expected relation-ship has switched.

The second trouble is closely akin to theforegoing. It has to do with the direction thenumerical values that are associated withvariations in degree run. (I went into this inchapter 2, page 13.) The assignment of nu-merical values, or the calculation of scores, isan arbitrary matter insofar as their direction isconcerned, and whether big numbers mean abig amount of the property or a little amountof it is often determined more by the ease ofcomputation than by anything else. It is pos-sible that, in a given study, the numericalvalues run in a surprising direction. The fol-lowing hypothesis provides the basis for anexample:

H-9. The longer the time a student isexposed to math instruction, thegreater will be his or her achieve-ment in math.

Suppose, in a study testing the hypoth-esis, a researcher had access to informationregarding student absences and used it tomeasure “amount of exposure to math in-struction.” Unless the researcher went to thetrouble of subtracting days absent from thenumber of days in the school year, the direc-tion of the values would no longer faithfullyreflect the variable as it is presently named.Bigger numbers (more days absent) would

31

mean smaller amounts of math instruction,and support for the hypothesis would be dem-onstrated by a negative correlation coefficient,that is, by evidence of an inverse relationship,not a positive correlation as you would other-wise anticipate.

In general, the analyst of the hypothesismust be sensitive to the direction of the nu-merical values in variables in the degreemode. That’s why I encourage you to includea phrase like “lo to hi...” in your elaborationof them. In this day and age of computerizeddata processing, it is not hard for research-ers, too, to lose track of the direction of scoreson their measuring instruments, and once ina while they forget to include that little com-mand in the computer program that makesthem run in the intended direction. The con-sequences can be devastating. I know!

Before finishing the discussion of vari-ables in degree, I’ll add a word about curvi-linear relationships. They don’t arise oftenenough in hypothesis statements for me todwell on them, but you should be forewarnedabout them. The expected relationship is nei-ther direct nor inverse but, rather, somethingmore exotic. A real, live example comes fromresearch on the relationship between anxietylevel and task performance. Studies haveshown that as a person’s anxiety increases,task performance improves—but only up tosome intermediate level of anxiety. Beyondthat level, increasing anxiety produces dec-rements in performance. Plotted on a graphwith anxiety level as the horizontal axis andperformance level as the vertical axis, therelationship would look like an upside-downU. The relationship is direct up to a point,then becomes inverse. There are many othershapes a curvilinear relationship might take

ANATOMY OF THE HYPOTHESIS

(an exponential curve, a growth curve, etc.),but I promised not to dwell.

WHAT IF BOTH VARIABLES ARE INKIND?

Expectations regarding the way the datawill fall in a percentage or contingency tablewith three or more columns and three ormore rows are so difficult to express (or evento think about) that researchers assiduouslyavoid them. It is hard to state a precise hy-pothesis before running out of breath in sucha circumstance, since it requires specifyingexpected differences between nearly everypair of cells vis-a-vis every other pair of cells.

If the dependent variable consists of justtwo categories, however, there is a neat andcommonly used trick available that makes itsound as though the kind variable were indegree. It amounts to expressing the propor-tion or percentage of cases expected in one ofthe categories of the dependent variable andmaking a prediction about differences in thepercentages among categories of the inde-pendent variable. I’ll use an illustration tomake this more transparent.

H-10. Teacher separations from theschool district will be greateramong teachers who received theirtraining in universities than amongthose trained in teachers colleges.

The independent variable (“location oftraining”) is in kind, right? Right. The depen-dent variable (“separation from the schooldistrict”) is in degree, right? Wrong! A giventeacher either separates or doesn’t separatefrom the school district, clearly a variation inkind.

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What’s going on here? The sentence stat-ing the hypothesis has a comparative struc-ture, and it contains the tipoff phrase,“teacher separations . . . will be greateramong,” suggesting that the dependent vari-able is in degree. (See page 28.) What’s go-ing on is that, because the categories of thedependent variable are of an either-or vari-ety, the percentage of “separating teachers”automatically implies the percentage of“nonseparating teachers,” and it isunnecesary to mention the latter. The de-pendent variable now looks like a variationin degree, with values running from “lowpercentage separating to high percentageseparating.”

This is an extremely common practice inresearch. Actually, the hypothesis would havebeen clearer if it had contained a phrase like“separation rate,” “incidence of separation,”or “percentage of separations” instead of sim-ply “teacher separations.” That would havemade the nature of the dependent variablemore apparent.

It wouldn’t matter much if, in dissecting ahypothesis like H-10, you were to declare thedependent variable as varying in degree. Ex-cept for one thing! The statistical treatmentused for analyzing data where both variablesare in kind is altogether different from thestatistics for data where one of the variables istruly in degree. Contingency or percentagetables require different inferential statisticsthan tables of means. This is beyond the scopeof the manual, but if you are seriously pursu-ing research, you will find out about it sooneror later. In any event, do . . . repeat, do . . . makea note on your dissection table when you findthat a kind variable has been jiggled into onethat sounds like one in degree.

THE UNIT OF ANALYSIS

Unit of analysis is the name we will hence-forth use instead of “objects of study” to referto the persons, things, or events that a re-searcher seeks to explain or understand andthat represent the focus of an investigation.

Why the switch from the language ofchapter 2? In explaining about variables backthen, it seemed helpful to distinguish be-tween objects and their properties, a fairlystraightforward idea that could be under-stood without relying on technical terms.Hypotheses, though, concern linkages be-tween variables, not variables in isolationfrom one another, and ambiguities or otherproblems arise when there is not a clear cor-respondence between the objects of the linkedvariables. Recall from chapter 3 one of thethings I said must be true in order to examinerelationships between variables: “each objectunder investigation must have been mea-sured or otherwise assigned a value on bothvariables” (page 18). This implies that bothvariables are properties of the same object. InH-7: for instance, the two variables, “sense ofpowerlessness” and “strength of oppositionto budget referenda,” are two properties of a“citizen.” This is quite uncomplicated; theunit of analysis is “the citizen.” H-2 is simi-larly uncomplicated, though the unit of analy-sis is no longer a person but a larger entity:“size of instructional faculty” and “extent ofcentralization” are two different propertiesof “the community college.”

Now try the following hypothesis:

H-11. The greater the amount of infor-mation contained in a graphic dis-play, the larger the number of er-

33

rors students will make in imme-diate recall.

Matters are not so clear. One of the vari-ables, “amount of information,” seems to bea property of a “graphic display,” while “re-call errors” is a property of a “student.” Theyare not properties of the same object! Whatbrings them together, though, is the implicitnotion that students are exposed to thegraphic displays (they literally see them), andin this sense the amount of information inthe perceived display can be considered aproperty of students. Or the emphasis mightbe turned around. The researcher could bemore interested in graphic arts than studentlearning and regard “the display” as the unitof analysis—displays as seen by students. Thedifference is a subtle one, but in either case,the properties would attach to the same ob-jects.

THE N OF CASES

The number (N) of cases used in a studyis closely associated with the unit of analy-sis. In fact, one of the surest ways of discov-ering what the investigator considered hisor her unit of analysis is to look at the datapresentations for the N on which the statisti-cal relationships are based. The N shouldcoincide with a count of the units.

To keep things straight as you analyzehypotheses found in actual studies, you woulddo well to write down the N of cases in thedissection table, following your designationof the unit of analysis. If 114 citizens werestudied in connection with H-7, write N=114after designating “the citizen” as the unit ofanalysis. If, in connection with H-2, the corre-lation between faculty size and centralizationwere calculated for 23 community colleges,

make the N part of your record. Although weshan’t go into it, the interpretation of statisti-cal analyses depends heavily on the adequacyof the N.

LEVELS OF ANALYSIS

Some of the hairiest problems of researchhave to do with variables at several differenthierarchical “levels.” The issue concerns theproper unit of analysis. Consider H-1 again,repeated here for convenience.

H-1. Academic achievement will begreater among pupils taught beautocratic teachers than amongpupils taught by permissive teach-ers.

Suppose a study were conducted to testthe hypothesis using two intact classroomsof 20 students each. The teacher of one ischosen for being autocratic, the teacher ofthe other for being permissive. (Teachers andstudents are at two different levels—oneteacher per 20 pupils.) What is the properunit of analysis? It would be feasible, forinstance, to calculate an average achievementlevel for the students in each class (a proce-dure technically called “aggregation”) andcompare the means between the teachers.That would yield an N of 2, clearly too smallfor statistical interpretation. Or should oneconsider “the student” as the unit of analy-sis, yielding an N of 40? (It would help, ofcourse, to include more teachers in the study,along with their students, but the issue ofthe proper unit of analysis would remain.)

I mention the problem without resolvingit. It is a matter of considerable debate thesedays among educational research method-ologists. Achievement scores of individualstudents, for instance, can be aggregated to

ANATOMY OF THE HYPOTHESIS

34

“Other things being equal” does notmean that the cars must be identical in everyconceivable respect except for engine design.Such a condition is literally impossible tomeet. Rather, the phrase means that they arealike only in ways (other than engine de-sign) that reasonably could affect gas mile-age. An investigator would hardly need tocertify that the heater controls were in theexact same location, for example, or that thecars all had a fleck of paint missing from theright rear fender or that the test driver hadzipped his or her jacket with precisely thesame hand motion in each test. “Otherthings” means other relevant things, that is,other causes, known or unknown, of the de-pendent variable.

The novice researcher would do well tohang cet. parib. on his or her hypotheses, atleast until it gets to be terribly repetitive andboring. It might serve as a reminder to giveserious thought to the “other relevant things”in the objects of study and the testing condi-tions that might affect the dependent variableand to devise plans to keep them constant orotherwise control for them.

A NOTE ON THE NULLHYPOTHESIS

The so-called “null hypothesis” plays adistinctive role in the research process andshould not be mistaken for the substantivehypothesis discussed throughout themanual. Whereas the latter makes a defini-tive prediction concerning the relationshipbetween the independent and dependentvariables, the null hypothesis asserts that norelationship will exist between them beyondthat which could arise by chance.

the classroom level, to the school level, andto the district level, maybe even higher, andeach of these could serve as the unit of analy-sis. I can only warn you that substantial is-sues, both substantive and statistical, are as-sociated with the levels of aggregation andthe unit of analysis.

THE INVISIBLE CETERISPARIBUS

Fewer than one hypothesis in 50 that yousee in the flesh will have the phrase ceterisparibus printed at the end, and yet, whetherthe author knows it or not, it is always there.One of the basic tenets of the philosophy ofscience is that any phenomenon has numer-ous causes, not just one— the principle of mul-tiple causation. The Latin for “other thingsbeing equal” is the scientist’s way of ac-knowledging the existence of other causeswhile focusing on one of them. Consider thishypothesis:

H-12. Automobiles with rotary engineswill get better gas mileage thanautomobiles with piston engines,cet. parib.

Here the phrase means that the hypoth-esis is expected to told true if all the otherthings that affect a car’s gasoline consump-tion are equal, or constant. These other thingsmight include the weight of the automobile,the amount of wear on the engine, the kindof gasoline used, the speed it is driven, andso forth. The hypothesis predicts that, withall these other factors constant, the enginedesign itself will be found to affect gas mile-age as specified.

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Both of these seemingly contradictory hy-potheses are involved in studies testingcause-effect relationships. The substantivehypothesis is phrased early in the researchprocess. Ordinarily it is derived from, or itconnects with, a line of reasoning about thephenomenon under investigation, and itguides the researcher, as I have mentioned,in planning and conducting the study. Byembodying a definite (albeit tentative) pre-diction, it requires the researcher to thinklong and hard about alternative hypothesesand about the “other relevant things” thatneed to be constant in order to draw a stronginference that his or her reasoning is on theright track.

The null hypothesis, on the other hand,comes into play late in the research process, atthe point where a test of statistical signifi-cance is about to be applied to the relationshipobserved between the variables. In the courseof conducting a study, for instance, regardingthe superiority of rotary engines over pistonengines in gasoline consumption (H-12), therecomes a time when the gas consumption ofthe two sets of cars has been determinedunder equivalent testing conditions and therelationship has been displayed in a table ofmeans (one variable in kind and one in de-gree). The vital question now facing the re-searcher is whether the difference in the meansbetween the two sets of cars could have arisensimply by the workings of chance or whetherthe difference is so large that it is unlikely tohave been the product of pure chance, and asignificance test is in order. Enter the nullhypothesis.

Without going too deeply into the matter,suffice it to say that statistical theory allowsthe researcher to calculate the probability that

ANATOMY OF THE HYPOTHESIS

the observed difference could have been amatter of chance. (Even a large difference ingas mileage between the sets of cars couldarise by chance, though the probability of ithappening would be very low. In general, thesmaller an observed difference, the greaterthe probability that it occurred by chancealone.) The researcher selects a probability(or significance) level at the study’s begin-ning to use in deciding whether or not ob-served differences fall within the bounds ofchance. The .05 level is a common criterion,meaning that any difference that could occurfewer than 5 times in 100 is unlikely to havebeen the product of pure chance.

The researcher then proceeds to do thecalculations and to test the null hypothesis,the hypothesis that the difference was withinthe bounds of what he or she chose as thecriterion of chance. One of two answerscomes from the significance test: (1) the ob-served difference in gas mileage was notlarge enough to exceed the criterion ofchance—the researcher accepts the null hy-pothesis; (2) the difference was too great toregard as due to the workings of chance—the researcher rejects the null hypothesis. Forexample, let’s say the group of rotary en-gine cars averaged 50 miles per gallon andthe group of piston engine cars averaged 40miles per gallon. Using a .05 criterion level(p<.05), the null hypothesis would be ac-cepted if calculations showed that a differ-ence of that size could occur by chance alonemore frequently than 5 times in 100. How-ever, if calculations indicated that the differ-ence of 10 miles per gallon would occur bychance alone fewer than 5 times in 100, thenull hypothesis would be rejected.

When you get right down to the nitty-gritty of empirical research, the only thing

36

the researcher does is to accept or reject nullhypotheses. And even that is an “iffy” busi-ness, since null hypotheses are hedged withprobabilities. To make things worse, the nullhypothesis is rarely interesting. What theresearcher is interested in is the substantivehypothesis and the correctness of the rea-soning that lies behind it. Yet the null hy-pothesis is silent with respect to such rea-soning. Rejection of the null hypothesis doesnot affirm the truth of the substantive hy-pothesis. Just because a difference was toogreat to be attributable to chance (at a givencriterion level), the researcher does not knowfor certain what did produce the difference.The point is important enough to repeat:Rejection of the null hypothesis does not auto-matically imply acceptance of the substantivehypothesis!

So what about the substantive hypoth-esis? How in the world do you get back toit? You can only get back to it by way ofinference. You do your best to arrange theconditions of the study to eliminate as manycompeting hypotheses or alternative expla-nations of the relationship as possible. Youplan your observations so that, once the nullhypothesis is rejected, the most reasonableinterpretation is the one expressed in thesubstantive hypothesis. The confidence youcan place in the substantive hypothesis andits underlying conceptualization depends onthe strength of this inference (often referredto as the “validity of inference”). In the end,one never proves a substantive hypothesis,in the ultimate sense of proof. One only gainssupport for it—an increment of confidencein it.

So both substantive and null hypothesesplay a part in research, the substantive hy-pothesis giving guidance and meaning to the

entire research process and the null hypoth-esis appearing at the juncture when statisticaltests of significance are applied to the data.

HYPOTHESES INVOLVINGTHREE OR MOREVARIABLES

While this chapter (and the next) dealswith the elementary form of the hypothesis,involving two variables, a word is in orderabout more complicated forms with three ormore variables.

COMBINED HYPOTHESES

The first, which for want of a better term Icall a combined hypothesis, is not really compli-cated at all. It merely strings together a seriesof elementary hypotheses in one sentence.When two or more elementary hypothesesshare a common independent (X) or depen-dent (Y) variable, an author may combinethem for the sake of saving space or reducingredundancy.

H-13. Twelve-year-old boys who aremembers of the Boy Scouts aremore courageous, courteous, andkind than boys who are not mem-bers of the Scouts.

“Courageousness,” “courteousness,” and“kindness” are three Y variables varying indegree that share the common X variable,“Boy Scout membership,” present versus ab-sent. A less facetious specimen:

H-14. Per-pupil expenditure of a schooldistrict (Y) is directly related to(1X) the assessed valuation ofproperty in the district, (2X) theproportion of the labor force inwhite-collar occupations, and (3X)

37

ANATOMY OF THE HYPOTHESIS

the concern for education amongadult citizens and is inversely re-lated to the proportion of theschool-age population in church-related private schools, cet. parib.

Four elementary hypotheses share thesame Y variable. You would expect to find atest of each of these predictions in the “Re-sults” section of the research report, perhapsusing a multiple regression technique.

In your early attempts to dissect hypoth-eses, you would lay them out one at a time onthe dissection table.

PREDICTION OF CONTINGENTRELATIONSHIPS

Truly more complicated are hypothesesthat predict contingent relationships betweenvariables. They involve an X variable, a Yvariable, and a “moderator” variable, as de-scribed in chapter 3, pages 23-24. Indeed, thatsection gave an illustration from the theory ofjob redesign. You should review the section,but I will run through an explanation again tofirm it in mind.

It is easiest to explain the idea of contin-gent relationships (and, indeed, to state ahypothesis regarding them) if we consider theX and the W variable to vary in kind, al-though, in principle, one or both of them canvary in degree.

This complex hypothesis predicts that therelationship between X and Y will differ, de-pending on the particular value the objects ofstudy have on the W variable. It says that therelationship between X and Y will be such-and-such when the W variable’s value is Wa,but the relationship will be something elsewhen the value is Wb. To make this concrete,

let’s pick apart the following hypothesis of acontingent relationship.

H-15. Leaders (Xa) of informal groupswill be more accurate (Y) than non-leaders (Xb) in estimating the opin-ions of group members on issuescentrally relevant to group func-tioning (Wa), but leaders (Xa) willnot differ from nonleaders (Xb) intheir accuracy of estimating theopinions of group members on is-sues irrelevant to group function-ing (Wb).

I have tried to help you locate the vari-ables in the web of words by symbolizingthem. You may be able to find the three onyour own. “Accuracy in estimating opinionsof group members” would be one—the de-pendent variable (varying in degree). An-other variable would be something like “lead-ership status,” with the two categories of Xa“leader” and Xb “nonleader.” The W variableconcerns the “relevance to group function-ing” of the issues on which the estimation ofaccuracy is made, with Wa representing “cen-trally relevant issues” and Wb representing“irrelevant issues.” If we were to express thepredicted relationships using the symbols pre-sented earlier, they would look like this:

Relationship: Y: Xa > Xb [for Wa]

Y: Xa = Xb [for Wb]

Thus, the relationship between X and Y isexpected to be “contingent” on the value of W.

The statistical procedure for testing a hy-pothesis of this order entails more than check-ing two relationships separately. From thestandpoint of significance testing, it also re-quires a test of whether the magnitude ofrelationships differ from one another by some

38

value greater than chance. In statistical par-lance, it is called testing for an “interaction.”

Following is another hypothesis predict-ing a contingent relationship, with the vari-ables and their categories again highlightedin parentheses.

H-16. High redundancy in lectures in anintroductory statistics course (Xa),in contrast to low redundancy (Xb),will lead to greater retention ofcourse content (Y) among studentswith weak backgrounds in math(Wa), while high redundancy inlectures (Xa) will produce less re-tention of course content (Y) thanwill low redundancy (Xb) amongstudents with a strong math back-ground (Wb).

In this instance, the hypothesis predicts thatthe redundancy variable has just the oppositeeffect on learning for the two kinds of student.

Contingent relationships have become in-creasingly prominent in behavioral and edu-cational research in recent years. A wholeline of research in the psychology of teach-ing, for instance, has developed around whatis called the “aptitude-treatment interaction”(ATI for short)—the idea (like the one ex-pressed in H-16) that the effectiveness of in-structional techniques is contingent on theaptitudes or other attributes of the student.Social psychology has produced a numberof contingency theories of leadership, pro-posing that the style of leadership effectivein promoting group productivity when thegroup is composed one way will not be aneffective style when the group is composeda different way. Industrial psychologists havedeveloped theories holding that the effects

of various working conditions or work set-tings on worker satisfaction are contingenton the basic motivations of the workers ex-posed to those settings. Other theories pre-dict that people behave in certain ways whentheir personal attributes “match” character-istics of the situation in which they find them-selves and in other ways when there is a“mismatch” between personal and situationalcharacteristics. On inspection, such theoriesturn out to involve predictions of contingentrelationships.

Other examples could be given, but nowwe must turn to pathologies of elementaryhypotheses.

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C H A P T E R 5

PATHOLOGY OF THEHYPOTHESIS

anatomy and have honed your dissectionskills.

A more important reason for learningabout the pathology of the hypothesis thanbeing able to pick apart someone else’sphrasings of them, I believe, is being able tophrase your own in proper fashion. Hypoth-eses contract sundry diseases that preventthem from growing into proper form. Im-proper hypotheses can prove fatal to yourresearch project.

The diseases fall into two major classes—those that afflict variables and those that at-tack specifications of relationships. I’ll takethem up according to the following outline:

1. Malformations of the variable

A. Only one variable

B. Absence of a comparison

C. Unknown categories

AUTHORS OF RESEARCH REPORTSevery now and again serve up sentences theysay are hypotheses but aren’t, at least as I havedefined a proper hypothesis. It may be thatthe author knows perfectly well what a properhypothesis is but doesn’t worry as much as Ido about stating it in the “right” way. Or itmay be that the author doesn’t know muchabout research. (Nearly 90 percent of the pub-lished research in our field, according to sev-eral estimates, represents the first and the laststudies the authors will ever conduct, so youcan see that most of what you read is theproduct of a novice.)

The crucial clinical test of a hypothesis inproper form is whether or not you can stretchit out on a dissection table and find all its partsin working order. If something is missing, youcan consider it defective. The test is only valid,of course, to the degree you know your

40

2. Abnormalities in specifications of re-lationships

A. A question only

B. Assertion only that a relationshipexists

C. Assertion that no relationshipexists

As you will see, these are not clear-cutcategories. Some pathologies blend into oth-ers, and you may not be able to diagnose theroot-cause of the disease by examining a clini-cal specimen outside its natural habitat (thestudy itself).

MALFORMATIONS OF THEVARIABLE

ONLY ONE VARIABLE

Statements about the distribution of asample or population on a single variable arenonhypotheses, since a proper hypothesis nec-essarily involves two variables (and a rela-tionship between them). Here’s an example ofa statement suffering from this complaint:

Statement 1. “The most important findingof our study confirms the hypothesis thathigh-school civics teachers of the staterarely teach about threats to civil libertiesin their local communities.”

The only variable is “frequency of teach-ing about local threats to civil liberties.” Theso-called hypothesis merely alludes to thestanding of the state’s civic teachers on it, thatis, they “rarely teach about it.”

Here is another example of the same sort:

Statement 2. “This research set out to testthe hypothesis that American school sys-

tems are organized according to Weber’sbureaucratic model.”

Presumably, the investigators believedthere were other organizational models forschool system organization besides the “bu-reaucratic model.” The statement asserts thata count of American systems in the severalcategories would show all (most? a majority?)of them in the “bureaucratic” category. Thus,it is a statement about the distribution ofschool systems with regard to a single vari-able in kind.

Two more statements also pan out as non-hypotheses because they involve only a singlevariable:

Statement 3. “For the reasons we havecited and on the basis of previous re-search, we expect to find that fewer than10 percent of high-school principals arefemale.”

Statement 4. “Nebraska school board mem-bers will mainly be in the business andprofessional occupations rather than inagriculture, clerical, or blue-collar occu-pations, if our results are in keeping withthe theorizing of George Counts (1927).”

Descriptive surveys are replete with sta-tistics describing the standing of a sample orpopulation on each of a number of variables—means, percentages, frequency distributions,standard scores, and so forth. As valuable assuch information may be, they deal with onevariable at a time, and statements characteriz-ing a population with respect to a variable arenot true hypotheses.

NO COMPARISON MADE

A statement intended to be a hypothesis,involving an independent variable in kind,

41

PATHOLOGY OF THE HYPOTHESIS

might allude to only one of its values, failingto mention the other value(s) against whichcomparison is to be made. That is to say, thestatement contains a Y variable and an indica-tion of Xa but no reference to its contrastingvalues, Xb, Xc, etc.

Statement 5. “Teaching teams with for-mally designated leaders will display lessconsensus in views regarding appropri-ate disciplinary practices to use in theclassroom.”

Less than what other kinds of teams? Thecomparison is not completed.

Statement 6. “The study tested the hypoth-esis that enactment of state antidiscrimi-nation statutes during the early 1970s in-creased the percentage of females em-ployed as line officers in state public ser-vice agencies.”

Although the dependent variable mentionsonly one value of gender, that should pose noproblem because the other value, “male,” canbe taken for granted. More troublesome is theabsence of a second value for the independentvariable. If “enactment of antidiscriminationstatutes” is Xa, what is Xb?

The disease I’m describing here is notusually disabling. It commonly afflicts inde-pendent variables of the present-absent vari-ety, so it is easy to figure out from a study’scontext that the unmentioned Xb is simplythe absence of Xa. Inspection of the tables orother details of the research usually permitsthe clinician to doctor up the author’s state-ment and render it a healthy specimen.

Occasionally you will discover, upon ex-amining the study context, that a statementyou thought had the more serious diseasediscussed under the previous heading—

”only one variable”—turned out to sufferfrom the more rectifiable problem consid-ered here. Look again at statement 4 on page40. It could happen that the state in whichschool board members were located was asecond variable, “Nebraska” being one of thecategories, and that the author just failed tomention the other category, say “California.”Or maybe the unmentioned comparison wasbetween Xa “school board members” and Xb“city council members.” Only a more inten-sive diagnosis would tell.

UNKNOWN CATEGORIES

Far more virulent than the preceding isthe disease in which a name is given to theindependent variable (presumably a varia-tion in kind) but none of its categories is men-tioned. The disease can attack the dependentvariable, too, or both at once, but forsimplicity’s sake let us concentrate on theindependent variable.

Statement 7. “The severity of disciplineproblems in the classroom is a product ofthe teacher’s own personality.”

The X variable, “teacher personality,” isnamed, but what categories are involved?There are numerous ways in which personali-ties can be said to differ, such as ascendantversus submissive, intropunitive versusextrapunitive versus impunitive, innerdi-rected versus other directed, and so forth.Certain aspects of personality are even for-mulated as varying in degree. Need forachievement or tolerance of ambiguity arecases in point. Statement 7 affords no clue asto what the variation on the X variable is.

Failure to specify how properties are con-ceived to vary is so common a pathology thatI will present some additional specimens, withthe unelaborated variables emphasized.

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Statement 8. “The religious makeup of thecommunity is an important factor in de-termining the success of school tax elec-tions.”

Statement 9. “The level of teacher moralewill be correlated with the type of controlstructure observed in the school organiza-tion.”

Statement 10. “The rapidity with whichdepartmental faculties of community col-leges adopt instructional innovations isdetermined by the social relations that pre-vail among the members.”

The pathology described in the presentsection necessarily is compounded by the dis-ease discussed next. Between the two, thespecimens can only be regarded as terminalcases.

ABNORMALITIES INSPECIFICATIONS OFRELATIONSHIPS

The generic pathology described underthis heading is the absence of an unequivocaldesignation of how one variable is expected tocovary with the other. The disease may attackstatements in which the variables themselvesare perfectly normal.

Statements that fail to make precise pre-dictions come under three guises, and most ofthem are easy to spot.

QUESTION ONLY

Although questions are useful in the earlystages of formulating a problem for investiga-tion and can give rise to tentative answersposed in the form of a true hypothesis, ques-

tions alone make no predictions and, hence,are not hypotheses.

Statement 11. “Are parents better informedby letter grades or number grades on re-port cards?”

This statement contains no prediction, henceit’s not a hypothesis. I hardly need to givemore examples. The questionmark at the endof the sentence should instantly alert you.

ASSERTION ONLY THAT ARELATIONSHIP EXISTS

Statements thought to be hypotheses maydeclare that a relationship exists between twovariables without specifying the nature of therelationship. They do not say whether theexpected relationship is direct or inverse (ifthe variables were in degree) or how the de-pendent variable is expected to differ fromone value of the independent variable to an-other (when the latter is in kind). Followingare three specimens:

Statement 12. “Men and women will differin their rates of processing complex audi-tory signals.”

Statement 13. “The socioeconomic level ofstudents in secondary schools will be re-lated to their grade averages in vocationalsubjects.”

Statement 14. “The number of differentstudents whom a teacher instructs in thecourse of a week affects the likelihood ofthe teacher experiencing burnout.”

Note, in the last two specimens, use of theindeterminant phrases “will be related to” or“affects.” They are cues that the relationshipmay remain unspecified. Some other cuephrases include:

43

PATHOLOGY OF THE HYPOTHESIS

which he or she would like to draw infer-ences, in the event the null hypothesis wererejected. Researchers who limit their prob-lem formulation to a series of null hypoth-eses seriously inhibit themselves in reason-ing through the connections that might, andmight not, be expected between variables.

Researchers most susceptible to the dis-ease of substituting null for substantive hy-potheses are novices who have been exposedto courses in statistical techniques, where thenull hypothesis is emphasized, but who areunaware of the general logic of the researchprocess within which the statistical tools areapplied.

On occasion, experienced researchers willformulate hypotheses predicting that two par-ticular variables are unrelated and their doingso would be altogether proper. It happensmainly in a well-investigated area of studyusing well-tested measures or experimentalmanipulations. It also happens in studies im-plicating intervening or moderator variables,contingent relationships, and the like. In thetwo-variable case, however, predictions ofthe absence of relationships are so easy toaffirm with data that sophisticated research-ers shy away from them. Such a hypothesiscan be supported for a number of reasons thathave nothing to do with the soundness ofone’s theories, explanations, or answers toquestions. Any one of the following can leadto an empirical finding of no relationshipbetween a pair of variables:

• insensitive measuring devices

• little variation on one or both vari-ables

• unreliable measures

is a cause ofcontributes tohas an impact onis a function ofdeterminesis affected byis a factor in

Look back at statements 7 through 10 inthe preceding section. Behold that they, too,contain indeterminant phrases (as well as vari-ables that cannot be elaborated). When suchphrases are used to connect the independentand dependent variables, you can be prettysure the statement has contracted the diseasediscussed in this section.

ASSERTION THAT NORELATIONSHIP EXISTS

The null hypothesis discussed toward theend of chapter 4 is a statement predicting thatno relationship, other than that expected bychance, exists between two variables. As Itried to point out, it is not the same thing as asubstantive hypothesis. The disease describedhere most often arises when the null hypoth-esis is substituted for the substantive hypoth-esis.

Statement 15. “There will be no significantdifference between fathers and mothersof lower-class children in the roughness ofthe disciplinary techniques they apply totheir male children.”

If null hypotheses like this were the onlyhypotheses offered in a study—if there wereno conceptual hypotheses to supplementthem—then the reader (and the researcher)would be in trouble. You would have noway of knowing what substantive hypoth-esis the researcher had in mind and about

44

• invalid measures

• inadequate or improper research de-sign

• errors made in recording observations

• miscoding of data

• inaccuracy in computations

• mistakes in writing a computer pro-gram

• silly variables to begin with

The more ignorant, careless, or naive theresearcher, the greater the odds that he or shewill find support for hypotheses that predictthe absence of relationships. That is not anespecially sound basis on which to groundknowledge of the world around us.

®

Clearinghouse on Educational ManagementCollege of Education • University of Oregon1787 Agate Street • Eugene, OR 97403 ISBN 0-86552-115-8

For anyone doing empirical research today—be they graduatestudent, beginning academic, or established scholar—this manualshould be read and reread again, again, and again. All will benefitfrom Sandy Charters’s wise, witty, and lucid discourse on the“distinctions and rules and procedures for unraveling variables,examining relationships between them, and analyzing hypotheses.”And for those of his students, colleagues, and friends whose profes-sional lives were enriched by Sandy, this work will stand as a lastingreminder of the remarkable gifts of this brilliant teacher and distin-guished scholar.

On Understanding Variables and Hypotheses is destined todo for scientific research what Elements of Style did for writing.

Philip K. Piele

What Charters contributes here is just what is needed today tocorrect a current bias and tilt in favor of qualitative methods. In theface of a paradigm shift in policy research in which qualitativemethods are being exalted and quantitative methods are being under-valued, Charters’s treatise on clear conceptual definitions and preciseoperational hypotheses will play a pivotal role, I hope, in reintegrat-ing the best of both the qualitative and the quantitative traditions.

Richard A. Schmuck

ONUNDERSTANDINGVARIABLES &HYPOTHESESIN SCIENTIFICRESEARCHby W. W. Charters, Jr.