aptitude-treatment interaction as a framework for research ... · interaction is defined...

Journal of Consulting and Clinical Psychology1991, Vol. 59, No. 2, 205-216

Copyright 1991 by the American Psychological Association, Inc.0022-006X/91/S3.00

Aptitude-Treatment Interaction as a Framework for Researchon Individual Differences in Psychotherapy

Richard E. SnowStanford University

Aptitude-treatment interaction (ATI) methods are designed to take individual differences intoaccount systematically in treatment evaluation. This article reviews the general concepts of apti-tude and ATI and summarizes lessons learned in ATI research on educational treatments thatshould help ATI research on psychotherapeutic treatments. Recommendations for research designand data analysis address problems of aptitude distributions, multivariate aptitude complexes,detective work with scatterplots, disattenuation, treatment and therapist characteristics, therapist-client matching, ecological validity, outcome variables, statistical power, aggregation, and personindependence. Example studies and hypotheses about the nature of ATI processes are also in-cluded.

In many fields of psychological, social, educational, and med-ical science, treatments are designed as interventions to achievesome individual or common good for human beings. Whenalternative treatments aimed at the same goal are available, thequestion is, Which treatment is best? Even when one treatmentis adopted, a continuing question is, How can this treatment bemade better? Because the persons treated usually are observedto differ in their response to treatment, and also to differ fromone another in many other correlated ways, an important addi-tion to these questions i s , . . . best or better for whom, when,and why?

The aptitude-treatment interaction (or ATI) paradigm wasinvented to address these questions in consort. ATI methodol-ogy is designed to take individual differences among treatedpersons into account systematically in treatment evaluation—to assess the degree to which alternative treatments have differ-ent effects as a function of person characteristics and thus deter-mine whether particular treatments can be chosen or adaptedto fit particular persons optimally. Beyond methods for assess-ing interactions among person and situation variables, how-ever, the approach offers a framework for new theories of apti-tude interpreted as personal readiness to profit from particulartreatment situations.

This article summarizes lessons learned in ATI research oneducational treatments that should help advance ATI researchon psychotherapeutic treatments. Dance and Neufeld (1988)have discussed the basic principles of ATI method with exam-ples from psychotherapy research, so these need not be reiter-ated here. But the extensive experience with ATI in educationalresearch suggests some clarifications and extensions of theirdiscussion as well as some further recommendations.

I gratefully acknowledge the helpful comments of two anonymousreviewers on a draft of this article.

Correspondence concerning this article should be addressed toRichard E. Snow, School of Education, Stanford University, Stanford,California 94305.

Background

Terms and Concepts

Because there is misunderstanding abroad about ATI, onefirst needs to be clear on terms and concepts. The usage recom-mended here is as follows:

Aptitude should refer to any measurable person characteristichypothesized to be propaedeutic to successful goal achieve-ment in the treatment® studied; propaedeutic means needed aspreparation for response to treatment. In other words, individ-uals differ in their readiness to profit from a particular treat-ment at a particular time; aptitude constructs are theoreticalconcepts fashioned to interpret these observed differences inperson-situation interaction terms. An aptitude, then, is a com-plex of personal characteristics identified before and duringtreatment that accounts for a person's end state after a particu-lar treatment.

It is important to note that this usage of the term aptitudediffers from that common in English-language psychologythrough much of this century; that is, as here defined the do-main of aptitude is not limited to intelligence or some fixed listof differential abilities but includes personality and motiva-tional differences along with styles, attitudes, and beliefs aswell. Also, no particular theory or measurement model for per-sonality or ability is implied. According to Dance and Neufeld(1988), an ATI approach assumes a trait model in which apti-tudes are presumed both stable and continuous. But there areno such requirements. It is happenstance that most aptitudeconstructs studied so far have been represented by tests or ques-tionnaires built on classical psychometric models; althoughsuch models may use the term trait as shorthand and may im-pose continuous numerical scales, most apply without assum-ing fixed or continuous traits in any substantive sense. ATI re-search does seek complementary person and treatment charac-teristics that seem relatively stable, because characteristics thatare easily changed pose no lasting problems. And treating apti-tude variables as continua has certain statistical advantages.

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206 RICHARD E. SNOW

But modifiability and continuity of aptitude differences repre-sent questions for research, not assumptions; most ATI re-search has not yet examined aptitude change as a function oftreatment, or the interrelation of traitlike and statelike proper-ties of aptitude, or the multivariate distributional character ofaptitude constructs. These seem to be especially importantquestions for further ATI research in psychotherapy.

In promoting such research, the ATI approach aims at newkinds of aptitude theories. The concept of aptitude recom-mended here returns to the original European meaning, em-phasizing adaptation and the mutual fit (or misfit) of personand situation. An aptitude is thus a relational construct, inter-preting the behavior of person-in-situation, and characteristicsof the situation are as much a part of the definition of a particu-lar aptitude construct as are characteristics of the person (seeSnow, in press-a, in press-b, for discussion of the relational andsituational character of this aptitude concept).

Treatment has an obvious, broad meaning as any manipula-ble situation variable. But here it also includes characteristics ofthe environment in which therapy takes place (e.g., clinic vs.private office, group vs. individual) and therapist characteris-tics (e.g., gender, age, religion); although these variables aretechnically not manipulable, client experience is manipulableby assignment rules with respect to them. Just as aptitude is arelational concept, so too is treatment, because persons con-struct and adapt their situations to fit their own characteristics,at least to some degree.

Interaction is defined statistically as the degree to which re-sults for two or more treatments, or one treatment over two ormore trials, differ for persons who also differ on one or moreaptitude measures. Both aptitude and treatment variables maybe qualitative (i.e., nominal scale measures) or quantitative (i.e.,ordinal, interval, or ratio scale measures), tested or observed orself-reported, or demographically defined. The results of treat-ment (i.e., the criterion or outcome variables) may similarly beof any sort.

A final class of variables important in ATI research areusually called process or transaction variables. Examples mightbe indices describing patterns of discourse between teachersand students or therapists and clients. Some research attemptsto understand ATI effects by tracing the processes that operateduring person-situation interaction in more detail. But theterm transaction, not interaction (as in human interaction), ispreferred in describing these variables to reduce confusion withstatistical interaction.

A Simple Example

ATI is said to be present when for some group of persons anaptitude variable shows a different relation to an outcome vari-able in one treatment than it does in another. A typical study ofinstruction might contrast a high structure treatment (moredidactic, direct, and teacher-centered) with a low structuretreatment (more inductive, indirect, and student-centered). Theoutcome variable might be learning after some weeks in treat-ment as reflected by an achievement posttest. With a cognitiveability or achievement pretest as the aptitude variable, it is oftenfound that the pretest-posttest relation is stronger in low struc-ture than in high structure treatments. It appears that the com-

pleteness and external control provided by high structure in-struction helps initially less able students, reducing the differ-ence between them and initially more able students, whereaslow structure treatment accentuates this initial student differ-ence. In the extreme, low structure is clearly the best treatmentfor high ability students, whereas high structure is clearly bestfor low ability students. A related pattern of results is often seenwhen these two instructional treatments are contrasted usingtest anxiety as aptitude. Highly anxious students do better withexternally imposed structure; it presumably affords control ofattention toward the task and away from self-doubts andworries. Low structure treatment is bad for anxious students,perhaps because it requires self-control of task attention; non-anxious students can provide this for themselves and so do wellwithout high external structure.

There may be parallels connecting ability, anxiety, and treat-ment structure in psychotherapy as well. As argued above andthrough much of this article, however, these sorts of simplefindings need deeper analysis and qualification in many waysbefore their use in practice. Often ATI effects signal the need forprogrammatic research on aptitude and treatment constructsand their improved assessment, not conclusions ready for appli-cation.

History and References

ATI hypotheses can be seen in ancient Chinese and Hebrewwritings on education, in early Greek and Roman teachings,and in some European educational philosophies across the cen-turies (Snow, 1982). Binet invented the intelligence scale toserve interactionist purposes. But the modern definition of ATIfor psychology stems from Cronbach (1957). Thereafter, a sub-stantial ATI research program developed in instructional psy-chology (see Cronbach, 1967, 1975; Cronbach & Snow, 1977;Snow, 1977b, 1987,1989a, 1989b; Snow & Lohman, 1984). Morerecently, the concept of aptitude as here defined, the methodol-ogy of aptitude research, and the requirements for buildingaptitude theories have begun to be studied in relation to theneeds not only of educational but also of industrial and clinicalpsychology. To save space, these developments are not reviewedhere, and background citations are given only for special refer-ences other than those listed above.

In passing, however, it is worth noting that some of Cron-bach's earliest ideas about ATI were derived in thinking aboutresearch on psychotherapy (see Edwards & Cronbach, 1952).Some related methodological suggestions (Cronbach, 1953,1958; Cronbach & Gleser, 1953) also addressed the complexitiesof research on person variables in this setting. As current re-search addresses these issues anew, it needs to learn from theearly work in psychotherapy as well as from experience in edu-cation.

Some General Admonitions

Three general warnings provide initiation for the specificrecommendations offered later. These may guide thinkingabout problems in ATI research on psychotherapy that cannotbe anticipated here.

The limits of simplification. For both research and exposi-

SPECIAL SECTION: APTITUDE-TREATMENT INTERACTION 207

tory purposes, all science must simplify. Especially in a newfield, however, investigators must frequently step outside oftheir simple models and methods to identify complications andguard against distortions that might mislead or foreclose apromising line of inquiry. Much ATI research in education hascertainly been limited by too simple a view of the phenomenon.

This exposition mainly considers simple experiments inwhich two or three treatments (TA, TB, and Tc) are compared ona single outcome measure (O) and a primary aptitude variable(A,). But secondary aptitudes (A2) are brought in at times toshow complications and to clarify lessons to be learned fromthem. Indeed, the recognition that aptitude variables, in partic-ular, should noit be considered only one at a time is an impor-tant first lesson. The world of person characteristics abounds incorrelations, and it is unlikely that one aptitude effect is isolatedfrom others. Every research design involves multiple aptitudesand higher order interactions whether it includes them formallyor not.

Similarly, treatment and outcome variables have hidden cor-relates that can moderate results across contexts and thus acrossstudies. In research in education and also in psychotherapy, onemust take a more complex view of replication (and of meta-analysis) than that typically taken in laboratory psychology(where troublesome interactions also occur across contexts).Some complications involving multiple treatment and outcomevariables, and related difficulties, are addressed in later sec-tions. The overarching point is that each experiment is a casestudy, limited to its time, place, and human constituents. Thebest way to understand its results and to link them to the resultsof other studies is to obtain the richest possible description ofits context and process and to limit simple generalizationstherefrom (see Cronbach, 1982a, 1982b, 1986).

The limits of statistical significance testing. A different sortof simplification limits and distorts progress by automaticallyremoving from further consideration ATI effects that fail toreach some conventional level of statistical significance. Cer-tainly investigators need a decision rule to focus attention. Butp - .05 does not divide ATI effects into two classes: reportableand zero (i.e., unreportable). And a table of p values or F ratiosor asterisks is not a report of results. Every ATI report shouldprovide descriptive statistics within treatments both for resultsjudged significant and for those judged nonsignificant. Consis-tent nonsignificant trends are at least as valuable for the pur-poses of further research as are incoherent significant results.And estimates of relationships including confidence intervalsaround them are more valuable than null hypothesis tests forthese purposes.

A huge amount of ATI research in education has been wastedthrough failure to recognize the primacy of statistical powerconsiderations in significance testing. In other words, Type Ierrors have been avoided at the expense of what may be a vastnumber of Type II errors. Investigators need to decide what sizeeffect they want to be able to detect and what power level isneeded to do so. Inasmuch as most ATI studies cannot practi-cally obtain the sample sizes needed to achieve adequately pow-erful tests, considering and reporting the actual power of astudy to detect ATI (alongside the results obtained) helps toavoid simple null conclusions and to improve research design

for future tests. A number of lessons for research design flowfrom the power issue.

The limits of existing methods. There is also a natural ten-dency to simplify by allowing existing methods, rather than aconceptualization of the substantive phenomenon, to dictatethe course of research. Ready-made aptitude measures and com-parison treatments can be gotten off the shelf for trial. The datacan be fitted into canned statistical analyses. But the kinds ofaptitude and treatment contrasts that derive from earlier theo-retical traditions may not be the best candidates for ATI re-search in psychotherapy. A huge amount of research effort ineducation has also been wasted on relatively blind searchesthrough the catalogue of existing variables.

There may be existing aptitude and treatment constructs inpsychotherapy that are ripe for ATI research. But there are alsolikely to be new conceptions of aptitude and treatment deriv-able from thinking about persons-in-situations and analyzingcases in that light, without reliance on existing nomenclature.In either case, there is no substitute for careful, deeply substan-tive consideration before aptitude measures are adopted andtreatment contrasts are designed.

Recommendations on Basic Designs and Analysis

This section offers more specific recommendations regard-ing basic designs and data analysis for ATI research. A followingsection takes up some advanced problems. Because space islimited, investigators should consult the book-length presenta-tion (Cronbach & Snow, 1977) for full explication on mostpoints.

Research Designs

Four basic ATI designs may serve useful purposes in psycho-therapy research. There are also various complex designs thatbuild on these but are not taken up here.

Standard design. A simple randomized between-personsdesign and hypothetical result akin to that discussed by Danceand Neufeld (1988) is shown in Figure la. The regressions of Oon A, differ for three treatments (TA, TB, and Tc). To optimizeoutcome in practice, one would apply TA to persons above Pointx, and Tc to persons below Point x, on A[. If the treatmentsdiffer in cost, decisions may change. For example, if TB is lessexpensive than TA and not much different in effect for personsabove Point x, then it might be used instead of TA; this changesthe treatment choice point from Point x to Point y on the apti-tude continuum. There are formal methods for converting Ovariables to a utility scale, thus transforming the picture (seeCronbach & Gleser, 1965). But note that this conversion caneither make or break practical ATI considerations. For exam-ple, if TA is least expensive, the conversion shifts the TA regres-sion line upward in Figure la, perhaps making it the treatmentof choice for all persons in the sample.

Cost analysis of particular existing therapies is an importantbut secondary issue; the first question for research is why partic-ular ATIs occur as they do. Existing evidence from individualstudies needs to be pursued more deeply, through case-by-caseanalysis. If theoretical interest attaches mainly to a particulartreatment contrast, then attention should focus on clues in the

208 RICHARD E. SNOW

a)x y

AI

b)

c) d)

Figure 1. Schematic representation of regression results in four types of ATI research: (a) standard design,(b) treatment revision design, (c) aptitude growth design, and (d) regression discontinuity design.

case analysis that suggest what other aptitudes might be broughtinto subsequent studies. By selecting aptitudes that then exhibitATI, one demonstrates that the treatment contrast is to thatdegree understood. If the theoretical focus is on the meaning ofa particular aptitude construct, then case analysis may suggestwhat treatment manipulations in further studies might clarifythis meaning further. Experimental manipulation of ATI showsthat the aptitude construct is to that degree understood. Onecan start from either focus or both jointly. And the analysis andclassification of accumulated earlier cases in some research pro-gram, practice, or clinic could use ATI thinking to generateimportant research hypotheses even where aptitude and treat-ment variables have not been systematically studied in interac-tion (see Kanfer & Phillips, 1970, on this recommendation).

Treatment revision design. One variant examines a singletreatment and attempts to improve it with respect to some apti-tude, as pictured in Figure Ib. The between-persons version ofthis design was first proposed by Bunderson (1969) and used informative evaluations of computerized instructional programs.The regression of O on A, for Tc is a starting point, obtainedperhaps in an initial correlational exploration of Tc effects. Theinvestigator then uses clues from cases low in the O-on-A, dis-tribution to guide revisions, thus creating TB. Suppose a secondstudy with new persons then produces the TB regression pic-tured. Another round of analysis and revision and a third studymight produce the TA regression pictured. The aim is to reachoptimum outcome by adapting treatment to remove the nega-tive effects of low A, over a series of correlational studies (thatadd up to an experiment).

A threat to this result observed in educational studies is sug-gested by the dashed regression slope. Treatment revisions thatimprove outcome for low A, persons may reduce its effective-ness for high A! persons, who were initially well treated. Thismay suggest that something important for high A, persons hasbeen altered or removed in the treatment revision process andmay also hint that changes have brought some A2 into rele-vance.

A within-person design may also be considered. Psychother-apy might conceivably be designed in multiple stages, so long asinterim O measures exist. Each stage might then be a furtheradaptation of treatment with respect to A,. Mixed designs arealso possible, where half-samples are randomly assigned to anew treatment stage or retained in the initial stage.

Aptitude growth design. In another variant, A, is itself thetarget of treatment, so O is equivalent to A', as in Figure Ic. Tc

appears best for persons initially low in A,. After a period ofgrowth in this treatment, however, other treatments may be-come optimal for continued progress; a shift at Point x to atransitional TB and another shift at Point y to the finishing TA

can be imagined.The evaluation of such schemes may require multistage ex-

periments as in treatment revision designs. Also, when many Aor O assessments are available in a time series, other forms ofanalysis may be clearer and more powerful than the standardregression analysis. Rogosa (in press) has demonstrated agrowth curve approach to the study of ATI in such situations.

Regression discontinuity design. A variant that may be use-ful in evaluating ATI across certain other patient situations uses


a regression discontinuity approach. If persons are already as-signed to different treatments on the basis of A, (or some corre-late), then evidence for ATI comes from the degree to which acommon regression line does not fit the full data set acrossPoint x. Two kinds of discontinuity are suggested in Figure Id.The contrast of TA and Tc suggests a main effect; the two regres-sion lines are parallel, with that for TA shifted upward or that forTc shifted downward for all persons so treated. The contrast ofTA and TB suggests ATI; if extrapolated, the differing slopeswould intersect. Although extrapolations are tenuous, such re-sults at least suggest hypotheses worth further examination.

Suppose low standing on A[ (below Point x) is used in decid-ing to institutionalize persons for treatment, but the same ther-apy is applied to both inpatients and outpatients. The contrastbetween the TA and Tc slopes in Figure Id might be taken toindicate the depressing effect of institutionalization on thera-peutic progress. On the other hand, the contrast between the TA

and TB slopes might suggest a beneficial effect of the institu-tional context coupled with therapy. Obviously, regression dis-continuity can also be used to compare different therapiesacross institutional or other context lines.

Despite the amount of prior research on ATI in education,almost all examples use one or another form of standard de-sign. One might expect that instructional development workwould make use of the treatment revision design, but there arefew examples actually carried through the series. Despite muchexpenditure on treatments that work directly to develop intellec-tual skills for learning, evaluation studies have generally notused aptitude growth designs. Regression discontinuity is anobvious way to evaluate placements into special education pro-grams for retarded, learning disabled, and gifted students, butagain there are no good examples. Research in education hasreally not yet gone beyond the question of whether understand-able and useful ATI can be demonstrated. The shortcomings inmuch of this work lead to the suggestions for research on psy-chotherapy laid out below.

Preservation of Meaning in Aptitude Variables

A first goal is to preserve the substantive meaning of theaptitude construct by choosing appropriate models of measure-ment and statistical analysis. This end is served by several rec-ommendations.

Examine aptitude distributions. Assumptions about continu-ous, normal, linear distributions should not be adopted blindly.Examination of obtained score distributions may suggest (andhas at times suggested) discontinuities that may have substan-tive meaning to be captured by forming discrete groups. Bi-modal distributions obviously suggest this. Also, distributionsthat are continuous and linear in one population or regionthereof may show anomalies in other populations or regions.On some continua, extreme scores may identify qualitativelydifferent psychological groups. And some aptitudes studied areat base discrete (e.g., certain style constructs; sex as a proxy forpsychological differences). Dance and Neufeld (1988) haverightly noted that aptitude variables that readily distribute intodiscrete classes should be analyzed and interpreted as such (seeGangestad & Snyder, 1985). Several discrete class measurement

models are available for use in ATI work (see, e.g., Haertel, 1984;Rindskopf, 1987).

Avoid forced categorization. But continuous measuresshould be analyzed as such. Regression methods provide esti-mates of strength and form of relationships in the most power-ful way. Splitting a distribution (e.g., at the median) inflates errorvariance by failing to use the discriminating power of the con-tinuum. Trichotomies or other forced levelings are worse be-cause they also ignore (at least in conventional analysis of vari-ance [ANOVA]) the ordinality of the continuum. Furthermore,forced splits are arbitrary and sample-bound, so they confuseattempts at replication (e.g., above-median anxiety in one sam-ple may be below-median anxiety in another).

Use norms where possible. If population norms exist for anaptitude measure, interpretation in a sample should be refer-enced to them. This adds meaning to any one study and locateseach study in its region of the population so that replicationscan be meaningfully compared.

Avoid standardization of scores in a sample. Standardizingscores has advantages but is hazardous in research on a samplenot referenced to norms. Particularly to be avoided is standard-ization within treatments. This common practice erases fromview variance differences in outcome resulting from treatmenteffects. In other words, regression coefficients, not correlations,should be used to compare treatments. Raw regressions areusually best. For some purposes, measurement scales for eitheraptitudes or outcomes can be transformed to add meaning, butnever separately within treatments.

Beware confounded extreme groups. Extreme groups designfits ANOVA and provides a powerful statistical test, but choos-ing such groups wisely is difficult. Especially in a new researchprogram, one rarely has the knowledge needed to do this effec-tively. One must assume linearity and an isolated aptitude.When a second aptitude is moderately correlated with the first,confounding occurs in proportion to the degree of correlation.As shown in Figure 2a, the shaded extreme groups on A, differalso on A2, thus clouding interpretation. A2 need not be mea-sured to cause this confounding; it exists as variance in thesample. If it is measured, then extreme groups might be definedto include it, but this involves sampling persons in more com-plex ways, using the bivariate contours. Extreme groups designalso seems to fit psychotherapy research poorly. Persons can beassigned randomly to treatment, but then all comers are usuallytreated. Throwing away the midrange data serves no good end.

Include a second aptitude explicitly. Theoretical interest of-ten attaches to one aptitude construct in relation to one treat-ment contrast, but including a second (or third) aptitude hasadvantages and is usually inexpensive. A2 might be chosen forits close relation to primary A and T variables in a conceptualnetwork or for its importance as a moderator in psychologygenerally. Figure 2b shows the effects of higher order ATI whenboth ability (At) and test anxiety (A2) are used as aptitudes tocontrast highly structured teaching (TA) with unstructured stu-dent-centered teaching (TB) as treatments. To avoid a three-di-mensional picture, Figure 2b identifies regions of the bivariateaptitude space labeled to show which treatment was best ineach. It shows that structured treatment was best for studentshigh in both ability and anxiety or low in both; unstructuredtreatment was best for students showing high-low, low-high,

210 RICHARD E. SNOW

a) b)

\ 'A\BEST"

AI

C)

Figure 2. Complications due to multiple aptitudes in ATI research: (a) confounded extreme groups, (b)higher order ATI, (c) troublesome scatterplot anomalies, and (d) useful scatterplot anomalies.

and middle level profiles. The results replicated. However, theaptitude-outcome relations may have been curvilinear in thesestudies; sample size was insufficient to test this. In any event,these results are seen to complicate considerably the simpleexample of ATI given early in this article.

Inspect relationships in scatterplots. An important rule is notto allow packaged computer analyses to dictate the results. Scat-terplots should be carefully inspected. Figure 2c shows somereasons why. When one attends only to regression slopes, astriking ATI appears. However, the white dot group may haveone and possibly two outliers; its regression slope would bemuch less steep without these points. One does not drop out-liers purely on statistical grounds; each is a real person. Rather,one studies the cases to find plausible reasons why they arewhere they are in the scatterplot. But recognizing the influenceone or two points may exert in a small-sample study and check-ing out that influence will temper otherwise enthusiastic con-clusions.

Two other notable features of Figure 2c are the restrictedrange on O exhibited by the black dot group and the apparentbimodality of both groups on A,. Treatment can make outcomevariance larger or smaller, so this further emphasizes that corre-lations within treatments are not the statistics to look at. Thebimodality is a question for further inquiry. If A, really is besttreated as discrete, other information from case analysis shouldjustify this, and further research can be planned accordingly.

The data of Figure 2c actually come from a memory experi-ment using college students in which scholastic ability scoresserved as A,. Hence, bimodality is probably peculiar to thissample. Also, there is only one treatment here; the black dots

are men and the white dots are women. This further under-scores the need to include secondary A variables; with ability asA! , sex might be chosen as A2 to index whatever other psycho-logical differences attach to gender. No matter what else oneconcludes here, results for men and women differ enough tojustify further inquiry.

Analyze other aptitudes in scatterplots. Figure 2d shows an-other reason to plot data person by person and to consider whatelse is known about each. These data come from a study ofstudents working in an innovative treatment based on smallgroup problem solving; A, is verbal ability and O is knowledgeacquisition after some weeks. The solid regression line showsthe overall relation of O to A,.

The scatterplot displays two features that deserve further de-tective work: There is a suggestion of curvilinearity, unusual foran ability-learning relation, and the points are densest in themiddle to upper region of A,. The plot looks as if one bivariatedistribution is superimposed on another with AO relations run-ning in contrary directions in each to reduce the overall linearregression. One could fit a single curvilinear function to thesedata, but an adaptation of the off-quadrant analysis proposedby Marks (1964) was considered simpler and more useful in thisinstance. Other aptitude dimensions, available from a personal-ity inventory administered at pretest, were used to search forsome A2 that might yield the dashed regression line in Figure 2d(i.e., that would distinguish cases above the solid regression linefrom those below it in the middle to upper region of A,). Itturned out that students in this region below the solid regres-sion line were on average more independent, achievement-mo-tivated, and task-oriented, and less altruistic and interperson-


ally oriented, whereas students in this region above the solidregression line showed the opposite pattern. A2 correspondingto the dashed line might thus be an aptitude complex roughlydescribed as independent task motivation versus interpersonalorientation and mildly correlated with ability in this middle tohigh range. The resulting hypothesis is that able students whoare also highly motivated and oriented toward independentwork do poorly in this treatment because it demands coopera-tive interpersonal activity in small groups, but able studentswho value interpersonal activity more than independent taskactivity do well in this treatment. A treatment that reduced oreliminated group work in favor of individual learning would behypothesized to reverse this relationship.

The point is that scatterplot and case analysis within treat-ments can yield important advances in ATI research on particu-lar treatments. Although one aptitude may be of primary inter-est, carrying collateral aptitude information along in a study tofacilitate this sort of detective work can yield valuable payoffs.

Disattenuate relationships. Observed regression slopes thatare marginally different can become markedly different whencorrected for measurement error in A or in both A and O. Re-search is properly interested in theoretical relations, so correct-ing both A and O for error is appropriate. Personality measuresare often not highly reliable, so the dictum to disattenuate O-Arelationships should carry special force for psychotherapy re-search. Reasonable estimates of reliability for each measure areof course required.

Preservation of Meaning in Treatment and OutcomeVariables

Relative to A variables, psychotherapy research has accumu-lated much more experience in considering T and O variables,so less needs to be said about them here. With ATI the issue,however, some lessons from educational research deserve note.

Describe treatments as fully as possible. Labels do not atreatment make. When educational treatments that appear su-perficially similar have produced unexpected results, a failureof replication has often been announced. But a closer look atdetails sometimes yields explanation. Also, the treatment in-tended may differ from the one implemented. Thick descrip-tion of the actual treatment is needed, and it should includecharacteristics of the situational contexts in which treatmentsare embedded. One needs to be able to trace varying results toother interactions that may be subtlety varying across contexts.In psychotherapy research, the production and use of detailedtreatment manuals should be standard operating procedure; itis a major step in this connection (see Smith & Sechrest, 1991).

Describe therapist characteristics and styles. Teachers mayor may not follow treatment prescriptions exactly, and theirvarying natural styles may fit one treatment better than an-other. In one study of 39 classrooms, for example, within-classcorrelations between measures of student test anxiety and math-ematics achievement ranged from +.36 to -.81 (Helmke, 1988).The immense range suggests that teacher style was an impor-tant moderator; in effect, the teachers were administering dif-ferent treatments. Therapists clearly also vary in this way (seeBeutler, 1991). Thus treatment description needs to includetherapist characteristics and styles.

Strive for ecological validity in experiments. Considerationsof Treatment X Therapist interaction suggest multifaceted ex-periments in which therapists are scripted to impose differentmanualized treatments for randomly different clients. Perhapstherapists can also be chosen to represent different levels ofsome characteristic. Obviously other treatment variables canalso be crossed with these. But the ecological validity of theresulting mixtures of conditions is an important issue.

In some educational studies, teachers have been scripted tovary treatments systematically across multiple classes. Tutorshave been trained to do this for different individual students.But careful analysis of transcripts sometimes shows that allteachers do not work equally well with all treatments. Crossingteachers and treatments in a multifaceted design can also pro-duce awkward unnatural conditions for some teachers and con-sequent artificial effects in the results. After all, neither teachersnor therapists are professional actors, and even actors do not fitall available scripts. Thus, the fit of therapist and treatmentneeds to be considered; degrees and kinds of misfit can besubtle. For this reason also, the use of pseudotherapists (alsopseudoteachers) is not recommended.

The methodological advice here is to sacrifice crossed designin favor of nested design wherever available therapists seem tofit some treatments naturally, and not others. Ecological valid-ity and the trade-offs between external and internal validity ofexperiments cannot be addressed here (see Cook & Campbell,1979; Cronbach, 1982a; Snow, 1974). But it is clear that experi-mental contrasts need to be made as representative of real prac-tice as possible if results of psychotherapy research are actuallyto be applied. It also seems clear that further research needs tofocus on the problem of training therapists (as well as teachers)to be competent in choosing and using the range of treatmentsthat different clients match.

Analyze therapist-client match. If therapists can be fitted totreatments, why not also to clients? Therapist-client matchingin psychotherapy has been studied for some years (see Beutler,1981; Chartier, 1971; Kelly, 1990; Razin, 1971). But this line ofresearch may not yet have fully recognized the complexitiesinvolved.

In education there is evidence that some teacher-studentmatches work well and others poorly (see, e.g., Brophy & Evert-son, 1981). However, much too simple a view has been taken ofwhat constitutes a beneficial match and how this can be de-tected. It may be found in interpersonal similarities in someinstances and complementaries in others. Perhaps it must betraced back from outcomes through transactional processesduring treatment and only then to therapist and client charac-teristics. The relevant characteristics may be both multivariateand different in therapist and client. Thorny methodologicalproblems attend these questions that have yet to be adequatelystudied. At least one recommendation is to avoid dyadic indi-ces in interpersonal matching; these often lead to artifacts andunnecessarily complex interpretations, which are revealedwhen analysis returns to the separate person dimensions (Cron-bach, 1958).

Include perceptions of treatment and therapist. The studiesof teacher style and student anxiety noted above replicate afrequent finding. Teachers who impose highly structured con-ditions reduce the negative effects of anxiety on learning; the

212 RICHARD E. SNOW

negative relations are stronger where teacher structure is notimposed. But some research that demonstrated this ATI experi-mentally also later showed the same result with a constant treat-ment that blended the two teaching styles; students were merelyclassified on their perceptions of treatment as high versus lowstructure (Dowaliby & Schumer, 1973). In other words, percep-tion of teacher style alone turned the anxiety-learning relationone way or the other. Thus, client perception of treatment, aswell as its actual characteristics, may often be an importantinteracting influence; there is some evidence from psychother-apy research that this is so (Garfield, 1986; Gurman, 1977a,1977b). This possibility also complicates research on therapist-client matching.

Include all relevant outcome variables. To evaluate treat-ments, one obviously needs to include all important outcomevariables. Educational studies have sometimes found differentATI effects for different O variables, thus providing insight intosubtle treatment processes. Unfortunately, each result hasusually been interpreted in isolation. In psychotherapy re-search, there are also examples of differing results for differentoutcome variables (see, e.g., Strupp & Hadley, 1977,1979); heretoo, multiple kinds of side effects and recidivism are alwaysspecial concerns.

Separate ATI findings should not be interpreted indepen-dently when O variables are correlated. Outcomes can some-times be orthogonalized to clarify interpretation. They can alsobe examined jointly if converted to utilities or some other com-mon scale, so that ATI effects on the difference between out-comes can be assessed. Judging from experience in educationalresearch, multiple outcome analysis can enrich the understand-ing of ATI substantially if it is designed to preserve the meaningof each measure.

Avoid expressing outcomes as difference scores. The meaningof O variables is also preserved by avoiding arbitrary indices of"difference" or "change." Although simple change measures areintuitively appealing, they are treacherous. Difference scoremetrics involve assumptions that are usually not met. Their useoften befuddles rather than clarifies the analysis. Besides, iftherapeutic process and outcome are multivariate, no one Ovariable should be singled out as special because it seems super-ficially similar to one A variable. Unless multiple time seriesmeasures are available, the recommendations of Cronbach andFurby (1970) should be observed (see also Beutler & Hamblin,1986). A similar argument, along with the consideration ofpower, dismisses covariance analysis in most instances.

Some Advanced Topics

This section touches only a few of the advanced issues thatmay come up as ATI research in psychotherapy progresses. Theaim is to anticipate likely complexities. Those noted are mainlyextensions of problems already discussed.

Power, Aggregation, and Person Interdependence

Power versus detective work. Because statistical power is vitalto detecting ATI, many of the above recommendations aim atenhancing it. But some—most notably the advice to entertainmultivariate or curvilinear hypotheses—would seem to run

counter to this emphasis, especially given the limits on samplesize typical of psychotherapy research (and of much instruc-tional research). There is usually a trade-off between improvingpower and exploring complexity. For a given sample size,simpler hypotheses are more powerfully tested than are com-plex ones. Design and analysis options that offer increased sta-tistical power usually do so by limiting the kinds of ATI effectsthe experiment can detect. For example, choosing extremegroups or stratifying or matching on aptitude before assign-ment to treatment can increase the power of the analysis, thusreducing the risk of missing a simple effect. But this increasesthe risk of missing meaningful but more complex ATI. To seethis, superimpose Figure 2a onto Figure 2b; an extreme groupsdesign using only A, would completely miss an important bi-variate effect. Sometimes statistical as well as experimentalcontrols can be used to reduce error terms and thus enhance thesensitivity of the analysis to one effect, but this also can lead tooversimplified, misleading conclusions. The alternative is toaccept lower statistical power as the price of preserving or in-creasing the value of the data for exploratory detective work.What strategy is best depends on a host of considerations, in-cluding the stage of the research program and the strength ofprevious theory development, as well as the risks an investiga-tor is willing to take in a particular situation. At the least, how-ever, an investigator should always estimate the power neededto test each hypothesis before the study and report it alongsideresults.

Sometimes one can increase power with respect to a mainhypothesis while still exploring many secondary issues. And atbase, of course, one can increase both the power of an experi-ment and its value for exploration by increasing its sample size.Although an investigator must conduct a needed study withwhatever sample can be practicably obtained, programmaticresearch should try to build up large samples for each primaryhypothesis. In education this is done by including multipleclasses (and thus teachers) in each treatment, inasmuch as treat-ments cannot usually be experimentally manipulated withinclassrooms. In psychotherapy, it may also be possible to aggre-gate into a single analysis multiple sites (e.g., multiple therapists,clinics, or other health care institutions). But psychotherapyresearch has two options in this process. It can assign sites totreatments as in educational research, or it can conduct thesame small experiment at each site, because individual clientsor small groups can be assigned randomly to one or anothertreatment as they come. Consider the first strategy, then thesecond.

Between-groups versus within-group regressions. In theHelmke (1988) example noted earlier, 39 classrooms displayed arange of correlations between student anxiety and learning out-come, and this was associated with variation in teacher styles.Each class thus has a within-group regression of O on A (i.e.,Helmke's within-class correlations need to be transformed toregression slopes using the respective standard deviations). Buteach class also contributes to a between-groups regression thatrelates class average O to class average A across the sample ofclassrooms. This between-groups regression can be very differ-ent from the individual class regressions, or their pooled regres-sion, and both can differ from the regression that would beobtained for the sample of individual students with class mem-


bership ignored. In other words, ATI can occur at two levels. Ifin the Helmke study classes differed in average anxiety, for ex-ample, the between-groups regression might be negative for lowstructure teaching styles, but within-class regressions mightvary from positive to zero to negative as class average anxietyincreased. High structure classrooms might show the same pro-gression of within-class relations as class average anxiety in-creased but a positive between-groups regression over the con-tinuum of class averages. Furthermore, in correlational studiesof this sort, teaching style differences might cause an ATI pat-tern across the within-classroom regressions while at the sametime being a result of class average differences in anxiety.

When sites are assigned to psychotherapeutic treatments, thelesson is that within-site and between-sites regressions have tobe disentangled and compared within and between treatments.To predict each person's response to treatment, one must lookat each person's A level in relation to the average A for the groupor site. Testing overall treatment regressions for persons withoutregard to site confounds between-groups and within-groupsources of ATI. Unfortunately, unless there are many sites andmany persons within sites, both between-groups and within-group regression tests are weak.

The second strategy of conducting miniature experiments inmany sites adds up to a more powerful regression comparisonand is preferred wherever it is possible. But between-siteswithin-treatment regressions still must be studied; because per-sons are not assigned randomly to sites, the sites may differ inaverage A. One uses a pooled within-site regression to do this.

Group therapy. The above problems are exacerbated whenpersons receive treatment in groups within site. Because of so-cial perception, comparison, and role-taking processes operat-ing in groups, members of such groups are not independent. Ineducational research on small groups, it has been shown thateffects can depend on the person's A, the mix of A in the group,and the role the person adopts in group interaction (Webb,1982,1983). Note also the effect of imposed group process onaptitude-learning relations discussed in connection with Fig-ure 2d.

Meta-analysis. Aggregating miniature experiments acrosssites might be seen as akin to aggregating studies in a meta-analysis. Here, however, it is the raw (or population standard-ized) data that must be amassed across sites with the appro-priate between- and within-regression analysis as outlinedabove.

This points to a general problem for meta-analyses in ATIresearch. Meta-analysis should not be applied to variables stan-dardized within studies, that is, to reported correlations. Yetmost studies do not give the descriptive statistics needed toconvert reported results to raw regressions and place them inpopulation distributions, much less the raw data needed to pro-duce scatterplots or coordinated between- and within-groupregression analyses across studies. Without this, meta-analysisof ATI research will likely lead to contorted and potentiallymisleading results; the only meta-analysis so far conducted ineducational ATI research suffers from these problems (seeWhitener, 1989).

The recommendation follows that psychotherapy researchshould establish an ATI data bank to accumulate the appro-priate raw data for eventual use in meta-analyses. Failing this,

its journals should establish reporting policies that ensure thepossibility of proper accumulation of ATI evidence across stud-ies. At a minimum, each ATI report should include raw means,standard deviations, regressions, and ranges for all A and Ovariables, within treatments. Intercorrelations among As andamong Os, and reliability estimates for each in the total sampleand within treatment groups, are also needed.

Aptitude Complexes

Composites, profiles, and types. In most educational re-search, and here so far, it has been assumed that persons aredescribed using a list of separate aptitudes. The recommenda-tion has been to establish a priority list, starting with the Avariable(s) thought most centrally important to a treatment ofinterest and bringing in others as they are expected to moderateprimary ATI or to be secondarily important in their own right,in some particular situation. If the list becomes long, one cansometimes reduce to composite A variables. In instructionalresearch with cognitive abilities, for example, a common strat-egy extracts a general ability factor and then a differential factorto contrast relative strength in verbal versus spatial abilities; abattery of cognitive tests is thus reduced to two orthogonal Acomposites. With personality variables, however, there are of-ten no strong theoretical or empirical bases for constructingcomposites. Also in most psychotherapy research as well asmuch educational research, sample sizes are too small to justifystatistical definition of composites.

As multiple A variables and higher order ATI have been stud-ied, the notion of aptitude complexes has emerged from therecognition that different aptitude combinations sometimes in-teract with the same treatment contrasts. Figure 2b gave anexample of an Ability X Anxiety interaction with teacher struc-turing. The same studies and other research suggest that a mo-tivational style distinction between achievement via indepen-dence and achievement via conformance interacts with thesame treatment contrast. Thus, when one is using conventionalATI methods (even holding T and O to single variables), a com-plicated analysis and a large sample are needed to estimate aregression equation involving four A variables and their inter-actions. As more variables are added, the conventional analysisquickly becomes weak, impracticable, and probably uninter-pretable.

But persons are whole beings, not simply lists of variables; inthe above example, each is a case point in a four-dimensional Aspace. Might such a space be partitioned into regions whereincommon effects of T on O can be expected? Such regions mightdefine new complex aptitude constructs relevant to particulartreatment situations. Figure 2b may outline a first crude stab atsuch constructs.

Using one prominent theory of achievement motivation, forexample, both ability and anxiety can be interpreted as in-fluencing arousal in achievement situations (as well as havingparticular cognitive effects). Perhaps high ability, high anxietypersons and low ability, low anxiety persons can be described asoveraroused and underaroused, respectively, when experienc-ing low structure treatment. By not imposing external regula-tion on behavior, such treatments demand internal regulation,which neither type of person can provide. High structure treat-

214 RICHARD E. SNOW

ment imposes external regulation, which has the effect of mov-ing both kinds of persons toward optimal conditions for learn-ing by reducing or increasing arousal, respectively, relative tothe low structure treatment that already provides optimalarousal conditions for intermediate ability-anxiety persons.Adding an index to contrast relative need for achievementthrough independent activity versus need for achievement viaconformance to external structure moderates the regionalboundaries of Figure 2b. The TB region expands for personsneeding independent activity and contracts for persons needingconformance to structure; perhaps some curvature of bound-aries is also introduced, inasmuch as achievement via indepen-dence has been shown to correlate with ability. Choosing satis-factory construct interpretations for these regions would re-quire much more case analysis, but note that this sketch is basedon empirical examples. At least this meager first step has re-duced four A variables to two and brought a T variable into thedefinition of aptitude in the Aptitude X Treatment regions thatresult.

To reach complex aptitude constructs, some investigatorshave applied forms of profile analysis to classify or match per-sons on aptitude profile similarity (or complementarity). Thispossibility deserves attention, but it brings in other problems.First, response to treatment ought to be part of the profile, assuggested above. Second, there are a number of different mea-sures of similarity, each with somewhat different meanings andcomplications; as noted in a previous section, dyadic measuresare particularly complicated and should be avoided. Finally,profile measures step even further away from the original,more directly interpreted A variables than do the regional par-titionings exemplified above, especially when many A variablesare combined to reduce profile complexity; there are attendantproblems in estimating profile reliability (see Gleser & Crespoda Silva, in press).

Various typological constructs are also possible. The TypeA-B distinction among psychotherapists (Chartier, 1971;Razin, 1971) is an old example. In some more recent research,there has been a return to typological descriptions to boil downmultivariate complexes. The Type A personality for heart at-tack risk is a well-known example. The Type T, or sensation-seeking personality, is a more recent addition (Farley, 1989).Again, in any such construct, response to treatments) needs tobe explicitly included if it is to guide research in psychotherapy.

New measurement models. There is a burgeoning new fron-tier in instructional psychology aimed at elaborating substan-tially the older, narrower conceptions of aptitude, learning-de-velopment, and achievement and devising new forms of assess-ment for the new constructs (see e.g., Snow, 1989c). Some workfocuses on improving the diagnosis of learning progress (see,e.g., Frederiksen, Glaser, Lesgold, & Shafto, 1990). Some re-search addresses measurement methods that combine cognitiveand motivational constructs (see, e.g., Kanfer, Ackerman, & Cu-dek, 1989). Some seeks to adapt or replace the assumptions oftraditional psychometric models (see, e.g., Frederiksen, Mis-levy, & Bejar, in press). Much of this work may be suggestive forimproving both aptitude and progress assessment in psycho-therapy. Some of these approaches connect particularly withthe problem of assessing aptitude complexes. But none are yet

sufficiently evaluated in educational research, much less in psy-chotherapy.

Some Formative Hypotheses

Methodological lessons are more likely to transfer from edu-cation to psychotherapy research than are particular substan-tive hypotheses, so method has been the main thrust here. Butthree general substantive themes can be seen in the ATI evi-dence to date that deserve brief note in conclusion; each offers ametalevel conceptualization that may help guide more specifichypotheses about ATI in psychotherapy.

Capitalization and Compensation Processes

Much evidence suggests that individual differences comeinto play as aptitudes as a function of situational demands andaffordances. Therefore, these demand-affordance conditionscan be manipulated in treatment design to capitalize onstrengths in some aptitudes while at the same time compensat-ing for weaknesses in others. A treatment that demands, oraffords the opportunity to exercise, a particular personal capa-bility or tendency can be made to use this characteristic as anasset in compensating—that is, in circumventing or remediat-ing—some other personal characteristic. To return again to theprevious example, perhaps teacher-imposed structure capital-izes on one kind of tendency—toward achieving via confor-mance to external structure, in order to compensate foranother—inability to control the negative arousal effects ofoverly high or low anxiety. Removing teacher structure capital-izes on an opposing tendency—toward achieving via indepen-dent, personal control of ability and arousal.

Different therapeutic treatments also differ in both the de-gree and kinds of demand-affordance structures they impose.Analysis of treatment contrasts in these terms may help identifythe aptitudes each calls into play and thus the kinds of capitali-zation-compensation processes that might be observed. A sim-ple example is the form of systematic desensitization that re-quires clients to generate and control vivid visual imagery; itcapitalizes on an ability that not all clients possess. A contrast-ing treatment will need to compensate for this inability, perhapsby using an opposing strength in verbal-analytic ability. A morecomplex example comes from Shoham-Salomon's (1991; seealso Shoham-Salomon, Avner, & Neeman, 1989) results withparadoxical interventions, which suggest how one treatmentmight sometimes work on both sides of an aptitude differenceto reflect different capitalization-compensation processes.Persons who are reactance prone defy therapist directives toengage deliberately in the symptomatic behavior; they mobilizetheir resistance and thus become able to control the symptom-atic behavior directly. Persons who are not reactance prone ap-pear better off initially in self-control therapy; with paradoxicaltreatment, however, they follow the therapist directives andthereby gain increased self-efficacy with respect to controllingthe symptoms eventually. Apparently then, paradoxical inter-vention capitalizes on high reactance to reduce symptoms im-mediately; it also circumvents low reactance to build an alterna-tive aptitude for reducing symptoms in the long run.


Zones of Tolerable Problematicity

Each treatment's demand-affordance structure needs to beunderstood, of course, in relation to the aptitude patterns of thepersons being treated, and these require description in termsrelative to populations, not just to samples at hand. In thisconnection, an emergent notion in ATI research posits that foreach person-treatment combination there is a threshold of de-mand near which optimal learning progress can occur. Treat-ment demand that is far below this threshold elicits algorithmicunmotivated response and thus little progress. Treatment de-mand too far above threshold is overwhelming and aversive,eliciting maladaptive response, either algorithmic and rigid orhelpless and random, and also little progress. In a zone of tolera-ble problematicity around this threshold, however, treatmentdemand engages heuristic psychological processes that enablethe assembly and control of adaptive response and thus pro-gress toward the goal.

Although this concept emerges from educational research oncognitive abilities in relation to learning and problem solving(Elshout, 1987), it has been used to interpret ATI results forachievement motivation and anxiety, such as those used as ex-amples here (see Snow, 1989a). It suggests that an importantfuture research goal should be to identify and understand thesethresholds and zones for each type of person-treatment combi-nation of interest. It also suggests that some important kinds ofATI may be curvilinear, especially when personality variablesserve as aptitudes. The implications for psychotherapy researchare the same. For each type of person and treatment situationthere is likely to be a threshold or zone within which optimaleffect is achieved and outside of which it is not. Research needsto focus on understanding this phenomenon.

Prototypical Person-Treatment Combinations

Discussion of aptitude complexes, demand-affordancestructures in treatments, and key thresholds and zones in theperson-treatment interface implies finally a different approachto conceptualizing ATI in psychotherapy that seems akin toMischel's (1984) brand of person-situation interactionism. Notall person variables or treatment variables are relevant to allpersons. Rather there may be bundles of person and treatmentfeatures that reflect prototypes of successful person-treatmentoutcomes. These prototypes may display local consistenciesalthough they may not apply across all contexts. ConventionalATI research methods may be used to help identify aspects ofthese prototypes or bundles. So may case-by-case analysis andaccumulation in one site. But the resulting ATI constructs willbe local theories, rich descriptions useful for understandingand using ATI in a particular time and place, with a particularrange of persons (Cronbach, 1975,1982b; Snow, 1977a). As per-sons or situations depart from the prototype, this local theoryno longer applies, although some other local theory might. Theresult is a loose confederation of miniature prescriptions thatmay even be in some ways inconsistent with one another; it isnot a unified grand design for psychotherapy. But such localtheories may prove useful whether or not general theories everprove possible in the ATI field.

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Received March 1,1990Revision received October 1,1990

Accepted October 15,1990 •

aptitude-treatment interaction as a framework for research ... · interaction is defined...

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