Job Demands and Worker Health: Three-Dimensional ...public.kenan-flagler.unc.edu/faculty/edwardsj/Edwards...Job Demands and Worker Health: Three-Dimensional Reexamination of the Relationship

Journal of Applied Psychology1993, Vol. 78, No. 4, 628-648 Copyright 1993 by the American Psychological Association, Inc

0021-9010/93/S3.00

Job Demands and Worker Health: Three-Dimensional Reexamination ofthe Relationship Between Person-Environment Fit and Strain

Jeffrey R. Edwards and R. Van Harrison

The most influential study of the person-environment (P-E) fit approach to stress was conductedby J. R. P. French, R. D. Caplan, and R. V Harrison (1982). Unfortunately, this study operational-ized fit using various transformations of difference scores, thereby introducing numerous substan-tive and methodological problems. In the present study, the authors reanalyze data from French etal, using a procedure described by J. R. Edwards (in press) that avoids problems with differencescores and captures the underlying three-dimensional relationship between E, P, and strain. Resultsresolve ambiguities in the French et al. findings and identify relationships between E, P, and strainthat, although consistent with P-E fit theory, cannot be adequately represented by fit measures suchas those used by French et al. Implications for P-E fit research are discussed.

The person-environment (P-E) fit approach to stress(Caplan, Cobb, French, Harrison, & Pinneau, 1980; French,Caplan, & Harrison, 1982) has become widely accepted amongorganizational stress researchers (Eulberg, Weekley, & Bhagat,1988). In essence, the P-E fit approach states that misfit be-tween the person and the environment may produce psychologi-cal, physiological, and behavioral strains (e.g., dissatisfaction,elevated serum cholesterol, and smoking) that ultimately in-crease morbidity and mortality. These basic principles underlienumerous theories of stress in organizations, such as those pro-posed by McGrath (1976), Karasek (1979), Schuler (1980),Beehr and Bhagat (1985), and Edwards (1992).

The most comprehensive study of P-E fit to date was con-ducted by French et al. (1982; see also Caplan et al., 1980). Thisstudy measured E and P variables on eight job dimensions,used five operationalizations of fit, and included 18 measuresof psychological and physiological strain. The results of thisstudy yielded three major conclusions. First, misfit was fre-quently associated with increased strain, particularly job-re-lated affect and psychological disturbance. Second, the rela-tionship between misfit and strain was often curvilinear, with aturning point where E and P were equal. Third, fit measuresrepresenting these curvilinear relationships often accountedfor significant variance beyond that explained by E and P mea-

sures, typically doubling the proportion of variance explainedin strain.

Although the French et al. (1982) study is undoubtedly alandmark in the P-E fit literature, it operationalized fit usingvarious transformations of the algebraic difference between Eand P. As is widely known, difference scores suffer from numer-ous substantive and methodological problems (Cronbach &Furby, 1970; Edwards & Cooper, 1990; Johns, 1981; Wall &Payne, 1973; Werts & Linn, 1970). In fairness, we acknowledgethat French et al. conducted their study before many of theseproblems had been identified and that methods that overcomethese problems have only recently been developed (Edwards, inpress). Nonetheless, these problems severely limit the conclusi-veness of what remains the most important P-E fit study to date.

Our purpose in this article was to reanalyze data from theFrench et al. (1982) study, using the procedure described byEdwards (in press). This procedure involves regressing strain onE, P, and certain higher order terms, such as the square of E andP, their product, and so on, supplemented by tests that explicitlyevaluate the conceptual models underlying the fit measuresused by French et al. As we show, this procedure avoids prob-lems with fit measures; clarifies and elaborates the relationshipbetween E, P, and strain; and shows that the magnitude of thisrelationship was often significantly underestimated.

Jeffrey R. Edwards, Darden Graduate School of Business Adminis-tration, University of Virginia; R. Van Harrison, Medical School andInstitute for Social Research, University of Michigan.

Support for this research was provided in part by Contract HSM-99-72-61 from the National Institute of Occupational Safety and Health,by the Institute for Social Research at the University of Michigan, andby the Darden Graduate School of Business Administration Founda-tion at the University of Virginia. We thank A. J. Baglioni, Jr., for hishelp in managing the data and Mark E. Parry, Shyamal Peddada, DonRichards, and Michael A. Seaman for their helpful comments duringthe preparation of this article.

Correspondence concerning this article should be addressed to Jef-frey R. Edwards, who is now at the School of Business Administration,University of Michigan, Ann Arbor, Michigan 48109-1234.

Overview of P-E Fit Theory

As indicated earlier, the central hypothesis of P-E fit theory isthat misfit between the person and the environment leads topsychological, physiological, and behavioral strains, which ulti-mately increase morbidity and mortality (Caplan, 1987; Frenchet al., 1982; Harrison, 1978,1985). P-E fit can take either of twoforms, one representing the extent to which the rewards andsupplies provided by the environment match the needs andpreferences of the person, and the other representing the extentto which the demands and requirements of the environmentmatch the skills and abilities of the person. Strains encompassvarious deviations from normal functioning, such as dissatisfac-

628

3-D REEXAMINATION OF PERSON-ENVIRONMENT FIT & STRAIN 629

tion, boredom, anxiety, depression, hypertension, elevatedserum cholesterol, smoking, and so on.

P-E fit theory proposes three basic hypothetical relationshipsbetween fit and strain. These relationships are embodied in thefive fit measures used by French et al. (1982) and Caplan et al.(1980). The simplest of these measures, labeled fit, consists ofthe algebraic difference between E and P (E - P) and wasintended to depict a monotonic relationship with strain (seeFigure la). This relationship is expected when, for example,strain not only decreases as supplies increase toward motivesbut continues to decrease thereafter, as when excess suppliescan be applied toward other motives or retained for future use.Two measures, labeled deficiency (E - P for E < P, 0 for E > P)and excess (E-PforE^P,QforE<P), were intended to depictasymptotic relationships with strain. Deficiency represents anegative relationship with strain only when E is less than P(Figure Ic), as when increasing supplies reduce strain up to thepoint of satiation but have little effect thereafter. In contrast,excess represents a positive relationship with strain only when Eis greater than P (Figure le), as when demands increase strainwhen they exceed abilities but not when they fall short of abili-ties. Two measures, poor fit (\E — P\) and the squared differencebetween E and P ((E - P)2, here labeled fit squared), wereintended to represent curvilinear relationships with strain (Fig-ures Ig and li, respectively). These relationships are expectedwhen either excess or inadequate supplies or demands areharmful, as when too much job complexity leads to overloadbut too little creates boredom. Although P-E fit theory clearlydistinguishes these different relationships, it does not specifi-cally predict which is more likely to occur in a given instance.Therefore, all five fit measures were used in the analyses re-ported in French et al. and Caplan et al.

Problems With Fit Measures Used byFrench EtAl. (1982)

Because the five fit measures used by French et al. (1982)were based on difference scores, they introduce numerous sub-stantive and methodological problems (Cronbach & Furby,1970; Edwards, in press; Edwards & Cooper, 1990; Johns, 1981;Wall & Payne, 1973; Werts & Linn, 1970). For example, thesemeasures confound the separate relationships of £ and P withstrain. For some job dimensions, only EOT P was significantlycorrelated with strain, suggesting that relationships for thecorresponding fit measures may have reflected the influence ofonly one component. If so, then results for those fit measuresare spurious (Wall & Payne, 1973).

Second, fit measures with different substantive interpreta-tions often yielded significant relationships with strain. For ex-ample, for job complexity, deficiency was negatively related tojob dissatisfaction, indicating that dissatisfaction fell as E in-creased toward P, but remained constant as E exceeded P (seeFigure Ic). However, excess was also positively related to jobdissatisfaction, indicating that dissatisfaction was constant as Eincreased toward P, but increased thereafter (Figure le). In ad-dition, poor fit and fit squared were both positively related tojob dissatisfaction (Figures Ig and li, respectively), indicatingthat dissatisfaction increased symmetrically as E either ex-ceeded or fell short of P. Taken together, these results suggest

that the actual underlying relationship was probably some hy-brid of those represented by the deficiency, excess, poor fit, andfit squared measures, but the exact nature of that relationshipremains ambiguous. Significant correlations for more than onefit measure were also found for other job dimensions and in-dexes of strain, resulting in similar ambiguities (Caplan et al.,1980; French et al., 1982).

Third, fit measures effectively impose an untested set of con-straints on the joint relationships of E and P with strain. Forexample, using fit to predict strain is equivalent to regressingstrain on E and P with their coefficients constrained to beequal in magnitude but opposite in sign (Edwards, in press;Edwards & Cooper, 1990). Deficiency, excess, poor fit, and fitsquared impose additional constraints on the coefficients on E,P, and certain higher order terms these measures implicitly in-clude, as detailed later in this article. Although these con-straints were not tested by French et al. (1982), their resultssuggest that these constraints may be overly restrictive. For ex-ample, the relationships of £ and P with strain often differed inabsolute magnitude or were of the same sign, contrary to theconstraint imposed by the fit measure. Similarly, relationshipsfor deficiency and excess often differed in absolute magnitude,contrary to the symmetry implied by the poor fit and fitsquared measures. Unfortunately, these comparisons are incon-clusive without explicit tests of the constraints imposed bythese measures. If these constraints are rejected, then the corre-sponding fit measures misrepresent the underlying relationshipbetween E, P, and strain.

Finally, fit measures reduce the inherently three-dimen-sional relationship between E, P, and strain to two dimensions.This is illustrated in Figure 1, which compares hypotheticaltwo-dimensional relationships between strain and the five fitmeasures used by French et al. (1982) to their three-dimen-sional counterparts. As Figure 1 shows, each fit measure embod-ies the effects of both E and P as joint predictors of strain. If Eand P are indeed distinct constructs, as indicated by P-E fittheory (Caplan, 1987; French et al., 1982; Harrison, 1978), thentheir relationship with strain is necessarily viewed in three di-mensions, with E and P constituting two perpendicular hori-zontal axes and strain constituting the vertical axis. Collapsingthis relationship into two dimensions violates the conceptualdistinctions between £and P, oversimplifies the potential com-plexity of their joint effects on strain, and prevents tests ofcertain effects suggested by P-E fit theory, such as variation instrain along the E = P line (French et al., 1982; Harrison, 1978).

Three-Dimensional Approach to Examining theRelationship Between P-E Fit and Strain

Problems with the fit measures used by French et al. (1982)can be overcome by using the procedure described by Edwards(in press; see also Edwards, 1991; Edwards & Cooper, 1990).This procedure involves regressing strain on E, P, and certainhigher order terms, such as the square of £ and P, their product,and so on. Because E and P are used as separate predictors,their effects on strain are not confounded, and the three-di-mensional relationship between E, P, and strain is preserved.Furthermore, when constraints on certain combinations of coef-

a. Two-Dimensional Depiction of Fit

5 i 1 1 1 1 1 1 r-

b. Three-Dimensional Depiction of Fit

- 4 - 3 - 2 - 1 0 1 2 3 4

E - P

c. Two-Dimensional Depiction of Deficiency

< Q£T 3

1- 4 - 3 - 2 - 1 0 1 2 3 4

E - P

. Two-Dimensional Depiction of Excess

- 4 - 3 - 2 - 1 0 1 2 3 4

E - P

d. Three-Dimensional Depiction of Deficiency

Three-Dimensional Depiction of Excess


g. Two-Dimensional Depiction of Poor Fit h. Three-Dimensional Depiction of Poor Fit

- 4 - 3 - 2 - 1 0 1 2 3 4

Two-Dimensiona! Depiction of Fit Squaredj. Three-Dimensional Depiction of Fit Squared

- 4 - 3 - 2 - 1 0 1

Figure 1 (left and above). Two- and three-dimensional depictions of relationships between person-environment (P-E) fit measures and strain.

ficients are imposed, the regression equations become mathe-matically equivalent to fit measures such as those used byFrench et al., thereby allowing explicit tests of their associatedconstraints. In addition, surfaces more complex than those rep-resented by fit measures can be analyzed, because the con-straints imposed by these measures can be relaxed and higherorder terms representing additional inflections and curvaturesin the underlying surface can be included.

The benefits of this procedure have been demonstrated byEdwards (in press), who examined the relationship between sat-isfaction and fit across nine job dimensions, using data from172 master of business administration students and 161 execu-

tives. Measures representing fit, poor fit, fit squared, andvarious forms of profile similarity (D2, D, \D\, and Q, see Cron-bach & Gleser, 1953) were compared with regression equationsthat relaxed the constraints imposed by these measures. In allbut one instance, the constraints were rejected. Three-dimen-sional plots revealed that, although many of the surfaces relat-ing E and P to satisfaction could be interpreted from the per-spective of P-E fit theory, most were substantially more complexthan the highly restricted models depicted by the fit and profilesimilarity measures. When the constraints imposed by thesemeasures were relaxed, the average proportion of variance ex-plained in job satisfaction was nearly tripled.

632 JEFFREY R. EDWARDS AND R. VAN HARRISON

The Present Study

In this study, we reanalyzed data from the French et al. (1982)study, using the Edwards (in press) procedure to clarify the rela-tionship between E, P, and strain. We first reproduce core re-sults reported by French et al., thus providing a baseline forcomparing subsequent results. Next, we report confirmatorytests of the restricted models represented by French et al.'s fitmeasures to determine whether the conditions required to sup-port these models are met. Finally, we report exploratory analy-ses, supplemented by cross-validation, to clarify the relation-ship between E, P, and strain. These exploratory analyses wereessential, because the vast majority of the restricted modelsunderlying the fit measures were rejected. Cross-validation wasalso required to identify exploratory models that transcend asingle sample and, hence, are likely to be generalizable andtheoretically meaningful. Taken together, our analyses resolveambiguities in the results reported by French et al. and revealmany relationships between E, P, and strain that, although con-sistent with P-E fit theory, are substantially more complex thancan be depicted by the fit measures used by French et al.

Method

The sample, measures, and data collection procedures used in theFrench et al. (1982) study are described in detail in Caplan et al. (1980).Only a brief description is provided here.

Sample

French et al. (1982) collected data from respondents in 23 occupa-tions at 67 different sites. Occupations ranged from blue collar (e.g.,forklift driver, machine-paced assembler, delivery service courier, andtool-and-die maker), to between blue and white collar (e.g., electronictechnician, police officer, train dispatcher, and industrial supervisor),to white collar (e.g., air traffic controller, programmer, accountant,engineer, scientist, professor, administrator, and family physician).These occupations were chosen because they represented a wide rangeof job characteristics, had exhibited high levels of psychosomaticstrain in previous research, and involved minimal exposure to physicaland chemical hazards, thereby permitting a focus on social and psycho-logical hazards of work. The sample was exclusively male, because ofthe difficulty of obtaining adequate samples of female respondentsacross all occupations at the time the data were collected (1972-1973).The number of respondents in each occupation ranged from 27 to 253,yielding a total sample size of 2,010.

To analyze P-E fit relationships, French et al. (1982) used a randomstratified subsample of 318, consisting of about 14 respondents fromeach occupation that were drawn from the full sample of 2,010. Thissubsample was used for two main reasons. First, French et al. hypothe-sized that P-E fit relationships would differ across occupations. Thiswas supported by follow-up analyses using the full sample, whichfound significant moderator effects based on occupational member-ship (French et al., 1982, pp. 83-89). Although these occupational dif-ferences are of interest themselves, the primary P-E fit analyses wereintended to detect general theoretical relationships that were not spe-cific to a particular occupational group. If the entire sample had beenused, results would have been biased in favor of certain occupations,most notably supervisory, administrative, and professional positions.Second, by using the subsample of 318, enough respondents were re-tained to form a second, nonoverlapping stratified subsample of equalsize for cross-validation. For these reasons, and also to maintain com-parability with French et al., we used the initial subsample to repro-

duce their results and to conduct confirmatory tests of the modelsunderlying their fit measures. We later incorporated the second sub-sample for exploratory analyses and cross-validation and then com-bined the two subsamples to estimate the final exploratory equations.

Data Collection Procedure

Data were collected using a self-administered questionnaire, whichcould be completed in about 1 hr by a person with a high school educa-tion. Most respondents were informed of the study at their places ofwork, usually by a letter indicating management and union endorse-ment and ensuring that responses would be anonymous and confiden-tial. Response rates varied by occupation, ranging from 25% for cer-tain blue-collar occupations to 50%-75% for police officers and univer-sity professors to nearly 100% for train dispatchers.

Measures

For our study, we analyzed two sets of measures contained in Frenchet al.'s (1982) questionnaire. One set consisted of parallel items measur-ing environmental supplies (E) and respondent preferences (P) regard-ing four job dimensions, including job complexity (six item pairs), roleambiguity (four item pairs), responsibility for persons (four item pairs),and quantitative work load (seven item pairs). An example item pair forquantitative work load was "How much work load do you have?" and"How much work load would you like to have?" with responses rang-ing from very little (1) to a great deal (5). Job complexity items used a7-point scale, whereas role ambiguity, responsibility for persons, andquantitative work-load items used 5-point response scales. Item re-sponses were averaged to yield E and /"scores.

Before our analyses, we scale centered E and P measures by subtract-ing the midpoints of their scales (4 for job complexity and 3 for roleambiguity, responsibility for persons, and quantitative work load). Thistransformation reduced multicollinearity in subsequent regressionanalyses and provided a meaningful interpretation of coefficients on Eand P when higher order terms were included (i.e., the slopes of £ and Pat the midpoint of their respective scales; see Aiken & West, 1991;Cronbach, 1987, Edwards, in press; Jaccard, Turrisi, & Wan, 1990).Although this transformation was not conducted by French et al.(1982), it did not influence scores on fit measures, their correlationswith strain, or tests of the constraints they impose; therefore, thistransformation did not compromise the comparability between ourresults and those reported by French et al.

The second set of measures consisted of seven indexes of psychologi-cal strain—including job dissatisfaction (4 items), work-load dissatis-faction (3 items), boredom (3 items), depression (6 items), anxiety (4items), irritation (3 items), and somatic complaints (10 items)—mea-sured on 3- to 5-point response scales. Sample items included "I amunhappy about my current work load," for work-load dissatisfaction;"The work on my job feels dull," for boredom; "I feel sad," for depres-sion; and "\bu had trouble sleeping at night," for somatic complaints.We averaged items for each index to yield an overall score.

Analysis

Reproduction of French et al. (1982). We calculated fit, deficiency,excess, poor fit, and fit squared measures for each of the four jobdimensions, following the procedures described earlier. We then cal-culated correlations between these measures and our seven indexes ofstrain. These analyses reproduced those reported by French et al.(1982) and Caplan et al. (1980) and provided a benchmark for compar-ing subsequent results.

French et al. (1982) also tested the increment in variance explainedby the deficiency, excess, and poor fit measures, after controlling for E


and P. We omitted these analyses, because they do not support therestricted models underlying these measures (as depicted in Figure 1)unless the coefficients on E and P happen to be zero. For example,consider a regression equation in which poor fit is significant aftercontrolling for E and P. If the coefficients on E and poor fit are positiveand equal and the coefficient on P is negative and of the same magni-tude, then this equation is algebraically equivalent to the excess mea-sure. Conversely, if the signs of the coefficients on Band Pare reversed,then the equation is equivalent to the deficiency measure. Caplan et al.(1980) also tested the increment in variance explained by fit squared,after controlling for fit. In this case, a nonzero coefficient on fit movesthe minimum of the U-shaped curve represented by fit squared (Figureli) away from the point where E and P are equal. By analyzing thebivariate relationships of deficiency, excess, poor fit, and fit squaredwith strain, we effectively constrained the coefficients on E and P tozero, as implied by the models underlying these measures. We returnto this point later, when we discuss the implications of the presentstudy for P-E fit research.

Confirmatory analyses. We used the Edwards (in press) procedureto conduct confirmatory tests of the restricted models represented bythe fit, deficiency, excess, poor fit, and fit squared measures. Thisprocedure begins with the researcher deriving an unconstrained re-gression equation for each fit measure. To do this, an equation contain-ing the fit measure as a single predictor is expanded to show its impliedconstraints. These constraints are then systematically relaxed, and anymissing lower order terms are added. Constraints that we identified forthe five fit measures, along with their corresponding constrained andunconstrained equations, are summarized in Table 1.

First, consider the fit measure, which uses the algebraic differencebetween £and jPas a single predictor of strain (S; e represents a randomdisturbance term):

S =

S =

Expanding this equation yields

- btP + e.

0)

(2)

This shows that the fit measure implicitly constrains the coefficientson E and P to be equal in magnitude but opposite in sign. The corre-sponding unconstrained equation simply contains Eand Pas separatepredictors:

S = btE (3)

Equation 3 relaxes the constraint on the coefficients on £and P, allow-ing them to independently take on whatever values maximize the vari-ance explained in strain.

Next, consider an equation containing the poor fit measure, whichrepresents the absolute difference between E and P. Although the con-straints imposed by this measure may not be readily apparent, theybecome obvious by considering the following piecewise linear equa-tion (Neter, Wasserman, & Kutner, 1989), which is mathematicallyequivalent to using the absolute difference between E and P to predictstrain:

5" = b0 + b,(l - 2W\E - P) + e. (4)

W represents a dummy variable that equals 0 when E > P, that equals 1when E < P, and that is randomly set to 0 or 1 when E = P Therefore,when E - P is positive, the term 1 - 2W reduces to 1 and the sign of £ -P is unaltered, but when E - P is negative, 1 - 1Wreduces to — 1 and thesign of E - P is reversed, yielding the same effect as an absolute valuetransformation. Note that when E - P = 0, the term (1 - 2W) (E - P)becomes 0, whether H'equals 0 or 1. Expanding and rearranging Equa-tion 4 yields

- b,P - 2btWP + e. (5)

Now consider an equation containing E, P, W,WE, and WP as separatepredictors (W is included because it is a component of the productterms WE and WP; see Cohen & Cohen, 1983):

S= ba b2P + (6)

Comparing Equations 5 and 6 reveals that the poor fit measure im-poses four constraints: (a) The coefficients on E and P are equal inmagnitude but opposite in sign; (b) the coefficients on WE and WPareequal in magnitude but opposite in sign; (c) the coefficient on WE istwice as large as the coefficient on E, but opposite in sign; and (d) thecoefficient on Wis 0.

Next, consider the deficiency measure, which equals E - P whenE P. This is represented by the followingregression equation:

= b0-bt W(E - (7)

When E < P, W= 1 and W(E - P) simplifies to E - P, but when E > P,W= 0 and W(E - P) = 0, yielding the same effect as the deficiencymeasure. As before, when E = P, E - P = 0 and W(E — P) again equals 0,regardless of W. Expanding Equation 7 yields

S = b0 - b,WP + e. (8)

Comparing Equation 8 to Equation 6 reveals that the deficiency mea-sure imposes four constraints: (a) The coefficients on WE and WPareequal in magnitude but opposite in sign, (b) the coefficient on E is 0, (c)the coefficient on P is 0, and (d) the coefficient on Wis 0.

Now consider the excess measure, which equals E- P when E > Pand 0 when E < P. This is represented by the following regressionequation:

*iO - W)(E-P) (9)

In this case, when E > P, W = 0 and (1 - W)(E - P) simplifies toE-P,but when E < P, W = \ and (1 - W)(E - P) = 0. As before, when E=P,E - P = 0 and (1 - W)(E - P) = 0, independent of W Expanding andrearranging Equation 9 yields

b, WP + e. (10)

Comparing Equation 10 to Equation 6 shows that the excess measureimposes four constraints: (a) The coefficients on E and P are equal inmagnitude but opposite in sign, (b) the coefficients on WE and WPareequal in magnitude but opposite in sign, (c) the coefficients on E andWE are equal in magnitude but opposite in sign, and (d) the coefficientonWisQ.

Finally, the constraints imposed by the fit squared measure can bederived by considering an equation containing the squared differencebetween E and P as a single predictor:

S=b0 + b:(E - P)2 + e.

Expanding and rearranging Equation 11 yields

5 = b0 + b,E2 - 2b,EP + btP2

(11)

(12)

Now consider an equation containing E, P, E2, EP, and P2 as separatepredictors (E and Pare included because they are components of thecurvilinear and interactive terms E2, EP, and P2; Cohen & Cohen,1983):

S = b0 + btE + b2P + + bJSP + + e. (13)

Comparing Equation 13 to Equation 12 reveals that the fit squaredmeasure imposes four constraints: (a) The coefficients on E2 and P2 areequal; (b) the coefficients on E2, EP, and P2 sum to 0 (given the firstconstraint, this is equivalent to stating that the coefficient on EP is


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twice as large as the coefficient on either E2 or P2 but opposite in sign;see Edwards, in press); (c) the coefficient on E is 0; and (d) the coeffi-cient on P is 0.

Once we identified the appropriate unconstrained equations, weestimated them and tested them for significance. We then tested indi-vidual coefficients to determine whether they were significant and inthe predicted direction. Next, we tested the set of constraints imposedby each measure, using the HYPOTHESIS subroutine of the Multivar-iate General Linear Hypothesis (MGLH) module of SYSTAT (Wilkin-son, 1990b) to determine whether the estimated coefficients con-formed to the prescribed pattern (this is equivalent to testing the dif-ference in R2 between the constrained and unconstrained equations,although the procedure used here also allowed tests of individual con-straints). Finally, we tested sets of terms one order higher than those inthe unconstrained equations to determine whether each equation wasadequately complex to represent the underlying surface. Support forthe model underlying the fit measure was inferred if (a) the overallunconstrained equation was significant, (b) the appropriate coeffi-cients were significant and in the right direction, (c) the imposed con-straints were not rejected, and (d) no significant higher order termsbeyond those specified by the unconstrained equation were found(Edwards, in press). It should be emphasized that these analyses testedhighly restricted versions of the fit, deficiency, excess, poor fit, and fitsquared models, as depicted by their corresponding fit measures (seeFigure 1). Failure to support these models did not preclude less re-stricted versions that were conceptually consistent with P-E fit theory,as our subsequent analyses show.

Support for the constraints imposed by the fit, deficiency, excess,poor fit, and fit squared measures involved establishing that the differ-ence in the squared multiple correlation between the constrained andunconstrained equations was not significant, which required adequatestatistical power to detect true differences (Cohen, 1988). With alphaset at .05 and a sample size ranging from 307 to 318, statistical powerwas .80 for detecting differences in the squared multiple correlation ofabout .025 for the fit measure and .0375 for the deficiency, excess, poorfit, and fit squared measures. As we show, actual differences in squaredmultiple correlations were often larger, averaging .029 for the fit mea-sure and .049 for the deficiency, excess, poor fit, and fit squared mea-sures.

Exploratory analyses. To clarify the joint relationship of E and Pwith strain, we conducted exploratory analyses supplemented by cross-validation. First, we used data from the first random subsample toderive 28 exploratory regression equations, 1 for each job dimensionpredicting each index of strain. We derived these equations by estimat-ing polynomials of progressively higher order (quadratic, cubic, etc.),adding the required variables as a set and stopping when the incrementin variance explained was no longer significant. We then repeated thisprocedure using data from the second random subsample. We com-pared results for the two subsamples and chose a set of equations com-mon to both subsamples by identifying the highest order polynomialthat emerged in both subsamples. For example, if one subsampleyielded a quadratic equation and the other successively yielded qua-dratic, cubic, and quartic equations, we chose the quadratic equation.If no single polynomial was significant in both subsamples, wedropped the equation. For the common equations, we then tested dif-ferences between the coefficients for the two subsamples, using theprocedure described by Cohen and Cohen (1983, pp. 312-317), to en-sure that the equations for the two subsamples were comparable (thesetests indicated no significant differences in the coefficients betweenthe two subsamples; all ps > .05). We reestimated the final equationsusing data from the combined subsamples.

The procedure just described should be distinguished from cross-validation as typically practiced in predictive research, in which coeffi-cients obtained from one sample are used to predict the criterion in

another sample. In those situations, the goal is to obtain an estimate ofthe cross-validated squared multiple correlation, which is representedby the squared correlation between the predicted and actual criterionvalues in the second sample (Darlington, 1990). In our situation, thegoal was to distinguish sampling variability from underlying regulari-ties suggesting meaningful theoretical relationships, using convergentresults from multiple samples as evidence for these relationships (Co-hen & Cohen, 1983). This procedure may be more appropriatelyviewed as replication than as cross-validation, at least as these termsare often used in predictive research (Mosier, 1951).

Controlling Type I error. Because of the substantial number ofcorrelation and regression analyses conducted, some method of con-trolling Type I error was required. We chose the sequential Bonferroniprocedure described by Holm (1979) for its simplicity and demon-strated error control (B. S. Holland & Copenhaver, 1988; Seaman, Le-vin, & Serlin, 1991). This procedure begins with the identification ofthe family of tests for which Type I error would be controlled. Hoch-berg and Tamhane (1987) indicated that a family should encompass aset of conceptually related inferences, regardless of their statisticaldependence, and Miller (1981) described a family as a group of relatedobservations analyzed within a single mathematical framework. In thepresent study, the 28 relationships between P-E fit and strain provided aconceptually related set of inferences, and the five fit measures, threeunconstrained regression equations, and final exploratory equationsrepresented different mathematical approaches, or frameworks, in-tended to depict these relationships. Hence, we defined a family as the28 relationships examined within each mathematical approach, yield-ing nine families in all.

Next, we listed in ascending order the probability levels for the 28bivariate or multiple correlations yielded by each approach. We thenmultiplied the first (i.e., smallest) probability by 28, representing thetotal number of tests. If this probability remained below .05, we thenmultiplied the next probability by the total number of remaining tests(i.e., 27). This procedure continued sequentially until we had correctedall 28 probabilities, and only those that remained below .05 were con-sidered significant. For each multiple correlation that reached signifi-cance, we tested the corresponding regression coefficients using thenominal alpha level (i.e., .05). This procedure held Type I error for eachfamily below .05, avoided the loss of power associated with the stan-dard Bonferroni correction (B. S. Holland & Copenhaver, 1988), andpermitted comparisons of the relative power of the various fit mea-sures and regression equations.

Results

Reliability and Intercorrelations of Measures

Table 2 shows descriptive statistics, reliability estimates(Cronbach's alpha), and intercorrelations for the E, P, and strainmeasures. With the exception of quantitative work load/P, allmeasures yielded reliabilities of .70 or higher. Corresponding Eand P measures were all positively related, with correlationsranging from .135 for quantitative work load to .683 for jobcomplexity. E measures for job complexity, responsibility forpersons, and quantitative work load were positively related, aswere their respective P measures. All strain measures were alsopositively related. Within rounding error, these correlationsmatched those reported by French et al. (1982).

Reproduction of French et al. (1982)

Table 3 shows correlations between strain and the fit, defi-ciency, excess, poor fit, and fit squared measures. For job com-


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plexity, poor fit and fit squared demonstrated the strongest re-lationships with strain, suggesting that strain was lowest at thepoint of perfect fit and increased symmetrically in either direc-tion. However, correlations for deficiency and excess were op-posite in sign but often different in absolute magnitude, imply-ing that the relationship between fit and strain was asymmetric.Furthermore, fit was negatively correlated with boredom, sug-gesting a monotonic relationship. Similar results were found forquantitative work load and, to a lesser extent, for role ambiguityand responsibility for persons. It should be noted that, in manyinstances, the correlations reported in Table 3 were smallerthan those for the separate E and P measures (Table 2), indicat-ing that the predictive power of the E and P measures takenseparately was often diminished by collapsing them into a fitmeasure.

Confirmatory Analyses

Results for the unconstrained regression equations for the fit,deficiency, excess, poor fit, and fit squared measures are pre-sented in Table 4, and F tests of constraints and higher orderterms are presented in Table 5. For simplicity, Table 4 showsonly those regression equations that reached significance usingthe sequential Bonferroni procedure, and Table 5 shows tests ofconstraints and higher order terms only for those equations thatwere significant and yielded the expected pattern of coeffi-cients (complete tables are available from Jeffrey R. Edwards).

Examining the unconstrained equations for fit shows that thecoefficients on E and P were significant and opposite in signonly for quantitative work load predicting work-load dissatisfac-tion (bi = 0.657, b2 = -0.808) and irritation 0, = 0.255, b2 =-0.210). Tests of the constraint imposed by the fit measureindicated that the coefficients on E and P did not differ inabsolute magnitude in either equation, F(\, 309) =1.42 and F(\,310) = 0.04, ps > .05. However, significant higher order termswere found for work-load dissatisfaction, ,F(3, 306) = 5.35, p <.01, indicating that the data deviated from the planar surfaceimplied by the fit measure (Figure Ib). In contrast, no signifi-cant higher order terms were found for irritation, F(3, 307) =0.91, p> .05, indicating that the underlying surface, in fact,resembled the plane depicted in Figure Ib, with the caveat thatthe slope for E was positive and the slope for P was negative.Hence, of the five significant correlations between fit and strain(Table 3), only one supported the model underlying the fit mea-sure.

Results for the unconstrained equation for deficiency, excess,and poor fit indicated that, in 14 of 28 analyses, the overallequation was significant. However, none of these equationsyielded the pattern of coefficients corresponding to the defi-ciency measure (i.e., negative coefficient on WE, positive coeffi-cient on WP, and nonsignificant coefficients on E, P, and W). Incontrast, the pattern of coefficients corresponding to excessand poor fit (i.e., positive coefficients on E and WP, negativecoefficients on P and WE, and nonsignificant coefficient on W)emerged for job complexity predicting work-load dissatisfac-tion and anxiety and for responsibility for persons predictingwork-load dissatisfaction. Tests of the constraints imposed bythe excess measure were rejected for job complexity predictingwork-load dissatisfaction, F(4,302) =2.72,p<.05, and anxiety,


Table 3Correlations Between Fit Measures and Strain

Fit measure

Job dimension &strain measure

Job complexityJob dissatisfactionWork-load dissatisfactionBoredomDepressionAnxietyIrritationSomatic complaints

Role ambiguityJob dissatisfactionWork-load dissatisfactionBoredomDepressionAnxietyIrritationSomatic complaints

Responsibility for personsJob dissatisfactionWork-load dissatisfactionBoredomDepressionAnxietyIrritationSomatic complaints

Quantitative work loadJob dissatisfactionWork-load dissatisfactionBoredomDepressionAnxietyIrritationSomatic complaints

Fit

-.035.154

-.256**.032.063.095

-.113

.075

.037

.042

.058

.092

.123

.032

-.135.072

-.236**.009.052.055

-.100

.191

.495**

.049

.248**

.120

.266**

.047

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-.194*-.034-.379**-.088-.076-.017-.190*

-.014-.022-.035

.005

.071

.074

.030

-.184*.005

-.287**-.023

.007

.040-.098

.076

.260**

.019

.160

.058

.145

.006

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.185*

.325**

.017

.171*

.213**

.194*

.038

.169*

.104

.132

.107

.083

.142

.021

.022

.176*-.031

.070

.121

.061-.061

.208**

.510**

.054

.241**

.126

.271**

.058

Poorfit

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.264**

.360**

.204**

.223**

.155

.202**

.137

.097

.130

.072-.011

.029-.015

.212**

.088

.295**

.063

.058-.011

.074

.188*

.419**

.049

.177*

.107

.220**

.060

Fitsquared

.228**

.190*

.322**

.146

.171*

.068

.174*

.087

.080

.128

.050-.046

.022-.027

.204**

.096

.303**

.062

.041

.006

.051

.188*

.404**

.043

.187*

.071

.199**

.018

Note. Ns ranged from 308 to 313. Table entries are product-moment correlations. Probability levels forthe 28 correlations tested for each fit measure were corrected using the sequential Bonferroni proceduredescribed by Holm (1979).*/><.05. **p<.01.

F(4,303) = 2.53, p < .05. However, the excess constraints werenot rejected for responsibility for persons predicting work-loaddissatisfaction, F(4, 305) = 2.10, p > .05. Higher order termswere also not significant, F(6, 299) = 1.04, p > .05, therebyindicating that the surface relating responsibility for persons/Eand responsibility for persons/P to work-load dissatisfactionresembled Figure If. Constraints for the poor fit measure wererejected for job complexity predicting work-load dissatisfac-tion, F(4,302) = 5.85, p < .01, and for responsibility for personspredicting work-load dissatisfaction, F(4, 305) = 3.97, p < .01.However, the poor fit constraints were not rejected for job com-plexity predicting anxiety, F(4,303) = 2.18, p > .05, and higherorder terms were not significant, F(6, 297) = 1.74, p > .05,indicating that the surface relating job complexity/E and jobcomplexity/P to anxiety corresponded to Figure Ih. Hence, al-though the deficiency, excess, and poor fit measures collectivelyyielded 29 significant correlations with strain, the deficiencymodel was not supported, and the excess and poor fit modelswere each supported only once.

Results for the unconstrained equation for fit squared indi-

cated that in 13 of 28 analyses, the overall equation was signifi-cant. However, the expected pattern of coefficients (i.e., nonsig-nificant coefficients on E and P, positive coefficients on E2 andP2, and negative coefficient on EP) was obtained only for re-sponsibility for persons predicting boredom. However, the con-straints imposed by the fit squared measure were rejected, F(4,305) = 3.34, p < .01. Hence, although the fit squared measureyielded 11 significant correlations with strain, the restrictedmodel underlying this measure received no support.

The preceding results strongly indicate that, with few excep-tions, the restricted models underlying the fit measures used byFrench et al. (1982) do not adequately represent the relationshipbetween E, P, and strain. This may seem counterintuitive, giventhat these measures were often significantly correlated withstrain. To clarify why these models were not supported, wepresent in Figures 2 and 3 three-dimensional plots of raw data,surfaces predicted by the five fit measures, and surfaces pre-dicted by the three unconstrained equations, using job com-plexity predicting boredom and quantitative work load predict-ing work-load dissatisfaction as examples. These examples were


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Table 5Tests of Constraints and Higher Order Terms

Fit* Excess & poor fitb Fit squared"

Strain measure

Higher Higher HigherFit order Excess Poor fit order Fit squared order

constraint terms constraints constraints terms constraints terms

Job complexityWork-load dissatisfactionAnxiety

Responsibility for personsWork-load dissatisfactionBoredom

Quantitative work loadWork-load dissatisfaction 1.42Irritation 0.04

2.72*2.53*

2.10

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5.85**2.18

3.97**

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1.043.34** 1.20

Note. Ns ranged from 308 to 313. Table entries are F ratios. For each model, tests are only reported forthose equations that yielded significant multiple correlations and the predicted pattern of coefficients.E = measure of environment; P = measure of person; W= a dummy variable that equals 0 when E > P, thatequals 1 when E<P, and that is randomly set to 0 or 1 when E = P.* For fit, a single constraint was tested, that is, the coefficients on E and P are equal in magnitude butopposite in sign (fr, = -b2). Higher order terms were tested as a set and included E2, EP, and P2, representinga quadratic model.b For excess, four constraints were tested as a set: (a) The coefficients on £and Pare equal in magnitude butopposite in sign (fi, = -fi2), (b) the coefficients on WE and WP are equal in magnitude but opposite in sign(fit = -fi5), (c) the coefficients on E and WE are equal in magnitude but opposite in sign (ft, = -&,), and (d) thecoefficient on W(b3) is 0. For poor fit, four constraints were tested as a set: (a) The coefficients on E and Pare equal in magnitude but opposite in sign (b, = -62); (b) the coefficients on WE and WP are equal inmagnitude but opposite in sign (ft, = -fi5); (c) the coefficient on WE is twice as large as the coefficient on E,but opposite in sign (fi, = -2bt); and (d) the coefficient on W(b^) is 0. For both excess and poor fit, higherorder terms were tested as a set and included E2, EP, P2, and the product of W with these terms (WE2, WEP,and WP2), which allows independent curvature and tilt in the triangular surfaces on eitherside of the E= Pline.c For fit squared, four constraints were tested as a set: (a) The coefficients on E2 and P2 are equal (b, = bs);(b) the coefficients on E2, EP, and P2 sum to zero (63 + fi, + 65 = 0); (c) the coefficient on E (fi,) is 0; and (d)the coefficient on P (b2) is 0. Higher order terms were tested as a set and included E3, E2P, EP2, and P3,representing a cubic model.*p<.05. **p<.01.

chosen because they yielded the strongest relationships acrossthe five fit measures but, nonetheless, rejected the models un-derlying these measures in every case. For both examples, rawdata were plotted using distance-weighted least squares, whichproduces a locally weighted surface that flexes to fit the data(McLain, 1974; Wilkinson, 1990a).

Raw data for job complexity predicting boredom (Figure 2a)indicated that boredom not only decreased as either E or Pincreased but also was lower in the region where E and P wereapproximately equal. This surface differed substantially fromthose predicted by the fit and deficiency measures (Figures 2band 2c), even though both yielded significant correlations withboredom. Surfaces predicted by the poor fit and fit squaredmeasures (Figures 2e and 2f) corresponded somewhat moreclosely to the raw data, but both indicated constant levels ofboredom along the E = P line, which is clearly not the case. Ofthe unconstrained equations, the fit squared equation seemedto best represent the data (Figure 2i).

Raw data for quantitative work load predicting work-loaddissatisfaction (Figure 3a) indicated that dissatisfaction was low-est in the region where E and P were approximately equal andincreased in either direction, with a more pronounced increasewhere E exceeded P(i.e^ where actual work load exceeded pre-

ferred work load). This surface was notably different from thosepredicted by the fit, deficiency, and excess measures (Figures3b, 3c, and 3d, respectively), even though each yielded signifi-cant correlations with work-load dissatisfaction. The surfacespredicted by the poor fit and fit squared measures (Figures 3eand 3f) were somewhat better, but both inappropriately forcedsymmetry on either side of the E=P line. Of the unconstrainedequations, the fit squared equation again seemed best, althoughit did not adequately depict the curvature along the E axis.Further inspection revealed that this curvature was caused by afew isolated cases and, hence, should not be given undue consid-eration in interpreting the overall shape of the surface.

Exploratory Analyses

Results for the final exploratory equations of the relationshipbetween E, P, and strain are reported in Table 6. Seven equa-tions indicated that strain was linearly related to either EOT P.In four of these equations, E was positively related to strain (roleambiguity predicting job dissatisfaction, work-load dissatisfac-tion, depression, and anxiety), whereas in two equations E wasnegatively related to strain (responsibility for persons predict-

a. Raw Data b. Fit

c. Deficiency d. Excess

e. Poor Fit f. Fit Squared

a ff

3-D REEXAMINATION OF PERSON-ENVIRONMENT FIT & STRAIN

g. Unconstrained Equation for Fit

641

h. Unconstrained Equation for Deficiency, Excess. & Poor Fit i. Unconstrained Equation for Fit Squared

Figure 2 (left and above). Three-dimensional plots of actual and predicted surfaces relating environment(E) and person (P) measures of job complexity to boredom. (Scales for E and P are reversed to allow betterviewing of the surfaces.)

ing job dissatisfaction and boredom). One equation indicated anegative relationship between P and strain (quantitative workload predicting job dissatisfaction). Because none of theseequations indicated significant relationships for both E and P,they provided no evidence for fit.

Three equations yielded significant coefficients for both Eand P. One equation (quantitative work load predicting bore-dom) yielded negative coefficients on both E and P, indicatingthat boredom was lowest when quantitative work load/E andquantitative work load/f were both high. Although plausible,these relationships were not predicted by P-E fit theory. In con-trast, two equations (quantitative work load predicting depres-

sion and irritation) yielded a positive coefficient on E and anegative coefficient on P, analogous to the fit model. Furtheranalyses indicated that, for quantitative work load predictingirritation, the coefficients on E and P did not significantlydiffer in absolute magnitude, F(l, 623) = 2.55, p > .05. Hence,the equation for quantitative work load predicting depressionsupported a weak version of the fit model, in which E and Pexhibited opposite but unequal relationships with strain,whereas the equation for quantitative work load predicting irri-tation supported a strong version of the fit model, in which Eand P exhibited opposite but essentially equal relationshipswith strain.

a. Raw Data b. Fit

..**

c. Deficiency d. Excess

e. Poor Fit f. Fit Squared

3-D REEXAMINATION OF PERSON-ENVIRONMENT FIT & STRAIN

g. Unconstrained Equation for Fit

643

h. Unconstrained Equation for Deficiency, Excess. & Poor Fit Unconstrained Equation for Fit Squared

Figure 3 (left and above). Three-dimensional plots of actual and predicted surfaces relating environment(E) and person (P) measures of quantitative work load to work-load dissatisfaction.

Six equations yielded positive coefficients on E2, negativecoefficients on EP, and a mixture of positive, negative, and non-significant coefficients on E, P, and P2. A complete interpreta-tion of these equations and their corresponding surfaces re-quires the application of response-surface methodology (Box &Draper, 1987; Khuri & Cornell, 1987), which is beyond thescope of this article. Nonetheless, salient features of these sur-faces can be identified by comparing them with the surfacecorresponding to the fit squared measure (Figure Ij). For sim-plicity, we focus on three features. First, consider the slopealong the E = P line. This can be represented in equation formby substituting E for P in Equation 13:

S = b0 + b,E + b-f. + bi

= b0 + (6, + bz)E + (63

= b0 + diE + a2E2 + e.

+ b5E2 + e

b5)E2 + e

(14)

For convenience, we let a, = b\ + b2 and a^ = b3 + ft, + b5. AsEquation 1 4 shows, the slope along the E = P line has a linearcomponent (atE) and a curvilinear component (aÊ2). If the fitsquared constraints hold, then both £, and b2 equal 0 and Z>3, ft,,and bs sum to 0. Consequently, a\ and a^ are both 0, indicatingthat the surface is flat along the E = P line, as in Figure Ij. If a,differs from 0 but <% does not, then the surface has a linear slope


Table 6Final Exploratory Equations for E, P, and Strain

Strain measure EP P2 R2 Rl

Job complexityJob dissatisfactionWork-load dissatisfactionBoredomDepressionAnxiety

Role ambiguityJob dissatisfactionWork-load dissatisfactionDepressionAnxiety

Responsibility for personsJob dissatisfactionBoredom

Quantitative work loadJob dissatisfactionWork-load dissatisfactionBoredomDepressionIrritation

-0.0820.103

-0.467**0.0230.096**

0.215**0.252**0.138**0.138**

-0.158**-0.276**

0.1180.377**

-0.159*0.110**0.231**

-0.117*-0.226**-0.023-0.029-0.009

-0.004-0.006

0.011-0.029

-0.0400.070

-0.508**-0.455**-0.605**-0.266**-0.137**

0.131**0.212**0.154**0.060**0.047**

0.402**

-0.216**-0.207**-0.206**-0.099**-0.153**

-0.401*

0.0680.0230.124**0.0140.044

-0.110

.140**

.100**

.301**

.044**

.058**

.044**

.044**

.050**

.043**

.067**

.102**

.072**

.322**

.078**

.060**

.066**

.133

.093

.296

.037

.051

.041

.041

.047

.040

.064

.099

.069

.316

.075

.057

.063

Note. Ns ranged from 615 to 634. Values for environment (E), person (P), E2, EP, and P2 are unstandard-ized regression coefficients for equations in which all predictors were entered simultaneously. R2 is thesquared multiple correlation coefficient, and R\^ is the adjusted squared multiple correlation coefficient.Probability levels for the R2s were corrected using the sequential Bonferroni procedure described by Holm(1979), assuming a total of 28 tests; all remained significant at p < .001.*/j<.05. **/><.01.

along the E ~ P line, with the sign indicated by a,. If 02 ispositive, then the surface is curved upward (i.e., convex) alongthe E = P line, whereas if a^ is negative, the surface is curveddownward (i.e., concave) along the E = P line. (In either case, a,indicates the slope where E = 0, which represents the midpointof the E, P plane when data are scale centered.) Tests of a, and aâre conducted by dividing each by its standard error, which iscalculated using standard rules for determining the variance ofa sum of random variables. Alternately, a, and <% can be testedindividually or jointly by determining whether their corre-sponding coefficient sums differ from 0, using the MGLH mod-ule of SYSTAT. Note that, because E = P in Equation 14, P canbe substituted for E with no effect on the obtained results.

Next, consider lateral shifts in the surface along the E = -Pline, perpendicular to the E = P line. The magnitude and direc-tion of the shift along the E = -P line is given by the quantity(t>2 — bi)/2(b3 — ft, + b}). A positive value indicates a shift towardthe region where E > P, whereas a negative value indicates ashift toward the region where E<P. Note that, if the fit squaredconstraints hold, ft, and ft2 are both 0 and the surface remainscentered along the E = P line, as in Figure Ij. If ft, and b2 areequal in both magnitude and sign, the surface again remainscentered along the E = P line, although its slope at the midpointof that line (i,e., a,) is no longer 0.

Finally, consider rotations in the surface, such that its mini-mum no longer lies along the E = P line. The magnitude anddirection of these rotations are a function of ft3, b4, and ft5. Ifb3

and ft, are equal, then the surface does not rotate, independentof ft,. If ft3 is less than fts, the surface rotates clockwise, whereasif ft3 is greater than ft5, the surface rotates counterclockwise. In

either case, the magnitude of the rotation is determined notonly by the difference between ft3 and ft5 but also by ft,, withlarger rotations for smaller values of ft,. Note that rotations canoccur in combination with lateral shifts, such that the mini-mum of the surface is not only displaced laterally from the E =P line but is also no longer parallel to that line. Also note that,in addition to indicating rotations in the surface, ft3, ft,, and fts

influence the curvature of the surface along the E = P linethrough their effect on a^, as described earlier.

These principles were first applied to the equation for jobcomplexity predicting boredom, which yielded positive coeffi-cients on E2 and P2 and negative coefficients on E and EP. Thejoint test of a, and a^ was significant, F(2,611) = 62.03, p < .01,as were the individual tests of a,, .F(l, 611) = 78.08, p < .01, andof 02, F(l, 611) = 6.18, p < .05. The signs on a, and a^ werenegative and positive, respectively, indicating a steep negativeslope along the E = P line, with a slight upward curvature. Thequantity (b2 - ft,)/2(ft3 - ft, + fts) was 0.459, indicating a shifttoward the region where E > Pof about half a unit along the E=-P line. Furthermore, b3 was slightly larger than fts, indicating amodest counterclockwise rotation. In combination, these re-sults indicated a surface much like that depicted in Figure 2i,where boredom was lower when job complexity/E and job com-plexity/P were both high than when both were low and, for agiven level of/? where boredom was minimized when £ slightlyexceeded P rather than when Eand /"were equal, particularly atlow levels of E and P.

The equations for job complexity predicting job dissatisfac-tion and work-load dissatisfaction yielded positive coefficientson E2 and negative coefficients on P and EP. In both cases, a.


was negative and significant (p < .05) and ̂ was not significant,thereby indicating a negative linear slope along the E = P line.The quantity (b2 - 6i)/203 ~b4 + b5) was also small and negativein both cases (—0.042 for job dissatisfaction and —0.371 forwork-load dissatisfaction), indicating a small shift toward theregion where E < P. In addition, b3 was larger than bs, particu-larly for work-load dissatisfaction, indicating a counterclock-wise rotation. Taken together, these results indicated two majordeviations from the surface depicted in Figure Ij. First, as withboredom, job dissatisfaction and work-load dissatisfactionwere lower when job complexity/E and job complexity/P wereboth high than when both were low. Second, when E and Pwere both low, dissatisfaction was minimized when E wasslightly greater than P, but when E and P were both high, dissat-isfaction was minimized when E was slightly less than P.

The equation for job complexity predicting depressionyielded a positive coefficient on E2 and a negative coefficienton EP. However, a, and a2 were not significant either individu-ally or jointly, indicating that the surface was essentially flatalong the E = P line. The quantity (b2 - bt)/2(b3 - ft, + b5) was—0.148, and b3 was notably larger than bs, indicating a slightshift toward the region where E<Palong with a counterclock-wise rotation. These results indicated a surface much like Fig-ure Ij except for a counterclockwise rotation, such that when Eand P were both low, depression was lowest when E was slightlygreater than P, but when E and P were both high, depressionwas lowest when E was slightly less than P.

For job complexity predicting anxiety, the coefficients on Eand E2 were positive, whereas the coefficient on EP was nega-tive. The joint test of a, and c^ was significant, F(2,613) = 5.85,p < .01, as were individual tests for a:, F(l, 613) = 6.07, p < .01,and for a2, F(\, 613) = 11.63, p < .01. The signs on a, and a^ werepositive and negative, respectively, indicating that the surfacewas positively sloped but concave along the E = P line. Thequantity (b2 - b^)/2(b3 - ft, + 65) was -0.216, and b3 and bs wereessentially equal, indicating a slight shift toward the regionwhere E< /"with no appreciable rotation. Taken together, theseresults indicated that anxiety was lowest when job complexity/E was slightly less than job complexity/P and increased in eitherdirection and also that anxiety was higher when E and P wereboth moderate than when they were both either high or low.

Finally, the equation for quantitative work load predictingwork-load dissatisfaction yielded positive coefficients on E andE2 and negative coefficients on P and EP. Individual and jointtests of at and a2 were not significant, indicating that the surfacewas essentially flat along the E = P line. The quantity (b2 -bi)/2(b3 - 64 + 65) was -0.600, and b3 was notably larger than Z?5,indicating a moderate shift toward the region where E < Panda substantial counterclockwise rotation. These results indicateda surface similar to Figure 3i, in which, when quantitative workload/E and quantitative work load/P were both high, work-loaddissatisfaction was lowest when E was notably less than P, butwhen E and P were both low, work-load dissatisfaction waslowest when E was slightly greater than P

DiscussionSummary of Results

The results of this study provided little support for the re-stricted models depicted by the fit, deficiency, excess, poor fit,

and fit squared measures used by French et al. (1982). Althoughthese measures collectively yielded 45 significant correlationswith strain, the constraints imposed by these measures weresupported in only three instances. Relaxing these constraintsincreased adjusted squared multiple correlations from an aver-age of .024 for the constrained equations to .059 for the uncon-strained equations—more than doubling the proportion of ex-plained variance. Exploratory analyses identified four generalclasses of models. One class involved significant relationshipsfor either E or P and, hence, provided no evidence for fit. Asecond class indicated relationships of the same sign for E andP that, although theoretically plausible, are not accounted forby P-E fit theory. A third class involved opposite relationshipsfor E and P, corresponding to the fit model. Finally, the fourthclass consisted of various modifications of the fit squaredmodel, with slope or curvilinearity along the E= Pline, shiftsor rotations of the region of minimum strain from the E = Pline, or some combination thereof. Taken together, these mod-els bear certain basic similarities to those underlying the fitmeasures used by French et al., particularly the models for fitand fit squared measures, but also indicate substantively mean-ingful relationships that these measures cannot adequately rep-resent.

The results of this study resolved ambiguities in the findingsreported by French et al. (1982), thereby allowing firmer con-clusions regarding the relationship between E, P, and strain. Insome cases, our conclusions supported those drawn by Frenchet al., with certain modifications. For example, French et al.concluded that work-load dissatisfaction increased as work-load/E deviated from work-load/P particularly when E ex-ceeded P The present study supported this conclusion butadded that, at low levels of E and P, work-load dissatisfactionwas lowest when E slightly exceeded P, whereas at high levels ofE and P, work-load dissatisfaction was lowest when E was nota-bly less than P

French et al. (1982) further concluded that job dissatisfac-tion, work-load dissatisfaction, boredom, depression, and anxi-ety increased when job complexity//! deviated from job com-plexity/P They also noted several asymmetries, with a strongerrelationship for boredom when E fell short of P and strongerrelationships for work-load dissatisfaction, depression, and anx-iety when E exceeded P The present study supported theseconclusions, with four modifications. First, job dissatisfaction,work-load dissatisfaction, and boredom were higher when jobcomplexity//? and job complexity/P were both low than whenboth were high. Second, when job complexity//? and job com-plexity/P were both low, job dissatisfaction, work-load dissatis-faction, and depression were lowest when E was slightly greaterthan P, whereas when E and P were both high, these strainswere lowest when E was slightly less than P Third, for all levelsof job complexity//: and job complexity//? boredom was lowerwhen E slightly exceeded P than when E and P were equal,particularly when E and P were both low. Finally, anxiety washigher when job complexity/E and job complexity/P were bothmoderate than when they were both high or low.

Although many features of the three-dimensional relation-ship between E, P, and strain were not detected by French et al.(1982), these features are, for the most part, consistent with P-Efit theory (Caplan, 1987; French et al., 1982; Harrison, 1978,


1985). For example, Harrison (1978) noted that strain may beminimized at points other than perfect fit. We found this for jobcomplexity, for which a slight excess was often associated withlower strain when E and P were both low. This seems reason-able, given that perfect fit for very simple jobs may result inmonotony and, hence, strain. Conversely, at high levels of jobcomplexity/E and job complexity//? strain was often lowestwhen E was slightly less than P. This suggests that maintainingfit for complex jobs may be taxing and that conceding to aslight deficiency may result in lower overall strain. A similarinterpretation applies to the relationship between quantitativework load and work-load dissatisfaction, in which dissatisfac-tion was lower for a modest deficiency than for perfect fit whenE and P were both high.

P-E fit theory also indicates that perfect fit may yield differ-ent levels of strain, depending on the absolute levels of E and P(French et al, 1982; Harrison, 1978; see also Imparato, 1972).We found this for job complexity predicting job dissatisfaction,work-load dissatisfaction, and boredom, which were lowerwhen E and P were both high than when both were low. Thismay represent the effects of fit on other job dimensions, in thatcomplex jobs typically entail high pay, status, recognition, andother valued rewards (Harrison, 1978). Alternatively, this mayreflect the operation of two standards when actual job com-plexity is evaluated: one representing the personal preferencesof the employee, and another reflecting workplace, profes-sional, or societal norms that place value on complex jobs. Anx-iety also varied along the line of perfect fit for job complexity,with greater anxiety when E and P were both moderate. Thismay indicate that achieving fit at moderate levels of job com-plexity/E and job complexity/P involves greater uncertaintythan does achieving fit at high or low levels of E and P, resultingin increased anxiety (cf. Beehr&Bhagat, 1985; McGrath, 1976).Future research into P-E fit theory should include measuresnecessary to substantiate explanations such as these.

Our results also indicated that certain conclusions drawn byFrench et al. (1982) should be revised. For example, French et al.reported that job dissatisfaction, work-load dissatisfaction,boredom, and depression increased when role ambiguity/E de-viated from role ambiguity//? with stronger relationships forexcess ambiguity. In contrast, we found that job dissatisfaction,work-load dissatisfaction, and depression were essentially posi-tive monotonic functions of role ambiguity/E. We also foundthat, with the sequential Bonferroni correction, many of thecorrelations for role ambiguity discussed by French et al., in-cluding those for boredom, were no longer significant.

French et al. (1982) also concluded that either too much ortoo little responsibility for persons was related to increaseddissatisfaction and boredom, particularly when responsibilityfor persons was insufficient. In contrast, we found that jobdissatisfaction and boredom were simply negatively related toresponsibility for persons/E. French et al. also reported thatexcess responsibility for persons was associated with increasedwork-load dissatisfaction and anxiety. Using the first randomsubsample, we obtained results that supported the findings ofFrench et al. for work-load dissatisfaction, but when we con-ducted exploratory analyses using both subsamples, neither ofthese findings were supported.

Finally, French et al. (1982) reported that when quantitative

work load/E deviated from quantitative work load//? job dissat-isfaction, depression, and irritation increased, particularlywhen quantitative work load was excessive. In contrast, wefound that these strains were positively related to quantitativework load/E and negatively related to quantitative work load//?analogous to the fit model. French et al. also reported thatboredom increased symmetrically as quantitative work load/Edeviated from quantitative work load//? whereas we found thatboredom was negatively related to both E and P measures ofquantitative work load.

Limitations

Although the present study has substantially clarified andrefined the results reported by French et al. (1982), several limi-tations should be noted. Many of these limitations, such asusing only male respondents, collapsing across heterogeneousoccupations, relying on cross-sectional data, the potential con-founding of £ and P measures with fit, and bias resulting frommeasurement error, were discussed in the original reports (Ca-plan et al., 1980; French et al, 1982) and, hence, are not re-peated here. However, the present study contained some addi-tional limitations. For example, to maintain manageable sizeand scope, we omitted four job dimensions and 11 indexes ofphysiological and behavioral strain that were examined byFrench et al. Consequently, all of our analyses were based onself-report measures, which may have spuriously inflated theobserved relationships. In addition, to avoid bias resulting fromunequal occupational representation, we used only about onethird of the available data. It would be useful to conduct follow-up analyses of occupational differences using the full sample,such as those conducted by French et al. Furthermore, the twosubsamples used for our exploratory analyses and cross-valida-tions were both drawn from the full sample of 2,010 respon-dents rather than from the larger population of employedadults, thereby limiting generalizability (Murphy, 1983). Fi-nally, certain aspects of the three-dimensional surfaces yieldedby the exploratory analyses, such as shifts and rotations of theregion of minimum strain, were described but not formallytested. This was due to the mathematical expressions for sur-face shifts and rotations, which involve products, ratios, andpowers of the coefficient estimates from the quadratic equationand, hence, are not amenable to conventional tests of statisticalsignificance. Future research should attempt to provide moreobjective criteria for describing and testing the exploratory sur-faces yielded by the Edwards (in press) procedure (for one ap-proach, see Edwards & Parry, in press).

Implications for P-E Fit Research

This study has several implications for P-E fit research. First,fit measures that collapse E and P into a single score should beabandoned in favor of polynomial equations containing E, P,and appropriate higher order terms (Edwards, 1991, in press;Edwards & Cooper, 1990; Edwards & Parry, in press). As thisstudy demonstrated, fit measures yield ambiguous results, con-found the separate relationships of £ and P with strain, imposea highly restrictive set of constraints that are rarely supported,and reduce the inherently three-dimensional relationship be-


tween E, P, and strain to two dimensions. The Edwards (inpress) procedure avoided these problems and showed that inmost cases, the relationship between E, P, and strain could notbe adequately represented by the fit measures used by French etal. (1982). Because this procedure uses equations that subsumefit measures, it eliminates the need for these measures and,furthermore, allows tests of a much wider range of surfacesrelating E and P to strain.

A second, related implication is that tests of fit should notfocus on the increment in variance explained by fit measuresbeyond their components, as is often done in P-E fit research.These tests are flawed, not only because they rely on fit mea-sures but also because they do not support the model in ques-tion unless the coefficients on E and P happen to be zero,which is rarely verified. In any case, the fundamental questionin P-E fit research is not whether a given fit measure explainsvariance beyond E and P, but whether the joint relationships ofE and P with strain follow the functional form correspondingto the conceptual model of interest. These relationships can bereadily tested using appropriate polynomial regression equa-tions, thereby avoiding the need for tests of fit measures, eitherindependently or after controlling for E and P.

Third, hypotheses regarding bivariate relationships betweenfit measures and strain should be recast in terms of the direc-tion and relative magnitude of coefficients on E, P, and appro-priate higher order terms in polynomial regression equations.For example, hypothesizing a negative relationship between fitand strain is logically equivalent to hypothesizing a negativecoefficient on E and a positive coefficient on P (see Figures laand Ib). Similarly, a positive relationship for fit squared impliespositive coefficients on E2 and P2, a negative coefficient on EP,and nonsignificant coefficients on E and P along the E = P line(Figures li and Ij). As stated, these hypotheses correspond toweak tests of the fit and fit squared models, because theymerely specify the direction of the coefficients. Strong testswould add hypotheses regarding relative coefficient magni-tudes, as represented by the constraints imposed by the fit andfit squared measures. By stating hypotheses in these terms, re-searchers can consider evidence for both strong and weak ver-sions of fit models, which allows more complete tests of thesemodels and avoids reductions in explained variance caused byroutinely imposing constraints that may be more restrictivethan required by the model of interest.

Fourth, specific hypotheses should be developed for coeffi-cient patterns representing models more complex than the fit,deficiency, excess, poor fit, and fit squared models. Hypothesesfor these five models are embodied in their corresponding fitmeasures and, hence, are fairly easy to derive. However, a majoradvantage of the Edwards (in press) procedure is that it allowstests of models that are more complex than models underlyingfit measures. Hypotheses for some of these models can be de-rived from the coefficients reported in Table 6. For example, aU-shaped surface with a negative slope along the E = P line isrepresented by coefficients on E2, EP, and P2 corresponding tothe fit squared model, supplemented by negative coefficientson E and P. Similarly, a U-shaped surface with a clockwise rota-tion off the E = P line is represented by reductions in the abso-lute magnitudes of the coefficients on E2 and EP relative to thepattern predicted by the fit squared model, and a U-shaped

surface with a counterclockwise rotation is represented by re-ductions in the absolute magnitudes of the coefficients on EPand P2. A U-shaped surface with its minimum parallel to theE = P line but shifted toward the E > P region implies a nega-tive coefficient on E and a positive coefficient on P, whereas asurface shifted toward the E < P region implies a positive coeffi-cient on E and a negative coefficient on P. Hypotheses regard-ing other surfaces may be derived by determining the magni-tude and direction of the coefficients in their correspondingpolynomial equations (Edwards & Parry, in press).

Finally, equations derived through exploratory analysesshould be cross-validated whenever possible. Some equationsobtained in the preceding exploratory analyses contained cubicand quartic terms. Although these terms allowed rather precisedescription of the data, they represented relationships that defymeaningful interpretation, given current theory. Fortunately,none of these terms survived cross-validation, suggesting thatthey merely represented sampling variability. Without cross-va-lidation, these terms would have demanded rather elaboratetheoretical explanations that probably would have failed to gen-eralize beyond the data at hand.

Practical Implications

This study suggests several practical implications that gobeyond traditional guidelines for maximizing P-E fit (e.g.,Dawis & Lofquist, 1984; French et al., 1982; Harrison, 1978;1 L. Holland, 1985; Schein, 1978). First, even when perfect fit isattained, strain may be further reduced by changing the abso-lute levels of E and P. This was evidenced by surfaces relatingjob complexity to job dissatisfaction, work-load dissatisfaction,and boredom, which showed that strain was lower when both Eand P were high than when both were low. Second, strain maybe decreased by creating modest levels of misfit, again depend-ing on the absolute levels of £ and P. This was shown by surfacesfor job complexity that were shifted and rotated off the E = Pdiagonal. Third, for some job dimensions, strain may be de-creased by changes in E and P without regard to fit. This wasimplied by results for role ambiguity, which showed that strainwas essentially a positive monotonic function of actual role am-biguity. Of course, these recommendations are tentative, giventhat they are based on a single, cross-sectional study. Nonethe-less, they suggest that interventions can be more specific and,hence, more effective when the three-dimensional relationshipbetween E, P, and strain is considered.

Conclusion

This study has substantially clarified and refined the resultsreported by French et al. (1982) regarding the relationship be-tween P-E fit and strain. The French et al. results were oftenambiguous, because of the use of fit measures that collapsed Eand P into a single score. The present study used a proceduredescribed by Edwards (in press) that avoids the problems withfit measures and preserves the inherently three-dimensionalrelationship between E, P, and strain. This procedure resolvedambiguities in the original results and showed that the relation-ship between E, P, and strain was often more complex thancould be depicted by the fit measures used by French et al. By


using this procedure in future P-E fit research, researchers mayconduct more complete and precise tests of the three-dimen-sional relationship between E, P, and strain and explore the fullrange of predictions offered by P-E fit theory.

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Received February 27,1992Revision received October 15,1992

Accepted November 6,1992 •

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