CONJOINT MEASUREMENT ANALYSIS OF THE . MULTIPLICATIVE COMPOSITION RULE OONTAINEO IN EXPECTAIIcv THEORY " ‘ Dissertation for-{he Degree Of Ph. D. MICHIGAN STATE UNIVERSITY f '_ * JOHN GRISWOLD BERNER . 1976 j ’ IIIIIIIIIIIINNINIIIIIIINNIIIIIIIIIN L This is to certify that the thesis entitled CONJOINT MEASUREMENT ANALYSIS OF THE MULTIPLICATIVE COMPOSITION RULE CONTAINED IN EXPEC TANC Y THEORY presented by John GrisWold Berner has been accepted towards fulfillment of the requirements for the_EH_L_D_._degree in My Date QEMM /Z7% 0-7639 Major professor ._ _._._‘_ P83 an, M;W},, HOTEL r “357‘ “AAA/‘5‘- NW: 738301: JAN 135W .,.'..1 " n, | F" 3U:‘ ‘1 ‘ a . 1051804 H- \ -:‘ ’1‘“. til) (i ii: (.Juq ABSTRACT CONJOINT MEASUREMENT ANALYSIS OF THE MULTIPLICATIVE COMPOSITION RULE CONTAINED IN EXPECTANCY THEORY By John Griswold Berner Expectancy theory specifies that work motivation is a multiplicative function of behavior-outcome expec— tancy (E), outcome-outcome instrumentality (I), and out- come valence (VJ. The validity of this multiplicative composition rule has never been meaningfully tested be— cause past expectancy theory research has been charac- terized by the following methodological deficiencies: (a) the multiplication of nonratio scale measures of E, I, and V; (b) the use of across-subject, rather than within-subject, analyses; and (c) the improper opera- tionaliZation of I and V. The purpose of the present study was to test this composition rule using conjoint measurement analysis. The conjoint measurement method provides for the analysis of such composition rules in the absence of ratio scale data. It further provides for within-subject analysis John Griswold Berner of these rules. In implementing this method, corrections were made to ensure that I and V were properly opera- tionalized. Usable questionnaire data were collected from thirteen middle managers from the Detroit Metropolitan Area. Two of the thirteen subjects were found to satisfy the conjoint measurement requirements for the multiplica— tive composition rule contained in expectancy (EIV) theory. Evidence for an alternative to the multiplicative composi- tion rule, the dual distributive composition rule, was found for five of the remaining eleven subjects. This composition rule suggests an E + IV model of work motiva- tion. Multidimensional scaling (M—D-SCAL) and hierarchical clustering (HICLUST) were found to yield results consistent with those found for the conjoint measurement analyses. Implications of the results were discussed. Limitations of the study were addressed and suggestions for future research were outlined. CONJOINT MEASUREMENT ANALYSIS OF THE MULTIPLICATIVE COMPOSITION RULE CONTAINED IN EXPECTANCY THEORY By John Griswold Berner A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Psychology 1976 ACKNOWLEDGMENTS I wish to thank my adviser and committee chairman, Dr. Frank L. Schmidt, for his guidance and assistance in this endeavor and throughout my doctoral program. I also wish to thank Drs. David L. Wessel, Michael L. Moore, and Carl F. Frost for their encouragement and constructive criticism throughout the course of this research. ii TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES. CHAPTER I. II. III. IV. VI. VII. INTRODUCTION. REVIEW OF THE EMPIRICAL EVIDENCE. SUMMARY AND DISCUSSION OF THE EMPIRICAL EVIDENCE. Summary A DISCUSSION OF CONJOINT MEASUREMENT. Sign Dependence . Joint- factor Sign Dependence. METHOD. Procedure Subjects. Orderings RESULTS Consistency of Choice Sign Dependence Joint- factor Independence and Sign Dependence Multidimensional Scaling and Hierarchical Cluster Analysis DISCUSSION. Limitations of the Present Study. An Alternative to the Conjoint Measurement Approach. iii Page vi 21 29 31 38 44 47 47 52 52 53 53 S7 71 89 95 97 BIBLIOGRAPHY APPENDIX A. NARRATIVES USED IN WORK MOTIVATION QUESTIONNAIRE . . . B. NARRATIVE PAIRS DEFINING ITEMS IN WORK MOTIVATION QUESTIONNAIRE . iv Page 100 104 110 Table LIST OF TABLES Page Summary of research evidence . . . . . . . . 22 Sentences and outcomes chosen to represent different levels of E, I, and V. . 48 Consistency of subject choice. . . . . . . . 55 The effects of pairwise reversals on the pairwise tests of E, I, and V. . . . . . 61 Pairwise tests of independence and sign dependence. . . . . . . . . . . . . 63 Summary of pairwise tests of , independence and sign dependence . . . . . . 64 Joint-factor tests of independence and sign dependence. . . . . . . . . . . . . 76 Rho correlations of subject agreement in the rank orderings of the 32 E, I, V conditions. . . . . . . . . . 84 A comparison of the conjoint (axiomatic) and numerical approaches to the study of composition rules. . . . . . 99 Figure 10. LIST OF FIGURES Independence of A with respect to B x C. Independence of A with respect to B. Sign dependence of A on B. Sign dependence of A x B on C. Independence of A x B with respect to C. Matrix defined by all possible pairs of the 32 narratives Theorized orderings on the four levels of V for the pairwise tests of the sign dependence of V on I Hypothetical examples of rank-order violations and resultant values of rho in the test for the independence of I x V. Hypothetical example illustrating the principles of hierarchical clustering. Combined spatial-clustering representation resulting from HICLUST clUstering solution and two-space M-D-SCAL solution. vi Page 39 42 42 44 46 50 S8 74 81 85 CHAPTER I INTRODUCTION The decline of the human relations movement in in- dustrial and organizational psychology brought with it the realization that new and better approaches were needed for understanding and predicting worker behavior. In 1964, Vroom suggested one such new approach-~the application of expectancy theory to organizational behavior. Expectancy theory is currently ”perhaps the most widely accepted theory of work and motivation among today's industrial and organizational psychologists [Wahba and House, 1974, p. 121].” In essence, expectancy theory is a theory of be— havioral choice founded on the principle that people behave in ways which maximize their ”gains” and minimize their ”losses.“ Three basic variables provide the foundation for the theory: outcome-outcome instrumentality, outcome vealence, and behavior—outcome expectancy. Outcome-outcome instrumentality (I) refers to the degree to which one out- come is perceived as leading to the attainment of another outcome. This variable is theorized to take values from +1.00 (where outcome 1 is perceived as being a necessary and :sufficient condition for the attainment of outcome j) to —l.00 (where the absence of outcome i is perceived as always leading to the attainment of outcome j and the presence of outcome 1 is perceived as making impossible the attainment of outcome j). Outcome valence (V) refers to the anticipated satisfaction (or dissatisfaction) asso— ciated with an outcome. It also is theorized to take both positive and negative values. Behavior—outcome expectancy (E) refers to the perceived probability that a particular act will be followed by a particular outcome. Being a per- ceived probability, expectancy is theorized to take values from 0.00 to 1.00. The theory specifies two rules for combining these variables in order to arrive at an index of motivation. The first of these rules delineates the manner in which valence is determined. Proposition 1: The valence of an outcome to a person is a monotonically increasing function of the algebraic sum of the products of the valences of all the outcomes and his conceptions of its instrumentality for the attainment of these other outcomes. ‘In equation form the same proposition reads as follows: n V. = f. [ Z V I. ] ' = l . . . J J k=1 ( k 3k) (J I1) f' > O; 11.. = 0 Y JJ where Vj = the valence of outcome j I.k = the cognized instrumentality J (-l i Ijk i l) of outcome j for the attainment of outcome k (Vroom, 1964, p. 17] The second combination rule specifies the manner in which valences and expectancies interact to determine the strength of tendency for an individual to perform a given act. Proposition 2: The force on a person to perform an act is a monotonically increasing function of the algebraic sum of the products of the valences of all outcomes and the strength of his expectan- cies that the act will be followed by the attain- ment of these outcomes. We can express this proposition in the form of the following equation: Fi=fi[ IIIMIS H J(EijVj)] (i=n+1...m) - fi >0; in = 6, Q is the null set where Fi = the force to perform act 1 i' = the strength of the expectancy (05_E1jj l) 3 that act i will be followed by outcome j Vj — the valence of outcome j (Vroom, 1964, p. 18] The behavioral choice nature of the theory is reflected in the assumption that individuals ”choose” to perform those acts with the strongest positive or weakest negative forces. Industrial and organizational psychologists have examined the applicability of the expectancy theory model for predicting a variety of work related variables, ranging from job satisfaction (Porter and Lawler, I968; Graen, 1969; Mitchell and Albright, 1972; Mitchell and Nebeker, 1973) to leadership behavior (House, 1971), and have extensively researched the model's ability to predict job effort and performance (Georgopoulos, Mahoney, and Jones, 1957; Gal— braith and Cummings, 1967; Lawler and Porter, 1967; Hack- man and Porter, 1968; Lawler, 1968; Schuster, Clark, and Rogers, 1971; Arvey, 1972; Schwab and Dyer, 1972; Arvey and Mussio, 1973; Dachler and Mobley, 1973; Lawler and Suttle, 1973; Pritchard and DeLeo, 1973; Pritchard and Sanders, 1973). Research evidence has generally been sup- portive, resulting in the current popularity of the theory. Examination of the research, however, reveals that infer— ences about the validity of the multiplicative properties specified in the theory (Proposition 1: V = XIV, Proposi- tion 2: F = ZEV) have generally been drawn from studies which merely examined the predictability of certain theory specified EZIV products.1 Far fewer studies have attempted to more directly assess the validity of these combinatorial properties by comparing the EIV model with alternative models, and in those studies where this approach has been taken such 1In applying expectancy theory to the industrial set— ting, researchers have generally measured a single job effort + job performance expectancy for inclusion in the model. This reduces the expectancy theory model to EZIV, and in cases where the valence and performance-outcome instrumen- tality of only one ”second-level" outcome are incorporated into the model, it becomes simply EIV. Throughout the course of this discussion, the expectancy theory model will be re— ferred to as the EIV model with the understanding that the model becomes EZIV when the valences and performance-outcome instrumentalities of multiple ”second-level” outcomes are considered. comparisons have generally consisted of part-whole theory comparisons where the EIV model is compared with either its individual E, I, and V components or their pairwise products. In only two studies (Hackman and Porter, 1968; Pritchard and Sanders, 1973) has the EIV model been com— pared with an alternative model for combining all three E, I, and V variables. Those studies which have incorporated EIV model comparisons in an attempt to better assess the validity of expectancy theory’s multiplicative properties will now be reviewed. This will be followed by a discussion of the com- mon deficiencies shared by these studies. Finally, a pro- cedure for more meaningfully examining the validity of the multiplicative properties specified in expectancy theory will be described. This procedure is known as conjoint measurement analysis. CHAPTER II REVIEW OF THE EMPIRICAL EVIDENCE Several studies have contrasted the predictability of the EIV model with the predictabilities of its individual E, I, and V components. Schwab and Dyer (1973), using a sample of 124 blue collar workers working under a standard piece—rate system, compared EIV, E, I, and V predictions of the motivational effects of pay on job performance. Using a modified paired-comparisons technique, subjects were assigned pay valence, performance-pay instrumentality, and effort-performance expectancy scores ranging from 0 to 5. Performance was measured by averaging each subject's hourly productivity over a five week period. Results showed the EIV model correlated .39 (p < .01) with this criterion. E, I, and V correlations with the same criterion were .37 (p < .01), .13, and .17 (p < .05).2 Lawler and Suttle (1973) made similar comparisons using a sample of 69 managers from six retail stores. Sub— jects were asked to indicate their valences for each of 18 2In this study, as in all others reviewed, no informa- tion is provided with regard to whether the results represent statistically significant differences in predictor-criterion relationship. outcomes by rating them on a 9-point Likert scale ranging from extremely desirable (l) to extremely undesirable (9). Performance-outcome instrumentalities were obtained by having each subject indicate on a 7-point Likert scale the extent to which he perceived ”good job performance" leading to each outcome. Effort-performance expectancy was simi- larly measured‘by having each subject indicate on the same 7-point Likert scale the extent to which he perceived ”work- ing hard" leading to "good job performance.” Self, boss, and peer rankings of job effort were used as criterion measures. Results showed the full expectancy theory model (EZIV) correlated .39 (p < .01), .28 (p < .01), and .16 with these rankings. The same rankings correlated .37 (p < .01), .28 (p < .01), and .05 with E and .29 (p < .05), .19, and .22 (p < .01) with I. No correlations were com- puted for V. Pritchard and Sanders (1973) asked 146 postal em- ployees undergoing a 30 hour training program to indicate their valences for each of 15 job outcomes on an 11-point Likert scale ranging from -5 to +5. Instrumentalities were obtained by having each employee estimate the chances in ten that successfully completing the training program would result in each outcome. Because some subjects did not answer all items, mean responses were used as the final measures of V and I. Expectancy was measured by taking each employee's mean response to a series of three questions measuring perceptions about the relationship between ”work- ing hard" and successfully completing the training program. Using these measures, the EIV model was found to correlate .47 with self-reported effort in the training program, .16 with supervisor-rated effort in the training program, and .17 with supervisor-rated performance in the training pro- gram. E was found to correlate .13, .01, and .00 with these criteria, I correlated .22, -.02, and .02, and V correlated .54, .22, and .24. Graen (1969), using a sample of 169 females, com- pared EZIV and E correlations with performance under each of three simulated organizational climates. Subjects were randomly assigned to the three climate conditions. In the Reciprocating Climate, subjects perceived rewards as being contingent upon effective performance. In the Prompting Climate, sujbects perceived rewards as being inducements to effective performance. Subjects in the Control Climate perceived rewards as being neither contingent upon, nor inducements to, effective performance. .Valence was measured by asking each subject to rate the importance of each of ten outcomes. Instrumentality was measured by asking each subject to indicate on a 5-point scale what she felt her chances were of receiving each out- come if she performed effectively. Expectancy was measured by asking each subject to indicate on a 5-point scale what she felt her chances were of improving her performance if she ”really worked hard." ¥__—__-_ Performance on two kinds of tasks served as cri- teria. Search tasks required that the subjects locate and record certain specified numbers in a correlation matrix. Rounding tasks required that the subjects like- wise locate numbers in a correlation matrix, rounding them from six to two decimal places before recording them. Quality and quantity measures were obtained for both tasks. Controlling for ability and outcome importance dif- ferences, Graen found significant EZIV correlations with performance under the Reciprocating Climate only. More specifically, post—treatment quantity gain scores on two rounding tasks were found to significantly correlate with EZIV under this condition (.28 and .39). Graen concludes from these findings that organizational climate places an important boundary condition on the applicability of ex- pectancy theory. However, under the same condition, sig- nificant E correlations (.33 and .46) were obtained with these criteria, and E was also found to significantly negatively correlate with quantity gain on a rounding task under the Prompting Climate (r = —.23, p < .05). Equally unimpressive results have been found in studies comparing the full EIV model with El, IV, and EV part model alternatives. Dachler and Mobley (1973) com— pared EZIV and EIV predictions of performance in two plants. Plant 1 subjects (N=18l) were predominantly females working on sewing jobs and paid on an individual piece—rate basis. Plant 2 subjects (N=412) were male production workers paid on an hourly basis. 10 Valence was measured by asking each subject to indicate the desirability of each of 45 outcomes on a 5-point scale ranging from +2 to -2. Instrumentality was measured by having each subject rate on a 5-point scale his/her perceived chances of getting an outcome given that he/she was working at each of five levels of performance. Expectancy values were obtained by asking each subject to indicate on a 5— point scale his/her perceived probability of being able to consistently perform at each of the five levels of per- formance. EZIV and EIV scores were calculated for each level of performance, and the levels of performance cor— responding to each subject's maximum EZIV and EIV scores were then correlated with actual worker productivity to assess the relative utility of the two predictors. Mul— tiplicatively weighting EIV by E was interpreted as improv— ing worker performance predictability in plant 1 (r = .30, p < .01, versus r = .04), while no differences in performance predictability were found in plant 2 (r = .12, p < .05, ver- sus r = .11, p < .05). Boundary conditions similar to those discussed by Graen were cited to account for the results in plant 2. Mitchell and Albright (1972) conducted a similar study using a sample of 51 naval aviation officer volunteers. Likert scale ratings of the importance of each of 12 out- comes were used as measures of valence. Instrumentality was measured by asking each subject to indicate on the same 11 Likert scale the extent to which ”doing a good job” would increase his chances of receiving each outcome. Two measures of expectancy were used. The first required that each subject choose, from among five alternatives, the statement best describing how hard he had to work to perform well (E1). The second required that each subject choose, from among five alternatives, the statement best describing how much his performance would improve if he increased his effort significantly (E2). EIV values were found to correlate .22 and .50 (p < .01) with superior and self—ratings of effort and .29 (p < .05) and .36 (p < .05) with superior and self—ratings of performance. ElZIV values correlated .26 (p < .05), .64 (p < .01), .31 (p < .05), and .19 with these four criteria and EZZIV values correlated .01, .25 (p < .05), .16, and .08. On the basis of these results, the authors conclude that weighting EIV by E does not significantly increase the ability to predict job effort and performance. EZIV and ZIV predictions of job effort and per- formance were also compared in the previously described studies by Lawler and Suttle'(1973) and Pritchard and Sanders (1973). Lawler and Suttle found that weighting EIV by E increased the correlation with self—rated effort from .31 (p < .05) to .39 (p < .01), increased the corre- lation with superior-ranked effort from .17 to .28 (p< .01), anti decreased the correlation with peer rankings of effort 12 from .20 (p < .05) to .16. Even less supportive results were found by Pritchard and Sanders. IV correlations with supervisor-rated effort (.16) and supervisor-rated per— formance (.17) were unchanged when weighted by E, and the IV correlation with self-reported effort went from .50 to .47. In only two studies has an attempt been made to evaluate the importance of multiplicatively weighting EV by I. Neither study found that such weighting contributed to the prediction of worker behavior. Arvey and Mussio (1973) had each of 196 female clerical workers indicate their valences for ten outcomes by distributing 100 points among them on the basis of perceived importance. Instru- mentalities were obtained by having each subject indicate on a 5-point scale the certainty with which she felt "effec- tive performance" would lead to the occurrence of each out— come. Expectancy was measured by asking each subject to indicate on the same scale the extent to which she agreed or disagreed with the statement: ”If I apply a great deal of effort on my job, that is, work very hard, I will be re- garded by my superior as an effective performer.” EZV and EZIV values were correlated with supervisory ratings on each of seven job outcomes. EXV correlations were found to range from -.01 to .15 (p < .01), with a median of .04, while EZIV correlations ranged from -.04 to .07, with a median of .06. Superior ratings of overall job performance 13 also failed to differentially correlate with EZV and EZIV (.12 versus .11). Similar nonsupportive results were found by Pritchard and Sanders (1973) for their sample of postal employees. In all cases, weighting EV by I resulted in slightly smaller job effort and performance correlations. Somewhat greater support is said to exist for weight- ing El by V. Lawler and Porter (1967), using a slightly modified version of the EIV model, compared full-model pre- dictions of job effort and job performance with those ob- tained with V excluded from the model. Modification of the theory consisted of combining measures of effort-performance expectancy and performance-outcome instrumentality into a single measure of effort-outcome ”expectancy.” This reduces the expectancy theory model from EIV to "E”V for a single performance-related outcome and from EZIV to Z"E"V for mul- tiple performance-related outcomes. A sample of 154 managers indicated their valences and ”expectancies” for each of seven outcomes on 7-point Likert scales. Each subject's 7 "E”V scores were then placed into a multiple regression equation. Using this procedure, multiple correlations of .27 and .18 were found with superior rankings of job effort and job performance, .30 (p < .05) and .21 with peer rankings, and .44 (p < .01) and .38 (p < .01) with self-ratings. When ”expectancy” scores alone were used in a multiple regression equation, somewhat smaller 14 correlations with these criteria emerged (.22 and .17, .25 and .21, .32 (p < .01) and .25). The authors conclude from these results that valence functions as hypothesized in the expectancy theory model. Unfortunately, the authors' failure to cross-validate their findings raises serious doubt about the appropriateness of this conclusion. Even more impor— tantly, their use of multiple regression to examine the relative advantage of weighting or not weighting by valence is inconsistent with expectancy theory formulations. Ex— pectancy theory says nothing about treating the ”E”V values associated with different job outcomes as optimally weighted multiple predictors in a multiple regression equation. It instead specifies that the sum of these “E“V values be used as a single predictor. Hackman and Porter (1968) more correctly analyzed the same modified model. Eighty-two female telephone com- pany service representatives were asked to indicate their effort-outcome ”expectancies” for each of 14 outcomes on a 7—point Likert scale. Valence was measured by obtaining importance ratings for these 14 outcomes. Many performance criteria were used: superior ratings of job involvement, work quality, work quantity, judgment, dependability, ini- tiative, cooperation, and ability to learn; company records of error rates and sales effectiveness; and a composite ”effectiveness index" derived from these ratings and company records. 2”E”V predictor score correlations with these 15 criteria were found to range from .06 to .40 (p < .01), with the median correlation being .27 (p < .01). £"E" predictor score correlations with the same 11 criteria ranged from -.08 to .23 (p < .05), with a median of .11. On the basis of these findings, Hackman and Porter concur that valence warrants inclusion in the expectancy theory model. Results of a study by Gavin (1974) fail to support this contention. A total of 175 female and 192 male mana- gerial candidates at a large insurance company were asked to indicate the ”value” of each of 21 rewards on a 9—point scale ranging from "extremely undesirable” to "extremely desirable.” Effort-reward ”expectancies” for these 21 re- wards were obtained using a procedure similar to those used by Lawler and Porter (1967) and Hackman and Porter (1968). A modified Likert-type rating procedure was used to obtain superior ratings of performance on each of nine dimensions. Ratings were summed and correlated with both Z"E”V and Z"E” predictor scores. Correlations of .22 (p < .01) and .28 (p < .01) were found for the female sample; .28 (p < .01) and .25 (p < .01) for the male sample. Large correlations between the weighted (Z”E”V) and unweighted (2”E”) pre- dictors (.91 in both samples) were cited by the author to account for these findings. In the only study to date to compare the full EIV expectancy theory model with the alternative EI "model,” l6 Lawler and Suttle (1973) found no evidence that multipli- catively weighting by V contributes to the prediction of job behavior. EZI correlations with self, superior, and peer‘reported job effort were changed at most .01 by such weighting. An extraordinarily high correlation (r = .96) between the weighted and unweighted predictors was simi— larly cited by these authors to account for their results. The studies of Hackman and Porter (1968) and Pritchard and Sanders (1973) have been the only ones to compare the EIV model with an alternative model for combining E, I, and V. Results of these studies, which in both cases tested the additive model (E + I + V) as an alternative, are interpreted as showing modest support for the multiplicative model. As previously reported, Hackman and Porter obtained multipli- cative model (”E”V model) correlations with 11 performance criteria ranging from .06 to .40 (p < .01) with a median of .27 (p < .01). Additive model (”E” + V) correlations with the same criteria ranged from —.01 to .27 (p < .01), with a median of .17. Also as previously reported, Pritchard and Sanders found the multiplicative model to correlate .47 with self-rated effort, .16 with supervisory-rated effort, and .17 with supervisory—rated performance. Additive model cor— relations with these criteria were found to be .36, .07, and .09. Two studies (Schwab and Dyer, 1973; Galbraith and Cummings, 1967) have employed multiple regression techniques 17 in order to obtain what is said to be essentially the same kind of multiplicative versus additive model comparison in- formation. In these studies, the criterion was first re- gressed on E, I, and V to determine the amount of criterion variance explained by these variables when considered in an additive fashion. EIV was then added to the regression equation and the increment in criterion variance explained by this addition was tested for statistical significance. The size of this incremental change is said to indicate the extent to which the EIV interaction is "useful” for explain- ing criterion variance not explained by the additive effects of E, I, and V (Darlington, 1968). From this information, inferences are drawn about the appropriateness of the multi- plicative and additive models. Heneman and Schwab (1972) strongly endorse this approach and recommend that it be more widely used in future expectancy theory research.3 In the previously described Schwab and Dyer study (1973), applying this procedure to the data from their 3Unfortunately, like Porter and Lawler (1967), Heneman and Schwab fail to recognize that the introduction of EIV into a multiple regression equation is incongruent with the expectancy theory model. Any information obtained using this procedure is therefore of limited utility. In addition, the utility of this information is further re- duced by the fact that the additive model derived from multiple regression techniques is not the same simple addi- tive model employed in the Hackman and Porter (1968) and Pritchard and Sanders (1973) studies. This is, of course, attributable to the fact that introducing E, I, and V into a multiple regression equation has the effect of differ- entially weighting these variables (by something other than their standard deviations) to achieve maximum predictability. 18 sample of 124 blue collar workers failed to demonstrate EIV interaction ”usefulness." Introducing EIV into the re- gression equation increased the multiple correlation with hourly productivity from .39 (p < .01) to .42 (p < .01) for this sample. Galbraith and Cummings (1967) obtained similar re- sults upon applying a variant of this technique to the data from their sample of 32 factory workers. Subjects were asked to indicate the instrumentality of high performance for each of six outcomes. Valence was measured by asking the subjects to rank order the six outcomes by importance. No measure of expectancy was obtained. For each outcome, an objective measure of performance over a one month period was regressed on I, V, and IV in a step-wise manner. Re- sults showed that only six of the possible 54 interactions entered into the equations significantly. Finally, two studies have utilized experimental methods to test for some of the interactive relationships suggested by EIV theory. Pritchard and DeLeo (1973), in a partial test of the theory, experimentally manipulated in- strumentality and valence to test for an I x V interaction effect. Subjects were 60 mainly college students ranging in age from 16 to 27. The experimental situation was pre- sented as a real job, with the subjects told they were being employed on a part-time basis for one night only. Their task consisted of transforming catalogue numbers 19 according to a specified formula and then looking up the "special sale” prices that corresponded to the new cata- logue numbers. The number of catalogue numbers transformed and priced over a 90 minute period was the dependent vari- able. A 2 x 2 design was used with performance-pay instru- mentality and pay valence serving as the independent vari- ables. Performance-pay instrumentality was set at two levels by paying half the subjects on a piece-rate basis (high in- strumentality) and half the subjects on an hourly basis (low instrumentality). Two different pay rates were used to manipulate pay valence. Controlling for ability differences, results showed significant main effects for both instrumentality and valence. However, the main effect for valence was in the opposite than predicted direction. The predicted I x V interaction did not appear. Arvey (1972) tested for an E x I interaction in the laboratory. A sample of 180 male college undergraduates performed an arithmetic task under varying expectancy and instrumentality conditions. Three levels of expectancy and two levels of instrumentality were used. Expectancy was manipulated by telling different groups of subjects the proportion of ”top performers" in their group was likely to be either .20, .50, or .75. Instrumentality was manipu- lated by telling different groups of subjects the proportion 20 of ”top performers" receiving a reward in their group (ex- perimental points for their psychology class) was likely to be either .25 or .75. Subjects performed the task for 20 minutes and then filled out a questionnaire asking them to state their subjective expectancies and instrumentalities. On the basis of these responses, which closely corresponded to the objective probabilities of the manipulations, sub- jects were reclassified for analysis purposes. Using the number of correct answers on the arithmetic task as the dependent measure, results showed the main effect for instrumentality to be clearly nonsignificant (F = .30, p < .60). The predicted main effect for expectancy approached significance (P = 2.84, p < .06), and a test of linear trend (Snedecor and Cochran, 1967) revealed a significant linear relationship between expectancy and performance (t = 2.00, p < .05). No evidence was found for an E x I interaction (F = 2.06, p < .13). Subsequent to task performance, sub- jects were also asked how much they wanted the reward of experimental points, making it possible to test for an E x I x V interaction. Results of this test were not sig- nificant (F not reported). CHAPTER III SUMMARY AND DISCUSSION OF THE EMPIRICAL EVIDENCE In order to better assimilate and interpret the research evidence, results of the studies reviewed have been summarized for inclusion in Table 1. Examination of Table 1 suggests two general conclusions. First, as indi- cated by the bottom row in Table l, the components of ex- pectancy theory, whether alone or in combination, best predict self-reported job effort. This is not surprising since the theory is designed to predict motivation rather than actual performance (which is also dependent upon ability differences, role perceptions, etc.). What is surprising is that superiorereported job effort is not better predicted. Second, and more importantly, entries in the last column of Table 1 show there is little empirical evidence to indicate that the EIV model is superior to other alternative "models." The apparent implication of this finding is indisputable. The current widely held acceptance 21 22 .moSUNcnoou cofimmoHMOH onHp -Hze mconamEo mofiosum Ho moflwspm an monaocfl pom ow moNHuco canoe .AmoHBSHm mo Nonescv oommgo>m mcoHumHoHNoo mo Hogans ow Howoh m.z .m.H ou xomn m.N HonomHm ommuo>m ecu mcfiuwo>cou menu can .mommpo>m onEMHmz Hfiogu mcfioaflw .m.N Hogomflm ou m.H mqfiuuo>coo >9 woumasono oHoz one mcoHumHoHHoo ommgo>m on moHHHQo macaw “ouoz HNH u zv HNH 1 ZS HmH u zv Hm u zo HmH n zv meoeuHeene eN. NH. mH. HN. oe. HH< He 1 ZS HN u 2V HH 1 ZS NH O zv NH. --- NH. No. --- em. > + H + m HHH u zv HN u zo HN 1 2V Hm u 2V HH u zv Hm n zo NN. NH. ON. NH. em. me. >H He u 2v HN u 2v HH u zo HH u zo NN. --- NH. HN. --- Nm. >m Hm u 2U HH u zo HN u zv NN. --- --- mN. --- NN. Hm He n zo HH 1 2o HH u zo HH n zv HH u zo Hm. NH. HN. NN. --- em. > Hm 1 2o HH 1 ZS HH u zo HN 1 ZS HH u 2V mo. NH. No. me. --- mN. H HHH u zo Hm u 2o He u zo HN 1 ZS HN n zv HN. mm. NH. OH. --- HN. m HNN n zo Hm u zv HN u 2o He u zo HN 1 ZS He u zv mN. mN. eN. NH. HH. me. >Hm confinEou mumm oucmsuowuom uaommm mocmsuowhom ugowmm mflpoufiuu oucwehomuom ooupomom wouaomom oouyommm oopuomom Nouoflooum HH< o>Huoonno -HOHHomsm -HOHHQQSm -wHom . -mHom coapouwyu oocoofi>o noumomoh mo Shmeesm H canoe 23 of EIV theory and its multiplicative specifications is clearly not warranted by the research evidence.4 One of the few persons to fully recognize the non- supportive nature of the research evidence, Mitchell (1974), has suggested that the failure to find support for the mul— tiplicative EIV model might be attributable to some common methodological deficiencies which characterize the majority of the empirical studies.so far conducted to examine the model. The identification of each of these deficiencies points to the same general conclusion--that the EIV model operationalized for empirical testing generally deviates, in some way or ways, from the original theoretical statement of the model. The argument is made, therefore, that we re- frain from drawing conclusions about the EIV model until we have empirically tested more accurate representations of the overall theory. Mitchell’s primary focus is on the frequest improper conceptualization and measurement of the variables going into the model. For example, valence is theorized to refer to the anticipated satisfaction associated with an outcome. 4In the majority of the studies contributing to Table l, I and V measures for more than one "second-level" outcome were introduced into the EIV model. The argument can be made that this procedure prohibits testing the mul- tiplicative properties of eXpectancy theory independently from the additive property of the theory (Proposition 1: V = XIV). However, significantly different results were not found in those few studies where the use of single I and V measures permitted independent examination of these multiplicative properties (Schwab and Dyer, 1973; Pritchard and DeLeo, 1973; Arvey, 1972). 24 Yet, as Mitchell points out, valence is most often opera— tionalized as an importance measure, with subjects being asked to indicate the importance they place on given out- comes (such was the case in all but three of the studies summarized in Table 1). Mitchell further notes that, while valence is theorized to take both positive and negative values, negatively valent outcomes are seldom included in empirical tests of EIV theory (only two of the studies re— viewed contained negatively valent outcomes). The same kind of inconsistency is pointed out by Mitchell with regard to the measurement of instrumentality. In Vroom's original statement of expectancy theory, instru- mentality is theorized to take values from -1 to +1. Never- theless, in the majority of expectancy theory studies, in- strumentality is conceptualized and operationalized as a probability, taking only positive values (such was the case in all of the studies summarized in Table 1). Finally, Mitchell points to the inappropriateness of using across-subject analyses to test the EIV model. One of the characteristics of expectancy theory, either overlooked or ignored by researchers, is that it is a theory of behavioral choice. As previously mentioned, this property of the theory is reflected in the assumption that people "choose," from among alternative acts, the one with the strongest postive or weakest negative force (F = EZIV). 25 Thus, the EIV model is essentially a within-subject model. However, as Mitchell points out, it is seldom tested as a within-subject model. Instead, a single measure of force is typically calculated for each subject, followed by an across-subject analysis. The only study in which the ipsative nature of the EIV model has been recognized is that of Dachler and Mobley (1973). As reported earlier, subject perceptions of expectancy were obtained, in this study, for each of five levels of performance, making it possible to deter- mine the amount of force each subject associated with these five levels of performance. The level of performance asso- ciated with each subject's maximum force score was then correlated with actual performance. Using this more ipsative approach, correlations of .30 (p < .01) and .12 (p < .05) were found for plant 1 and plant 2 personnel. In an attempt to compare these coefficients with those ob- tained using the more typical normative approach, Dachler and Mobley later correlated each subject’s maximum force score (a normative measure) with actual performance. This approach yielded plant 1 and plant 2 correlations of .14 and .18 (p < .05). Thus, only minimal evidence is pro- vided by the Dachler and Mobley study that greater support will be found for the EIV model when it is more correctly tested as an ipsative model. Additional research is ob- viously needed, however, before this issue can be 26 satisfactorily resolved, and the theoretical apprOpriate- ness of employing within-subject analyses in future ex— pectancy theory research cannot be denied. Considered in total, the methodological deficien- cies recognized by Mitchell raise serious doubt about the legitimacy of using Table I evidence to draw conclusions about the validity of the EIV model. This becomes espe- cially apparent when it is realized that all of the studies contributing data to this table are characterized by at least one of these methodological deficiencies, and two- thirds of the studies share at least three of these de- ficiencies. However, an even more fundamental method- ological error also characterizes virtually all of these studies. This error is of such a fundamental nature that it makes the evidence presented in Table l virtually un- interpretable. Furthermore, until methodological changes are made to correct this error, changes of a much more sophisticated nature than those suggested by Mitchell's criticisms, future research on the multiplicative proper— ties of EIV theory will continue to be meaningless. Briefly stated, this methodological error consists of treating nonratio data as if it were ratio data. One of the more obvious features of expectancy theory research is that the variables going into the EIV model are most commonly assessed by using Likert-type rating scales (see literature review). Such scales lack a rational zero 27 point (although zero points are frequently assigned) and thus constitute, at best, interval scales. Because the zero points on interval scales are arbitrary, it is logically meaningless to multiply scores on interval scales (Nunnally, 1967). Only scores on ratio scales, which have rational zero points, can be meaningfully mul- tiplied. Thus, to,multiply E, I, and V interval scale scores in an attempt to assess the validity of the EIV model is equally meaningless. Nevertheless, this proce- dure has been adopted almost universally in past expec- tancy theory research. Schmidt (1973), who first recognized the implica- tion of this fundamental error, was able to demonstrate the empirical ambiguity which it creates.5 Two sets of artificial ”expectancy,” valence, and job effort data were generated.6 In generating each data set, care was 5Hackman and Porter (1968) were the first to rec- ognize the nonratio nature of expectancy theory measures and, thus, the inappropriateness of treating their product as a psychometrically valid measure of motivation. How- ever, while conceding this point, Hackman and Porter mini- mized its importance, arguing that the EIV product can be meaningfully judged by "practical validity criteria.” It is true that for any given situation the practica1.validity of the EIV product can be evaluated by examining its re- lationship with the criterion or criteria of interest. However, as Schmidt points out, the primary intent of most expectancy theory research has not been to establish its situation specific practical validity, but rather its theoretical validity, and it is precisely to this end that the multiplication of nonratio data is clearly inappropriate. 6In this study, as in others reviewed, effort- performance expectancy and performance-outcome instrumen- tality were combined into a single measure of effort— outcome "expectancy." 28 taken to ensure that the intercorrelations among these variables fell within the range of empirical findings. Transformations of the general form X + b (where X equals the original score and b some nonzero constant), which are permissible for interval measures because they do not change their meaningful rank order and equal interval properties, were then performed on the ”expectancy” and valence scores in each data set. This was followed by an examination of the different job effort correlations resulting from these transformations upon combining E and V multiplicatively. In the first data set, where the original "E”V correlation with job effort was .36, X + b transformations of "E” and V produced "E"V model correlations ranging from -.27 to .56. Essentially the same kind of results were found for data set two, where the original ”E"V correlation of .75 was found to vary from -.76 to .76 as a result of these transformations. Thus, in all cases job effort cor— relations with the multiplicative model were greatly in- fluenced by these transformations.7 The implications of these findings are obvious. It is senseless to attempt to establish the theoretical validity of the EIV model by multiplying interval measures _ 7It can be argued that B, when assessed as a sub- Jective probability, is actually a ratio measure. However, SChmidt was able to demonstrate that X + b transformations of V alone also produce dramatic fluctuations in multiplica- tive model correlations with job effort. 29 of E, I, and V and then correlating their products with an appropriate criterion measure. The results of this kind of examination are contingent upon the location of the arbitrarily placed (and therefore equally meaningful) zero points on these measures. Summary By way of summary, EIV theory is currently charac- terized by the following set of ironical circumstances. First, it is the most popular and widely accepted theory of worker motivation in existence today. Second, a more than cursory glance at the empirical literature strongly suggests that this widespread popularity and acceptance is unwarranted. Third, an even more thorough examination of the research reveals that certain prevalent method- ological shortcomings, especially the fatal error of mul- tiplying nonratio data, preclude one from meaningfully interpreting the empirical evidence. In short, little more is now known about the theoretical correctness of EIV theory than was ever known. Who is to say, therefore, whether those who hold EIV theory in high esteem despite the nonsupportive nature 8A5 acknowledged by Pritchard and DeLeo (1973), ex- perimental studies of EIV theory also require ratio scale measurement in order to be maximally meaningful, for only when the experimental levels of E, I, and V are measured on ratio scales can the tests for interaction effects pro- vide evidence about the presence or absence of multiplica- tive interactions. 30 of past research are wrong? New and innovative approaches to the study of EIV theory must clearly be implemented be- fore we can hope to answer this question. The purpose of the present study was to examine EIV theory by means of one such new approach--conjoint measurement analysis (Luce and Tukey, 1964; Krantz and Tversky, 1971; Krantz, 1972). This approach not only provides for meaningful examination of EIV theory in the absence of ratio data, it also pro- vides a mechanism for more correctly testing the EIV model as a within-subject model. Furthermore, in adopting this approach to the study of EIV theory, care was taken to cor- rectly operationalize the variables of instrumentality and valence and, thus, eliminate the shortcomings of past re- search with regard to the operationalization of these variables cited by Mitchell. CHAPTER IV A DISCUSSION OF CONJOINT MEASUREMENT The fundamental measurement of any attribute of a class of objects consists of assigning numbers (or other mathematical entities) to the objects such that the quali- tative properties of the attribute are represented by a numerical system having analogous properties. Stated another way, fundamental measurement is the representation of an empirical structure by an isomorphic numerical struc- ture (Krantz, Luce, Suppes, and Tversky, 1971). The em- pirical structure is most commonly referred to as a measure- ment structure, and the isomorphic numerical structure is most commonly referred to as a measurement scale. Measurement structures leading to the fundamental measurement of physical quantities are characterized by two qualitative empirical relations: the comparison relation (>) and the concatenation operation (*). The measurement of length best illustrates the significance of these em- pirical relations. To cite a frequently used example (Tversky, 1967; Coombs, Dawes, and Tversky, 1970; Krantz, Luce, Suppes, and Tversky, 1971), suppose that we want to measure the lengths of a set of straight rods. If we place 31 32 two of the rods, y and z, side by side and find that y extends beyond both ends of z we say that y is longer than 2. This is denoted y>z. Similarly, we can concatenate two or more of the rods by laying them end to end and compare the quali— tative length of this concatenated set of rods with that of another rod (or set of concatenated rods). The concatenation of rods y and z is denoted y*z, the observation that y*z is longer than x is designated y*z>x, and so on. If we con- tinued to perform concatenation and length comparison opera- tions on the rods, we would eventually discover that the empirical relations defined by these operations satisfy various qualitative laws. Some of these qualitative laws are: 1. If y>z and z>x, then Y>X 2. If y>z, then y*x>z 3. If y>z and x>w, then y*x>z*w It is these qualitative laws that constitute the measurement structure for the measurement of physical length. Numbers.assigned to the rods as measures of their length must therefore reflect these qualitative laws. For example, law #1 above requires that the number assigned to z be larger than the number assigned to x, and smaller than the number assigned to y. The other qualitative laws place similar restrictions on the assignment of numbers to the rods. When all of the qualitative laws satisfied by the comparison and concatenation operations are taken into 33 account, it can be shown that measuring the lengths of the rods requires that: (1) larger numbers correspond to longer rods and (2) numbers assigned to concatenated sets of rods equal the sum of the numbers assigned to their individual components (number assignment be additive with respect to concatenation). It can also be shown that regardless of the rod chosen to represent the unit of measurement, ratios of numerical assignment are uniquely determined by meeting these requirements. That is, while more than one measure- ment scale can be constructed to isomorphically represent the qualitative laws satisfied by the rods, the ratios of numerical assignment given to the rods by these scales will be the same. Thus, if measurement scale Y yields a ratio of numerical assignment equal to 4.3 for y/z, all other measurement scales satisfying the same qualitative laws will yield the same ratio of numerical assignment for y/z. In other words, the qualitative properties of physical length provide a measurement structure amenable to what is commonly referred to as ratio scale measurement. Other physical quantities, such as mass, are characterized by analogous measurement structures and are therefore also conducive to ratio scale measurement. Psychological variables such as motivation and anxiety can also be fundamentally measured on ratio scales. However, ratio scale measurement of these variables requires that qualitative laws different from those defined by > and 34 * be satisfied. This is attributable to the fact that psychological variables, unlike physical quantities, do not exhibit both > and * relations, but instead exhibit only > relations. Consequently, the qualitative laws de- fined by the joint appearance of these empirical relations in the case of physical measurement cannot be defined for psychological variables. Fortunately, qualitative laws which are quite different in nature, but which also pro- vide for ratio scale measurement, are definable for psycho- logical variables. These qualitative laws are defined by combining > with sources of additional structure other than *. The measurement structures which they comprise are called conjoint structures. Conjoint structures are defined by treating the variables we desire to measure as Cartesian products; that is, as dependent variables whose values are a function of two or more independent variables. The rules specifying these functional relationships are commonly called composi— tion rules. The nature of a composition rule determines the specific set of qualitative laws defining a conjoint structure. For example, the set of qualitative laws de- fining the conjoint structure for any variable X, where X = abc, differs from the set of qualitative laws defining the conjoint structure for any variable Y, where Y = a + bc. Whether the conjoint structure defined by a particular rule is satisfied is assessed by observing, via the comparison 3S relation >, the degree to which orderings on the dependent variable are related, as specified by the composition rule, with orderings on the independent variables. Thus, assess- ment of the extent to which the requirements for conjoint measurement are satisfied is achieved on the basis of ordinal information. Variables satisfying the qualitative laws de- fined by a composition rule are measurable in the sense that scales can be simultaneously developed for both the dependent variable and the independent variables, and values on these scales will satisfy the composition rule. To recapitulate, measurement of a variable via the conjoint structure approach requires that a composition rule describing the manner in which the variable is func- tionally related with two or more independent variables first be specified (hypothesized). This determines the specific set of qualitative laws defining the conjoint structure. If the variables satisfy this structure, ratio scales can be developed that will satisfy the proposed com- position rule.9 If they do not, scales satisfying the pro- posed composition rule cannot be developed. A determination of whether the variables satisfy the conjoint structure re- quires ordinal information only. 9In some cases, only interval scales can be developed on the basis of conjoint structures. This distinction is not emphasized in the present discussion because the specific con- joint structure to be examined in this study is one that per- mits the development of ratio scales. 36 Failure to find empirical evidence for a specific conjoint structure does not preclude the possibility of achieving ratio scale measurement via the conjoint measure- ment approach. It precludes only the possibility of develop- ing ratio scales that will satisfy the specific composition rule proposed. The possibility still exists that the em— pirical data will satisfy the conjoint structure defined by a different composition rule, leading to the development of scales that satisfy this composition rule. It is important to recognize this possibility be- cause it serves to illustrate one of the important purposes for which conjoint measurement analysis can be used. The essence of conjoint measurement, like all fundamental measurement, is to determine whether qualitative laws are sufficiently satisfied. to permit isomorphic numerical representation of a ratio scale nature. The primary dif- ference between conjoint measurement and the fundamental measurement of physical qUantities referred to earlier, is that rather than being defined by the > and * operations, the qualitative laws in conjoint measurement are defined by the > operation and composition rules describing the functional relationship among a dependent variable and two or more independent variables. In both of these approaches to fundamental measurement, failure to find empirical evi- dence for the required qualitative laws precludes ratio scale measurement on the basis of these laws. However, in 37 conjoint measurement this finding has additional utility because it indicates that the ordinal properties of the variables in question do not covary as specified by the proposed composition rule. Thus, by uSing conjoint measure- ment analysis, the validity of many theories presented as composition rules in two or more independent variables can be tested, with the testing procedure requiring ordinal data only. Furthermore, by specifying alternative com— position rules, conjoint measurement analysis can be used to test alternatives to these theories. It was with this purpose in mind that conjoint measurement analysis was used in the present study. To be more specific, conjoint measurement analysis was em- ployed to examine the validity of the multiplicative com- position specified in EIV theory. This was accomplished by observing whether the ordinal properties of force, ex— pectancy, instrumentality, and valence covary as specified by the conjoint structure defined by a multiplicative com- position rule in three independent variables. No attempt was made to develop actual scale values. Because past research on this topic is rendered meaningless by the mul— tiplication of nonratio data, and because the conjoint measurement approach to the analysis of EIV theory requires ordinal data only, it is believed that this study consti- tutes the first meaningful examination of EIV theory. The specific qualitative laws defined by a multiplicative 38 composition rule in three independent variables will now be discussed. It is these laws that were tested in order to examine the EIV model. Before proceeding with this discussion, a brief word about notation is warranted. As previously mentioned, the qualitative laws comprising a conjoint structure are defined by treating the dependent variable as a Cartesian product of two or more independent variables. In the present instance, the dependent variable is treated as a Cartesian product of three independent variables. If these three independent variables are denoted A, B, and C, this Cartesian product defines an A x B x C matrix, with each (a,b,c) cell in the matrix representing the value of the dependent variable when A = a, B = b, C = c. It is with reference to this particular notational scheme that the specific qualitative laws (ordinal properties) defined by a multiplicative composition rule will now be discussed. Sign Dependence ’One of the qualitative laws defined by a multiplica- tive composition rule in three independent variables is sign dependence. Sign dependence is a more general form of the property of single-factor independence and is best explained by first defining single-factor independence. Single-factor independence exists when the ordering induced by one of the independent variables is unaffected 39 by the levels at which the other two independent variables are held constant. For example, if the three independent variables are labeled A, B, and C as indicated earlier, single-factor independence for A requires: (a,b,c) : (a',b,c) if and only if (a,b',c') i (a',b',c') for all levels of B and C A graphical illustration of this property is presented in Figure l. b ' /-—F\ B B - l) \N\\llll b “no—M c c' c c' A=a A=a' Figure 1. Independence of A with respect to B x C The property of single-factor independence is analogous to an additive main effect in analysis of variance. For in— stance, if A is found to be independent of B x C, we conclude that A is additive with respect to B x C. Similarly, if B is found to be independent of A x C, we conclude that B is addi— tive with respect to A x C, and if C is found to be indepen- dent of A x B, we conclude that C is additive with respect to A x B. Any evidence of single-factor independence there- fore represents a violation of the multiplicative model. By comparison, the property of sign dependence, which as earlier stated is a more general form of 40 single-factor independence, is analogous to an interaction effect in analysis of variance. Thus, if A is found to be sign dependent on B x C, we conclude that A is multiplica- tive with respect to B x C. Likewise if B is found to be sign dependent on A)(C, we conclude that B is multiplicative with respect to A x C, and if C is found to be sign dependent on A x B, we conclude that C is multiplicative with respect to A x B. A multiplicative model in A, B, and C therefore requires that A be sign dependent on B x C, B be sign de- pendent on A x C, and C be sign dependent on A x B. Sign dependence is nothing more than the logical extension of single-factor independence for instances where one or both of the independent variables defining a set have variable sign, thereby making possible the partitioning of 10 To be the set into "positive” and ”negative" subsets. more specific, A is said to be sign dependent on B x C if B x C can be partitioned into "positive” and ”negative” subsets, denoted [B x C|+ and [B x C|-, such that: (l) the ordering induced by A within |B x CI+ is independent of the levels at which B and C are fixed, (2) the ordering induced by A within [B x Cl- is independent of the levels at which B and C are fixed, and (3) the ordering induced by A within [B x Cl+ is opposite the ordering induced by 0For purposes of the present discussion, a vari- able having variable sign is defined as one whose domain includes both positive and negative numbers. 41 A within |B x C|-. Stated differently, A is said to be sign dependent on B x C if upon partitioning B x C into ”positive" and "negative” homogeneous subsets it is found that: (1) within each homogeneous subset the ordering in- duced by A is independent of B x C and (2) the orderings in the two homogeneous subsets are in the Opposite direc- tion.11 Coombs and Huang (1970) point out that sign de- pendence is a consequence of two less complex properties. These properties are more easily illustrated than sign dependence and also provide for more straightforward methods of empircal testing. The first of these proper- ties is an independence property. It differs from the prOperty of single-factor independence in that it refers to whether one variable is independent of another variable. It is formally stated as follows: A is independent of B whenever: (a,b,c) i (a',b,c) if and only if (a,b',c) g (a’,b',c) for all levels of A and B with C fixed A graphical illustration of this simple independence property is presented in Figure 2. 11Somewhat different requirements for sign dependence exist when partitioning is not achieved on the basis of vari- ables having domains which include positive and negative num- bers, but is instead achieved on the basis of variables having domains which include either: (1) positive numbers, negative numbers, and zero, which permits partitioning into "positive," ”negative,” and "neutral" subsets, (2) positive numbers and zero, which permits partitioning into "positive" and ”neutral" subsets, or (3) negative numbers and zero, which permits par- titioning into "negative" and "neutral" subsets. However, because these bases for partitioning were not used in the present study, the different sign dependence requirements with which they are associated are not discussed. 42 Figure 2. Independence of A with respect to B The second of these properties is a sign dependence property. Just as the earlier described sign dependence property is a more general form of single-factor indepen— dence, this sign dependence property is a more general form of the simple independence property illustrated in Figure 2. In other words, it is an extension of this independence property for cases where B has variable sign. In formal terms it is stated as follows: A is sign dependent on B whenever: (1) (a,b+,c)_§(a',b+,c) if and only if (a,b'+,c)f_(a',b'+,c) (2) (a,b',c)_:(affif,c) if'and only if (a,b'-,c):_(a',b'-,c) (3) (a,b+,c)_f(ai,b+,c) if and only if (a',b-,c)f_(a,b',c) for all levels of A and B with C fixed A graphical illustration of this sign dependence property is presented in Figure 3. I“? A r a '1I%I: I Lil. b+ Ib'+ b‘ 'b" B #1 1 Figure 3. Sign dependence of A on B As previously stated, the more general property of sign dependence is a consequence of these two simple independence 43 and sign dependence properties. It is a consequence of these simple properties in the sense that for any vari- able A to be sign dependent on B x C it must be either: (1) Sign dependent on both B and C, (2) sign dependent on B and independent of C, or (3) independent of B and sign dependent on C. When both B and C have variable sign, A must satisfy the first condition; when only B has variable sign, A must satisfy the second condition; and when only C has variable Sign, A must satisfy the third condition. Thus, by knowing whether B, C, or both B and C have vari— able sign, it is possible to specify which of the above three conditions of simple independence and sign dependence A must satisfy to be sign dependent on B x C. This procedure was used for testing the sign de- pendence of E, I, and V in the present study. For instance, I and V are both hypothesized (and were operationalized) to have variable sign. Testing for the sign dependence of E on I x V was therefore accomplished by testing the sign dependence of E on both I and V. Likewise, because E is hypothesized (and was operationalized) to have positive sign only, testing for the sign dependence of I on E x V was accomplished by testing whether I was independent of E and sign dependent on V, and testing for the sign de- pendence of V on E x I was accomplished by testing whether V was independent of E and sign dependent on I. 44 Joint-factor Sign Dependence The other qualitative law defined by a multiplicative composition rule in three independent variables is joint- factor sign dependence. Joint-factor sign dependence exists when the joint effect of two of the independent variables is sign dependent on the third. Thus, A x B is said to be jointly sign dependent on C when C can be partitioned into ”positive” and ”negative” subsets, denoted C+ and C_, such that: (l) the ordering induced by the joint effect of A and B within C+ is independent of the level at which C is fixed, (2) the ordering induced by the joint effect of A and B within C“ is independent of the level at which C is fixed, and (3) the ordering induced by the joint effect of A and B within C+ is opposite that induced by the joint effect of A and B within C_. Stated formally, A x B is jointly sign dependent on C whenever: (1) (a,b,c+) _<_(a',b',c+) if and only if (a,b,c'+)f_(a',b',c'+) (2) (a,b,c-) _>_(a',b’,c-) if and only if (a,b,c")3_(a',b',c'-) (3) (a,b,c+)_:(a’,b',c+) if and only if (a',b',c-):i(a,b,c-) for all levels of A, B, and C A graphical illustration of this property is presented in Figure 4. C=c C=c' C=c- C=c' Figure 4. Sign dependence of A x B on C fi flflvmd_d_ , . _ ..., 7 _ 45 Like sign dependence, the property of joint-factor sign dependence is analogous to an interaction effect in analysis of variance. For instance, finding that A x B is jointly sign dependent on C leads to the conclusion that A x B is multiplicative with respect to C. One of the necessary conditions for a multiplicative combination rule in A, B, and C is therefore that A x B be jointly sign de- pendent on C, A x C be jointly sign dependent on B, and B x C be jointly sign dependent on A. With respect to EIV theory, this requirement trans- lates to finding E x I jointly sign dependent on V, E x V jointly sign dependent on I, and I x V jointly sign depen- dent on E. However, because E has positive sign only, the possibility of finding I x V jointly sign dependent on B does not exist. I x V must therefore instead satisfy the less general property of joint—factor independence (D. Krantz, personal communication, March 21, 1974). This property is formally defined as follows: A x-B is jointly independent of C whenever: (a,b,c)§_(a',b',c) if and only if (a,b,c')f_(a',b',c') for all levels of A, B, and C A graphical illustration of this property is presented in Figure 5. 46 Figure 5. Independence of A x B with respect to C CHAPTER V METHOD Procedure A 264 item Work Motivation Questionnaire was de- ve10ped to assess self-reported work motivation under vary- ing E, I, V conditions. Each item on the questionnaire con- sisted of two narratives, with each narrative describing the circumstances surrounding a job task assignment de- fined by a different E, I, V combination. After reading both narratives, subjects indicated under which of the two sets of circumstances they would most likely work hard to achieve successful task performance. Development of the Work Motivation Questionnaire involved several steps. First, sentences were written and outcomes chosen to represent each of two levels of E, four levels of I (two "positive“ and two ”negative”), and four levels of V (two ”positive” and two "negative”). They are presented in Table 2.12 Next, 32 different narratives were constructed from all possible E, I, V combinations of these sentences and 12Final selection of the sentences and outcomes that appear in Table 2 was made after some initial pilot work. 47 48 Table 2 Sentences and outcomes chosen to represent different levels of E, I, and V Expectancy If you work hard your chances of successfully performing this task are good. (E++) Even if you work hard your chances of successfully per— forming this task are poor. (E+) Instrumentality It is almost certain you will receive (outcome) if you successfully perform the task. (I++) There is a fair chance you will receive (outcome) if you successfully perform the task. (I+) It is almost certain that successfully performing the task will actually prevent you from receiving (outcome). (1") There is a fair chance that successfully performing the task will actually prevent you from receiving (outcome). (1') Valence (outcomes used) ++Receiving a promotion and substantial pay increase. (V ) Receiving a moderate pay increase. (V+) Being fired. (V") Being transferred to a less desirable job. (V’) outcomes (2 x 4 x 4 = 32).13 A selected sample of these nar- ratives is presented below. The entire set of 32 narratives is presented in Appendix A. 13In order to make the narratives more readable, the sentences and outcomes presented in Table 2 were often slightly altered. 49 ++,I+,V+) If you work hard you feel your chances of suc- cessfully performing this task are good. There is a fair chance you will receive a moderate pay increase if you successfully perform it. (E (E++,I',V+) If you work hard you feel your chances of suc- cessfully performing this task are good. However, while unsuccessfully performing it is likely to be inconse- quential, there is a fair chance that successfully per- forming it will actually prevent you from receiving the moderate pay increase for which you now appear destined. (E+,I+,V'-) Even if you work hard you feel your chances of successfully performing this task are poor. In addition, while it is unlikely that much of anything will happen if you perform this task unsuccessfully, there is a fair chance that successfully performing it will actually re- sult in your being fired. (E+,I",V-) As things stand now it appears all but certain you will be transferred to a less desirable job. However, it is almost certain you can prevent this transfer by suc- cessfully performing this task. Unfortunately, even if you work hard your chances of successfully performing it are poor. The matrix defined by all possible pairs (496) of these 32 narratives was then constructed. This was accom- plished by first randomly ordering the 32 narratives and then listing this random ordering from top to bottom and left to right as illustrated in Figure 6. Following the procedure outlined by McCormick and Roberts (1952), this matrix was divided into two mutually exclusive sets of 264 pairs each, such that within each set every narrative ap- l4 peared in 16 pairs. One of the sets was then randomly 14Application of the McCormick and Roberts tech- nique necessitated a 33 x 33 matrix. In order to apply this technique in the present study it was therefore necessary to ”generate” a 33rd narrative. This was achieved by treating one of the original narratives as two different narratives. The matrix defined by this procedure was the actual matrix divided. NARRATIVE 50 NARRATIVE 1 2 3 4 29 3O 31 32 \\\ I 1 2 2,1 3 3.1 3,2 \\\ \s 4 4,1 4,2 4,3 \\~ X \\. \ 30, 3O 29 31 31 31. 29’ 30’ \\\\ 32, 32 32, 32 29 3O’ 31 Figure 6. Matrix defined by all possible pairs of the 32 narratives 51 chosen and the 264 narrative pairs contained within it were used as items in the Work Motivation Questionnaire.15 The order in which these narrative pairs appeared in the questionnaire was determined by using the tables developed by Ross (1934). Use of these tables ensured that narrative pairs having one member in common were maximally separated. A listing of the 264 narrative pairs used in the Work Motivation Questionnaire is presented in Appendix B. In order to check whether each subject perceived the different levels of E, I, and V as having the same ranks and signs as those assigned by the researcher for anlaysis purposes, four additional items were included in the Work Motivation Questionnaire. These items required that the subjects: (1) rank order the four performance-related outcomes from least to most desirable, (2) specify which outcomes, if any, they found undesirable, and (3) indicate the chances out of ten they associated with each level of E and 1. Responses to these items were obtained after the Work Motivation Questionnaire had been completed. 15A small pilot project indicated that it was necessary to pair each E, I, V condition with at least 16 other E, I, V conditions in order to obtain data of suf- ficient variability and reliability for conjoint measure- ment analysis. On the basis of this finding, which is consistent with previous research (McCormick and Roberts, 1952; Rambo, 1959), it was decided that the above procedure would be used, even though it was realized that the re- sultant questionnaire would be extremely long and time con- suming. 52 Subjects COpies of the Work Motivation Questionnaire were mailed to 125 middle managers from the Detroit Metro- politan Area. All but three of the managers were cur- rently enrolled in the Advanced Management Program of the Department of Management at Michigan State University. Completed questionnaires were returned by 14 managers. Compared to other studies employing conjoint measurement analysis, this is a relatively large number of subjects. Orderings Questionnaire responses were used to obtain an ordering of each subject's self-reported force under the 32 different E, I, V conditions. CHAPTER VI RESULTS Consistency of Choice The extent to which a particular conjoint structure can be singled out as the appropriate structure depends in a presently unspecified way upon the extent to which the data are error free. Consequently, meaningful testing of a conjoint structure requires that the data be relatively infallible. In terms of the present study, this translated into the requirement that each subject exhibit reasonable consistency of choice across the 32 E, I, V conditions. Accordingly, two approaches were employed in an attempt to assess each subject's choice consistency. First, an estimate of the reliability of each sub- ject's rank ordering of the 32 E, I, V conditions was ob- tained. This was achieved by randomly splitting the original 264 item Work Motivation Questionnaire into two halves such that each of the 32 E, I, V conditions appeared in exactly eight items in each half. Responses on these two halves were then tabulated and, on the basis of these tabulations, two rank orderings of the 32 E, I, V condi- tions were obtained for each subject. Using the Spearman S3 54 rho rank-order correlation, these rank orderings were then correlated. This provided an estimate of the reliability of the rank ordering resulting from each subject's re- sponses to half of the original 264 items. In order to estimate the reliability of the rank ordering resulting from each subject's responses to the entire 264 items, these correlations were then adjusted using the Spearman- Brown formula. The first column of Table 3 reports these reliability estimates. The subjects are ordered from most to least reliable. As is evident from Table 3, with the exception of subject 19, the rankings of all subjects were quite reliable, and little variation was found among subjects.16 Consistency of choice was further assessed by evaluating the degree of intransitivity exhibited in each subject's responses. An intransitive triple is defined by the following set of conditions: A is preferred to B (A > B), B is preferred to C (B > C), and C is preferred to A (C > A). Responses to the 264 item questionnaire permitted a maximum of 462 such triples. Each subject's frequency of intransitive triples was counted and these frequencies were converted to percentages of this possible 16It is recognized that the Spearman-Brown formula is intended for use with interval data, and the use of this formula to obtain reliability estimates was therefore less than totally appropriate. The most meaningful infor— mation to be gained from these estimates is, therefore, that they vary little from subject to subject (with the exception of subject 19) indicating small reliability dif- ferences among the subjects. The magnitude of the esti— mates, on the other hand, should be viewed with caution. 55 Table 3 Consistency of subject choice Reliability of Subject Percentage of ifiiéiit Ragk grdgréggdgfigg: 32 Intriiiiéilzdclfiices ’ ’ Subject Responses 144' .96 5.42 72 .93 3.24 125 .93 5.20 20 .91 2.16 31 .90 3.46 148 .90 4.76 115 .89 2.60 100 .88 3.68 89 .88 6.92 82 .88 7.58 85 .86 4.98 119 .86 7.36 102. .85 13.86 19 .54 44.16 56 maximum. Examination of these percentages, which appear in the second column of Table 3, shows them to be in basic agreement with the estimates of subject reliability. That is, with the exception of subject 19, there was little apparent variation in the extent to which the subjects made intransitive choices. In an attempt to more explicitly determine whether these percentages reflected significant differences in subject intransitivity, the average per- centage was calculated (excluding subject 19). Using this average as the best estimate of the percentage of intransi- tive choices in the population, the 95% confidence interval was then calculated, resulting in an interval ranging from 3.40 to 7.56 (N = 462 possible intransitive triples). As is apparent, most of the percentages contained in Table 3 fall within, or close to, this interval. The most notable exception is subject 102, whose percentage of intransitive choices (13.86) falls significantly above this interval. In summary, the relatively high reliabilities of the majority of subjects' rank orderings, coupled with the relatively infrequent occurrence of intransitivity in their response choices, indicated that the data were generally of sufficient consistency to permit meaningful testing of a conjoint structure. The data for subject 19 were found to contradict this general finding. This subject was sub- sequently eliminated from all tests of the EIV model. 57 Sign Dependence It will be recalled that the sign dependence re- quirements for the EIV model are that E be sign dependent on I x V, I be sign dependent on E x V, and V be sign de- pendent on E x I. It will also be recalled that these requirements are the consequences of simpler pairwise in- dependence and sign dependence properties, with the sign dependence of E on I x V being a consequence of the sign dependence of E on I and the sign dependence of E on V, the sign dependence of I on E x V being a consequence of the independence of I from E and the sign dependence of I on V, and the sign dependence of V on E x I being a con- sequence of the independence of V from E and the sign de- pendence of V on I. Sign dependence was tested by testing these pairwise properties in the present study. The means by which these pairwise properties were tested can best be explained by reference to an example. The sign dependence of V on I, for instance, was tested by comparing, at each level of I, the observed with the predicted orderings on the four levels of V. Figure 7 presents the orderings on the four levels of V that are‘ predicted by the EIV model. As can be seen, there are eight such orderings; four each in the two planes defined by E+ and E++. Testing for the sign dependence of V on I therefore required making eight separate data-model rank-order comparisons. These comparisons were made by 58 Expectancy = E+ 1= 1‘ I+ I++ v++ 1 f 1 4 1 4 V+ r 2 2 3 I3 v' 3 3 2 2 V= 4 4 l 1 Expectancy = E++ I: 1’ 1+ I++ v++f 1 1 4 4 , v+ 2 2 3 3 v' 3 3 2 2 v= 4 4 l I l Figure 7. Theorized orderings on the four levels of V for the pairwise tests of the sign dependence of V on I Note: 'Theorized orderings are represented by the number sequence in each column, with 1 representing the least-often preferred outcome and 4 the most—often .preferred outcome. 59 calculating the Spearman rho rank-order correlation for each of the eight pairs of data-model rank orderings. The average of these correlations was then calculated in order to obtain an overall measure of the extent to which each subject's responses satisfied this sign de- pendence property. With one notable exception, the same basic pro~ cedures were employed to test the other pairwise proper- ties. In testing for the sign dependence of E on I and E on V, rank-order correlation comparisons were abandoned in favor of simple counts of the number (out of 16) of model congruent orderings on the two levels of E. This was thought to be a more meaningful method for testing these properties because with only two levels of E the possible values of rho were 1.00 (when the ordering on E was the same as that theorized) and -1.00 (when the ordering on E was opposite that theorized). Using the average value of rho as a test for these properties would have, therefore, provided somewhat misleading information. - One of the major difficulties in interpreting con- joint measurement analyses is that of establishing the comparability of results across the different independence and sign dependence tests. Usually this problem is brought about by the fact that different factors do not have the same number of levels. Consequently, violations of the same number and kind have a differential impact on 60 the resultant indices of average rank-order fit. For example, given factors A, B, C with 4, 3, and 2 levels respectively, a pairwise reversal in one of the tests for the sign dependence of B on C will have a much greater impact on the index of average rank—order fit for that property than will a pairwise reversal in one of the tests for the sign dependence of A on C.17 In the present study, the comparability of re- sults for the different pairwise tests was even further obscured by the fact that E not only had fewer levels than I and V, but also was tested, for reasons previously explained, using an entirely different index--namely, number of model congruent orderings. As an aid in establishing the comparability of the pairwise test results, Table 4 is presented. This table shows the effects of pairwise violations on each of the pairwise tests. Each pairwise test provided for a maximum of 16 such violations. The frequency of pairwise violations therefore provided a convenient method for equating results across the different tests. Note that 17A pairwise reversal is defined as a reversal of ranks on adjacent pairs. For example, in the below rank- ings of stimuli A, B, C, and D the differences in rank for C and D represent a pairwise reversal. Stimuli Rank Set 1 Rank Set 2 A l l B 2' 2 C 3 4 D 4 3 61 Table 4 The effects of pairwise reversals on the pairwise tests of E, I and V Number of Average Rho for Tests of: I Independent of E Number of Model Congruent Orderings RESEEEEI: IVS%§Seg:§§:g:ngfog V E giggngng e3: on I V Sign Dependent on I 1gn Dependent on V 0 .97 16 l .95 15 2 .92 14 3 .90 13 4 .87 12 5 .85 ll 6 .82 10 Note: Because all possible pairs of the 32 E, I, V condi— tions were not presented to the subjects, the mini- mum number of ties a subject's rank ordering of the 32 conditions could contain was 15. Tied ranks were therefore not considered to represent meaning- ,ful violations of the various conjoint properties. Consistent with this approach, tied ranks were not considered violations in the pairwise sign depen- dence tests for E. sistency of approach, the listed values of rho have been adjusted downward to take into account the average observed reduction in rho attributable to ties (.03). In order to maintain this con— 62 the independence and sign dependence tests of I and V were equally affected by these violations. This is to be expected because I and V both had four levels. The average values of rho for these tests are therefore directly comparable. Finally, because of the manner in which the pair- wise properties were tested,the same overall results (mean rho's or total number of model congruent orderings) fol- lowed from the two tests of each factor. Keeping this feature of the testing paradigm in mind, the results found for the pairwise tests of each factor are reported in Table 5. Subjects are ordered from least to most con— sistent according to the criterion of intransitivity of choice (see Table 3). In order to get a better idea of the extent to which the data satisfy the various pairwise tests, the results reported in Table 5 have been summarized for in- clusion in Table 6. Table 6 reports the number of sub- jects satisfying the pairwise properties at different criterion levels, ranging from the equivalent of one pairwise reversal or less to the equivalent of six pair- wise reversals or less. As is clear from Table 6, the pairwise properties for E were, in general, less well satisfied than those for I and V. I The question of paramount importance to the viability of the EIV model was, of course, how many 63 .mo. one am. oEouon >1Ho mumou omHz -HHmm may pom coHumH>oo opmwcmum mam some can .NOH woonnzm quosHoxo combo eHN. No. oo.N eeN. NN. No.HH NH. HN. NH NN. HN. HH om. NN. OH No. NN. NH NN. NN. OH NN. NN. N NN. NN. NH NN. oo.H HH oo.H NN. NH NN. NN. eH NN. NN. NH NN. NN. NH NN. NN. N cOHumH>on oumocmpm coo: NQH mm mHH mm VVH mNH mm wvH OOH Hm Nu mHH ON mmwcflpooho unoSchou Hoemo Hoemo H co unaccomoa cmHm > > do Homecomom :mHm H H :wommWowwdwmomwmw m Honesz m we HomecodoueH > . m Ho unaccomoeeH H w :o uaooaomon cmmm m Humansm Houumm > Houomm H . Houomm m oococcomoo :mHm one mucoUCoHoocH Ho momma omHBHHmH N oHoee 64 HNH M NNeHHooHo ucosumaou Hoomz .oz .om. A onmv mmoH Ho m HeH M mmefinooho peonywcoo Howmz .02 .NN. A oemv mmoq Ho N HmH M mquHowHo pcosamaou Hoomz .02 .NN. A oemv mmoH Ho H H do > :o uaooqomom :mHm > uaowcomon cmHm H m Ho “awesomoocH > m Ho ucowqomooCH H Nouomm > Houomm H > so unaccomon cMHm m memHm>om H so uaoecomom cmHm m omthHwH Houomm m we Honesz oucoocomoo cmHm one oucoocomoocfl Ho mommy omflzpflmm Ho HHmEESm o oHnoH 6S .eoHHHoon Ho>oH :oHHouHHo ogu um moHuHoHONH omHzeHmH esp ooHHmHumm mwcHHooHo Mame omonz HmH Ho usov muooHLSN Ho Hogans esp ohm mlouco oHan ”ouoz OH mH NH HH HH HOH M mNeHooeoo ucosumcou Hoemz .oz .NN. A oeNv mmoq go o HHH M NNeHHoooo ucosumcou Hoemz .oz .NN. A oemo mmoq 90 m HNH M mNeHooeHo , ucodpmcou Hoemz .oz .NN. A oemo mmoH Ho e H co uaoccomom :mHm > m we ueoocoooocH > Houomm > > do ucoodomoo CMHm H m Ho ueoocomoocH H Houomm H Houomm m > so Hcoecomom cmHm m mHmmHo>om H 20 uaooaomoa :mHm m omHBNHmH Ho Honesz H.©_u:oov o oHan 66 subjects, if any, satisfied all six pairwise properties. In order to attempt to answer this question, it was neces- sary to establish a criterion, or decision rule, for judging whether or not a pairwise property should be considered sat- isfied. Given the general consistency of the data (see Table 3), it was decided that the equivalent of four pair- wise reversals (rho Z .87, number of model congruent order- ings : 12) represented a reasonable minimum.requirement for considering a pairwise property satisfied. Using this cri- terion, Table 5 shows there were only three subjects, 31, 85, and 115, for whom all six pairwise properties were satisfied.18 It was concluded, therefore, that the EIV model remained a viable model for these three subjects only. A search was conducted to try to uncover any pattern or patterns of consistent violations that might account for why so few subjects satisfied the pairwise requirements for the EIV model. Two patterns were found. First, the rank orderings of five of the subjects (72, 82, 89, 119, 144) were found to indicate that, other things equal, these sub— jects would work harder to avoid a transfer to a less de- sirable job (V') than to avoid the termination of employment (V-'). Even more surprisingly, in the majority of instances 18Lowering the minimum requirement to the equivalent of five pairwise reversals for any pairwise property (rho > .85, total number of model congruent orderings Z 11) would— result in the addition of only one other subject, 148, to this group. 67 the rank orderings were found to further indicate that even if the chances of preventing a transfer were less than those of preventing the termination of employment, these subjects would work harder to prevent a transfer. These results are startling to say the least and conjure up many ideas, all of which point to the apparent in- appropriateness of the EIV model. The most likely explana- tion for these results, however, is that the subjects, being middle managers, had difficulty identifying with, and therefore placing themselves in, the situations de- scribed in the Work Motivation Questionnaire as being instances in which they were on the verge of being fired. This explanation, rather than pointing to the apparent inappropriateness of the EIV model, seemingly points to the unfortunate choice of using termination of employment as the most negatively valent outcome in the Work Motiva- tion Questionnaire. Whatever the explanation for these violations, they were also found in the rank orderings of two of the subjects(3l, 85)IWho satisfactorily met the pairwise requirements of the EIV model. This finding, coupled with the fact that these violations had an impact on the pairwise tests most frequently met by all subjects, those for I and V, but had no impact on the pairwise tests least frequently met by all subjects, those for E, seems to indicate that, while frequent, the extent to which 68 these violations account for the general lack of support found for the EIV model is probably minimal. A second kind of consistency was found in the rank- order violations for subjects 20, 100, 119, 125, and 148. More specifically, upon examining the orderings on E for these subjects, it was found that regardless of whether the probable consequences of successful task performance were positive or negative, these subjects generally showed a preference for working harder to achieve successful task performance when the chances for successful task performance were greatest. This suggested that E was acting in an in- dependent rather than a sign dependent manner for these subjects, and in order to further investigate this possi— bility, the number of pairwise reversals (out of 16) from the orderings predicted by the independence of E from I and V was counted for each subject. No pairwise reversals were found for subject 119, one was found for subjects 100 and 148, two were found for subject 125, and three were found for subject 20. By comparison, results of the pair- wise sign dependence tests of E for these subjects (see Table 5) show five pairwise reversals for subject 148, six for subjects 100 and 119, seven for subject 125, and nine for subject 20. It is clear from these results that 69 E satisfied pairwise independence and not sign dependence for these subjects.19 This finding was considered particularly signifi- cant because it not only served to provide at least a partial account for why these subjects failed to satisfy the pairwise requirements for the EIV model, it also served to suggest that the rankings of self—reported motivation for these subjects might be consistent with an alternative to the EIV model. This model is the dual distributive model, having the specific form E + IV. Because E is additive and not multiplicative with respect to I and V in this model, the pairwise requirements for E are dif- ferent from those in the EIV model. That is, E must satisfy pairwise independence instead of sign dependence with respect to I and V. Given the levels and signs of E, I, and V used in the present study, the pairwise re- quirements for I and V, on the other hand, are the same for both models. Thus, having determined that pairwise independence for E was satisfied by these subjects, their test results for the pairwise requirements of I and V 19E was similarly tested for pairwise independence in all other instances where it was not found to satisfy pairwise sign dependence. Likewise, in all instances where the pairwise independence properties of I and V were not satisfied, the orderings were retested to determine if they satisfied the opposite than originally hypothesized pairwise property. In no instance were these tests found to significantly improve rankeorder fit. 70 were reexamined. As Table 5 shows, these pairwise require- ments were fully satisfied (rho Z .87) by four of the five subjects (20, 100, 125, and 148), and almost fully satis- fied by the fifth, subject 119 (rho = .85 for the pairwise tests of I). It was concluded, therefore, that the dual distributive model remained a viable alternative for these five subjects. In summary, subjects 31, 85, and 115 were found to satisfy the pairwise independence and sign dependence re- quirements (and consequent simple independence and sign dependence requirements) for the EIV model. Subjects 20, 100, 119, 125, and 148 were found to satisfy the pairwise independence and sign dependence requirements for an alter- native to the EIV model, the dual distributive E + IV model. Accordingly, the joint factor independence and sign depen- dence properties for these models were next tested for these subjects. All other subjects were excluded from subsequent testing.20 -20As mentioned earlier, four items were included in the Work Motivation Questionnaire to assess whether each subject perceived the different levels of E, I, and V as having the same ranks and signs as those assigned by the researcher. The theory predicted orderings used in testing the various pairwise properties were derived from these assigned ranks and signs. It was therefore important that the ranks and signs assigned by each subject coincided with those assigned by the researcher. As a final check for sources of systematic violation from the pairwise properties of the EIV model, these items were examined to determine if any of the subject's assigned ranks and/or signs differed from those assigned by the researcher. No differences in rank were found and only two subjects, 89 and 102, were found to assign different signs. In both cases, this 71 Joint-factor Independence and Sign Dependence The joint-factor independence and sign dependence requirements for the EIV model are that I x V be indepen- dent of E, E x I be sign dependent on V, and E x V be sign dependent on I. The only joint-factor requirement for the dual distributive E + IV model is that I x V be independent of E. E x I and E x V need not satisfy any joint—factor requirements because E and I are not hypothesized to com- bine in the same manner with V in this model, nor are E and V hypothesized to combine in the same manner with I. All jointefactor properties were tested using the Spearman rho rank-order correlation. The joint-factor in- dependence of I x V was tested by correlating the ordering over the 16 I x V levels in E+ with the ordering over the same 16 I x V levels in E++. Tests for the joint-factor sign dependence properties of E x I and E x V were somewhat more complex. The joint-factor sign dependence of E x I on V was tested as follows: First, the ordering over the 8 E x I levels in V+ was correlated with the ordering over the 8 E x I levels in V++. Next, the ordering over the 8 E x I levels in V- was correlated with the ordering over the 8 E x I levels in V--. These two correlations were difference consisted of the subject stating that a transfer to a less desirable job was not undesirable! Accepting this statement at face value, appfapriate changes were made in the theory predicted orderings, and the pairwise properties for these subjects were retested. Improvements in data- model rank order fit were not found, indicating that the failure of these subjects to satisfy the pairwise require- ments for the EIV model cannot be attributed to their assignment of a positive sign to the transfer outcome. 72 then averaged to get an overall estimate of the agreement in E x I ordering when the sign of V was constant. The sign dependence of E x I on V requires that this correla- tion be highly positive. Each rank ordering was next cor- related with those rank orderings found when V was of dif- ferent sign. This resulted in four correlations, corre- sponding to the following combinations of V: V+, V'; V+, V‘-; V++, V-; V++, V". The average of these correlations was then computed to arrive at an overall estimate of the agreement in E x I ordering when the sign of V differed. The sign dependence of E x I on V requires that this cor- relation be highly negative. Thus, in testing the sign dependence of E x I on V, a total of six correlations were computed. From these six correlations, two average corre- lations were computed; one reflecting the degree of agree- ment in E x I ordering when V was of same sign, and the other reflecting the degree of rank-order agreement in E x I ordering when V was of different sign. The joint- factor sign dependence of E x V on I was tested using analogous procedures, with the resultant average correla- tions representing the degree of agreement in E x V order- ing with I of constant sign and I of different sign. Attempts to establish the comparability of the results for the test of the independence of I x V with those for the tests of the sign dependence of E x I and the sign dependence of E x V were complicated by the fact 73 that a single correlation was calculated to test the in- dependence of I x V, while two separate indices of average correlation were calculated to test the sign dependencies of E x I and E x V. Thus, instead of attempting to firmly establish the comparability of results across the tests, a more individual approach was taken with regard to es- tablishing reasonable test result requirements for each test. It was decided that a minimum correlation of .90 represented a reasonable criterion for the joint-factor independence test of I x V, and minimum mean correlations of .88 and —.83 represented reasonable criteria for the joint-factor sign dependence tests of E x I and E x V. Figure 8 presents several examples of some of the kinds and numbers of violations corresponding to a correlation of approximately .90 in the test for the independence of I x V. When the average reduction in rho attributable to ties is taken into account (.02 for V (I) of constant sign and .07 for V (I) of different sign), the minimum mean correlation requirements for the joint—factor sign dependence tests of E x I and E x V correspond to the occurrence of a single triad reversal in each of the two correlated orderings for V (I) of constant sign and a 74 Example A Example B Example C Rank Set 1 Rank Set 2 Rank Set 1 Rank Set 2 Rank Set 1 Rank Set 2 l l l l l 2 2 2 2 6 2 Hi 3 3 3 3 3 4Q: 4 4 4 4 4 ' 3 5 10 5 5 5 5 6 6 6 2 6 p 8P 7 7 7 7 7 7g) 8 8 8 8 8 6 9 9 9 ll 9 12 l“ 10 5 10 10 10 10 11 ll 11 9 ll 11 12 12 12 12 12 9 l3 l3 13 15 l3 l6 ‘ l4 l4 14 14 l4 14 15 15 15 13 15 15 16 16 l6 16 16 13 rho = .91 rho = .91 rho = .91 Figure 8. Hypotheical examples of rank-order violations and re- sultant values of rho in the test for the independence of I x V Note: Values of rho have been adjusted downward to take into account the average observed reduction in rho attributable to ties (.02). 75 single triad reversal in each of the four correlated orderings for V (I) of different sign.21 Results of the joint-factor tests are presented in Table 7. The three subjects who satisfied the pair- wise requirements for the EIV model are listed first. As Table 7 shows, only one of these subjects, 31, fully met the established joint-factor independence and sign dependence requirements for the EIV model. Subject 85, however, met all requirements with the exception of the sign dependence of E x V on I when I has different sign, and the mean correlation of -.81 obtained for this test differs by only .02 from the established minimum require- ment of -.83. In essence, then, subject 85 also satisfied the joint-factor requirements for the EIV model. Subject 115, on the other hand, clearly failed to meet the joint- factor sign dependence requirements for E x I. The EIV model was therefore ruled out as a viable model for this 21A triad reversal is represented as follows in the two kinds of rank-order correlations calculated. V (I) of Constant Sign V (I) of Different Sign Rank Set 1 Rank Set 2 Rank Set 1 Rank Set 2 l 1 l 8 2 2 2 7 3 5, 3 4. 4 4 , 4 53 5 3‘ 5 6F 6 6 6 3 7 7 7 2 8 8 8 l 76 Table 7 Joint-factor tests of independence and sign dependence Ex;I Sign Dependent ErcV Sign Dependent on V on I Subject I)Sk terion, it is said to have high stress, meaning that the underlying structure of the data (if any exists) is not well represented by the configuration of points comprising the solution. Computer programs designed to perform MDS 22In metric MDS, which was not used in the present study, the goodness-of—fit criterion can be defined in terms of a linear or polynomial relationship (up to degree 4) between the proximity measures and the resultant inter- point distances. 79 are iterative in nature. Through a process of successive approximations, the MDS solution is adjusted until a solu- tion with lowest stress is reached. This solution is then plotted. Depending on the intent of the researcher, two basic kinds of information can be sought from a MDS solu- tion. One is greater insight into the processes giving rise to the data, and corresponds to the identification of interpretable axes for the spatial representation. The other is greater insight into the overall pattern of subject (stimuli) similarity and dissimilarity suggested by the data, and corresponds to the identification of dis- cernible clusters of points within_the spatial representa- tion and the relative proximities of these clusters to each other and to other points. It was with the primary intent of gaining this second kind of information that MDS was employed in the present study. Hierarchical clustering starts with the same kind of proximity data and from this data breaks the subjects (stimuli) into groups, or clusters, of similar subjects. The clusters formed are hierarchical in the sense that each successive clustering is obtained by merging pre— viously established smaller clusters. Thus, the progres- sion from smaller to larger clusters forms a sort of hierarchy with the smaller clusters at the bottom of the hierarchy representing the most homogeneous groupings. 80 A hypothetical example which illustrates the basic principles of HC is presented in Figure 9. Matrix 1 in Figure 9 represents the original proximity matrix for subjects A, B, C, and D. The larger the number in Matrix 1, the greater the subject similarity. B and C are the most similar and, thus, form the first cluster in the hierarchy. This, in turn, defines a new proximity matrix, Matrix 2, in which B and C are substituted by the cluster B,C. Note that the cell entries for B,C correspond to the larger of the two values for B and C in Matrix 1. That is, the entry of 7 in the cell defined by the pairing of A with B,C is the larger of the two values for the pairing of A with B (3) and A with C (7) in Matrix 1, and the entry of 6 in the cell defined by the pairing of D with B,C is the larger of the two values for the pairing of D with B (6) and D with C (4) in Matrix 1. Subject A and cluster B,C are the most similar in Matrix 2 and,thus, form the second cluster in the hierarchy. This, in turn, defines proximity Matrix 3, leading to the final clustering A,B,C,D. The tree diagrams below each proximity matrix show the progres- sion up the clustering hierarchy as each new cluster is defined. As is apparent from this example, HC provides much the same kind of structural information about a set of data as does MDS. There are two important differences to these approaches, however. First, HC does not provide 81 Proximity Matrices Matrix 1 Matrix 2 Matrix 3 3 A 7 9 B,C 7 A,B,C l 6 4 D l 6 D l A B C D A B,C D A,B,C D Clustering Hierarchy II”?! I”? (I A B C D A B (I D A IS C I) Figure 9. Hypothetical example illustrating the principles of hierarchical clustering Note: Matrix entries represent proximity measures: the larger the entry the greater the proximity. 82 a spatial representation while MDS does. Second, each point in a MDS configuration is located by reference to all other points. As a result, a MDS configuration is dominated by large-distance similarities, and the local structure of a MDS configuration is, therefore, seldom reliable. In HC, on the other hand, the local structure, or smaller clusters, are more reliable than the larger clusters. This is because the smaller clusters are deter- mined primarily by a few small-distance similarities, while the larger clusters are determined by many large- distance similarities ”. . . which often present conflict- ing evidence as to which smaller clusters should be merged [Kruskal, 1972, p. 3].” In short, MDS provides more re- liable large-distance information while HC provides more reliable small-distance information. Because of the complementary nature of these dif- ferences, MDS and HC are often used on the same data. More specifically, MDS is used to obtain a spatial configuration (usually two dimensional) of the overall structure of the data and HC is used to obtain reliable information about the local structure (clusters) within this configuration. The clusters are then repreSented by means of Venn-like set diagrams overlaid on the scaling configuration, re- sulting in a good overall ”picture" of the large and small-distance structure of the data. This combination of the two techniques was used in the present study. 83 The decision to use these techniques was based on the assumption that, if the conclusions suggested by the conjoint analyses were correct, greater agreement in the overall ranking of the 32 E, I, V conditions should be found among subjects satisfying the same model than among subjects satisfying different models. Accordingly, these techniques were applied to the correlation matrix pre- sented in Table 8. This matrix contains the rho rank- order correlations of agreement, corrected for unreli- ability, for the original thirteen subjects tested.23 Using the M-D-SCAL program for MDS deveIOped by Kruskal and Carmone and the HICLUST program for HC developed by Johnson, the data were found to produce the combined spatial-clustering configuration presented in Figure 10. A stress value of .2336 was found for the M-D-SCAL solu- tion, indicating that the spatial configuration in Figure 10 meets the criterion of monotonicity of relationship be- tween subject similarities and interpoint distances to a reasonably good extent.24’25 23Due to the noninterval nature of the data, the appropriateness of correcting these values of rho for attenuation due to unreliability can be questioned. How- ever, because only the ordinal properties of these cor- rected coefficients were used in the subsequent MDS and HC analyses, correction of these coefficients was not con- sidered to represent a serious source of systematic error. 24Stress is formally defined as follows for a M-D-SCAL solution: - 84 mmm. OOO.H HHm. mmw. vmm. Nam. ooo.H mow. mom. NOO. NOO. NOH --- HOO. NON. ONO. OON. OOO. NNN. NON. ONN. NON. ONO. NNN. OOH -- OOO. OOO.H NON. OOO.H NHN. ONO. NNN. OHN. HNO. OOO. NNH --- OOO. HOO. ONO. NOO. HNO. OOO. ONO. OOO. HOO. OHH --- OHN. ONO. HNN. ONO. OOO. ONN. OOO.H OOO. NHH --- NON. OOO.H OON. NOO. HNN. NON. ONO. NOH --- NNN. OOO. NNO. HNN. NNO. OOO.H OOH --- OOO.H OON. ONO. ONO. OOO. ON --- NNO. OHO. OOO.H NNN. NN OHO. ONO. ONN. NN --- NOO. ONN. NN --- ONN. HN --- ON NOH OOH NNH OHH NHH NOH OOH ON NN NN NN HN ON Nonesz puonn3m mcoHuHccoo > .H .m mm one Ho mmcHHooHo Mame may cH ucoEoonm uuonnSm Ho mcoHumHoNHoo ocm m oHan 225E303“ 'T—NCDU-H (133.0 85 \\ Figure 10. Combined spatial-clustering representa- tion resulting from HICLUST clustering solution and two-space M—D-SCAL solution 86 In general, the "picture” presented in Figure 10 is consistent with the conclusions suggested by the con-. joint measurement analyses. The small clusters, which represent the greatest similarity in overall ranking, are completely comprised of subjects found to satisfy the same model. Proceeding from left to right, the first small cluster is comprised of the two subjects found to satisfy the EIV model (31 and 85), the second small cluster is comprised of two of the subjects found to satisfy the testable requirements for the E + IV model (119 and 148), MM 2 2 (DIST (M) - DHAT (M)) Stress = Mgé 2 (DIST (M) - DBAR) "M where: DATA (1) through DATA (MM) = The data values of proximity for the subjects (stimuli). DIST (1) through DIST (MM) = The distances between pairs of points corresponding to these data values. DHAT (1) through DHAT (MM) = The regression function values resulting from monotone descending regression of DIST on DATA. Arithmetic average of the DIST values. 25Due to the iterative nature of computer programs like M—D-SCAL, it is possible to obtain a MDS solution having greater stress than the approximate ”true” minimum. This is called the local minimum problem, and a convenient method for checking whether a solution is a local minimum solution is to obtain additional MDS solutions by programing the specific computer algorithm being used to commence with different initial configurations. If the stresses for these solutions are similar to the stress for the initial solution, one can be relatively sure that the initial solution is not a local minimum solution. This procedure was employed in the present study. Two additioanl M-D-SCAL solutions were obtained and were found to have stresses of .2553 and .2689. Thus, there is little reason to suspect that the original solution presented in Figure 10 is a local minimum solution. DBAR 87 and the third small cluster is comprised of the three other subjects found to satisfy the E + IV model (20, 100, and 125). By comparison, the subjects found to satisfy neither model (72, 82, 102, 89, 115, 144) are separated by the greatest distances and are members of the largest clusters. The one apparent contradiction in Figure 10 is that the two small clusters made up of E + IV model sub— jects were not found to combine. A closer look at the joint—factor sign dependence tests for these subjects, however, suggests an explanation for this apparent con— tradiction. As previously mentioned, there are no in- dependence or sign dependence requirements for the joint effects of E x I and E x V in the E + IV model because no assumptions are made about the manner in which these joint effects combine with V and I. It is, therefore, possible for subjects satisfying the E + IV model to differ with respect to the rank orderings associated with these joint effects, and consequently with respect to the overall rank orderings of the 32 E, I, v conditions.26 As Table 7 26The hypothetical data presented below illustrates how this can happen. Note that the orderings of both sub- jects satisfy the two pr0perties for the E + IV model that are required for this particular subset of data. First, I is independent of E as indicated by the fact that the order- ings induced by I are the same for E+ and E++. Second, E is independent of I as indicated by the fact that the order— ings induced by E are the same for all levels of I. When one turns to the overall orderings within each plane (see 88 indicates, among the five subjects found to satisfy the E + IV model (20, 100, 119, 125, 148), a similar pattern was found in the joint-factor sign dependence results for subjects 20, 100, and 125, and a similar pattern was found in the joint-factor sign dependence results for subjects 119 and 148. The conclusion suggested by these results is that the greatest correspondence in overall rank order- ing should be found among these two subject groupings. As indicated in Table 8, the pattern of intercorrelations among these subjects shows this to be the case. The average correlation among the overall rankings of subjects 20, 100, and 125 was .989 and the rankings of subjects 119 and 148 correlated 1.000. By comparison, the average inter- group correlation was .956. The fact that these two subject groupings were found to form relatively homogeneous clusters is therefore not surprising. More importantly, it does not represent a contradiction to the conclusions suggested by the conjoint measurement analyses. parentheses below), however, subject differences emerge (which would show up in the joint-factor sign dependence tests of E x 1). Consequently, the orderings of these two subjects for the entire set of E, I, V conditions will also differ. Valence = V++ Valence = VM 1: 1‘ 1+ I++ I: 1‘ 1+ I++_ E++113i1038isi -++i13111!815'1 ii)! (2)} (:)J(:) ’ E ‘(3);T7) I(4) :(2) - + E . g + 10 i 9 ; o g 2 - E (71' (4)? (2)i(1), E 1(6); (9) *(3): (1)} CHAPTER VII DISCUSSION The results of this study suggest two general con- clusions. The first and most obvious conclusion is sug- gested by the supportive results found for the multiplica- tive and dual distributive models. Contrary to expectancy theory formulations, these results point to apparent in- dividual differences in work motivation, with the expectancy theory model being an appropriate model for some, and the dual distributive model being appropriate for others. Unfortunately, it is necessary to underscore the word ”apparent" because the dual distributive model could not be fully tested in the present study. Thus, one of the more improtant areas for future research suggested by this study is that the dual distributive model be more thoroughly tested.- The importance of more fully researching this model is further pointed out by its apparent illogical nature. For example, according to the dual distributive model, as the probability that hard work will lead to successful task performance increases, so does the motivation to work hard, even when the consequences of successful task performance 89 90 are undesirable! Strange though this may seem, results consistent with this example were found in the present study. The higher ranking given to the first of the two below E, I, V conditions serves to illustrate this point: (E++I++V--) It is almost certain that successfully per— forming this task will actually lead to your being fired, whereas not much of anything is likely to happen if you perform it unsuccessfully. If you work hard you feel your chances of performing this task are good. (E+I++V--) Even if you work hard you feel your chances of successfully performing this task are poor. In addi- tion, while it is unlikely that much of anything will happen if you perform this task unsuccessfully, it is almost certain that successfully performing it will re- sult in your being fired. Note that these descriptions specify that nothing of consequence will result from unsuccessfully performing the task. Had this phrase not been included, a plausible explanation for the higher ranking of the first description would exist. Subjects could have then assumed that unsuc- cessfully performing the task would also lead to being fired, and therefore opted to work harder in the first condition, reasoning that at least they would receive any intrinsic reward there was to be gained from performing the task successfully. It would, therefore, be possible to argue that the subjects' reSponses do not really repre- sent support for the E + IV model. However, because the inclusion of this phrase should have prohibited the subjects from making this assumption, the viability of the argument' is questionable. 91 It is of further interest to note that an additional characteristic of the general stimulus situation would seem to rule out another plausible basis for arguing that the subjects' rankings of these two descriptions do not really represent support for the E + IV model. On every other page of the Work Motivation Questionnaire, the subjects were re— peatedly instructed to assume that the tasks themselves were neither appealing nor unappealing. Had this procedure not been followed, it could be argued that the subjects' preference for the first description reflects a strong com- petence motive, whereby the subjects were actually willing to sacrifice their jobs in order to achieve a task of high intrinsic value. In fact, it could further be argued that the preference for the first description is actually con- sistent with the expectancy theory model. The basis for this argument is shown in the below equations for the two descriptions. These equations show how responses to the two descriptions could then be considered to reflect the sum of two EIV products. Description 1: Force to achieve successful task performance E++I++V-~ + E++Ipositive Vpositive Description 2: Force to achieve successful task performance E+I++V-- + E+Ip051tlve Vp051tlve The first EIV product to the right of each equality represents the contribution to total force associated with the outcome of termination of employment.. This is, of course, negative in both instances, with Description 1 having the larger 92 negative product. The second EIV product to the right of each equality represents the contribution to total force associated with the intrinsic value of successfully achiev- ing the task. This is positive in both instances, with Description 1 having the larger positive product. In the absence of instructions to consider the tasks themselves neither appealing nor unappealing, it could be argued that this EIV product was very large for some subjects. Conse- quently, the resultant force for Description 1 was more positive (less negative) for these subjects, and their preference for this description is, therefore, indicative of support for the EIV model and not the E + IV model. The presence of these instructions, however, should have acted to minimize the role played by intrinsic satisfaction and the need for feelings of competency. This serves to weaken the basis for this argument, and, instead, forces one to return to the uncomfortable conclusion that the re- sults for these subjects do, in fact, represent apparent support for the E + IV model. Thus, the need to more fully examine the tenability of the dual distributive model becomes even more evident. The second general conclusion suggested by the research evidence is less obvious and more speculative. The basis for this conclusion lies not in the supportive results found for the two models, but rather in the non- supportive results found for subjects 72, 82, 89, 102, 93 115, and 144. As indicated in Table 5, those pairwise requirements for the EIV model not satisfied by these subjects were generally close to being satisfied. In other words, few of the pairwise test results for these subjects represent a radical departure from the EIV model. This suggests that the failure of these subjects to fully satisfy the EIV model might be attributable to greater inconsistency in their response choices. Examination of the consistencey of choice data in Table 3, however, shows that these subjects were almost as consistent as those found to fully satisfy a model. The average reliability for the subjects found to satisfy a model was .89. The average percentage of intransitive choices for this group was 4.51. By comparison, for the subjects failing to satisfy a model these averages were .90 and 6.60. Further— more, when subject 102 is excluded from this group, these averages become .91 and 5.15. Thus, contrary to expecta- tion, the data do not appear to indicate that the failure of these subjects to fully satisfy the EIV model can be attributed to greater inconsistency in their response choices. The conclusion instead suggested is that these subjects were equally consistent in reporting their motiva- tions, but the models underlying these self-reported motif vations consist of approximations to the EIV model. The plausibility of this interpretation is inter- esting for the following reason. In the present study, 94 subjects were asked to report what their motivations would be under relatively simple situations. They were never asked to consider more than one behavior contingent out- come in any given hypothetical situation, and they always received explicit information about the nature of this be- havior contingency. Yet, if the conclusion suggested by the nonsupportive results found for subjects 72, 82, 89, 102, 115, and 144 is correct, there is reason to believe that, even in relatively simple situations, an individual's motivation is more apt to be a function of an approximation to the EIV model (or conversely an approximation to the E + IV model). This suggests that as the situation becomes more and more complex and there are more, less explicit, behavior contingencies to consider, the model underlying an individual's motivation becomes less and less an approxi- mation to the EIV model. This is, of course, conjecture, and the viability of this conjecture remains to be sub- stantiated by future research. However, as Behling and Starke (1973) point out, research in the related area of decision making has produced results consistent with this general line of reasoning. More specifically, research has shown that subjective expected utility (SEU) theory describes decision making behavior only in very simple situations. This finding is particularly relevant because SEU theory states that people choose in a way that maxi- mizes subjective expected utility. EIV theory can 95 therefore be considered a special case of SEU theory. Thus, while this entire discussion is admittedly even more speculative than the conclusion on which it is based, research on SEU theory suggests that this specula- tion is at least worthy of future empirical investigation. Such investigation would, of course, entail examination of the EIV theory model (and the E + IV model) under con— ditions of varying complexity. Limitations of the Present Study As in all studies, there are several limitations of the present study that should not go unnoticed. First, it is important to recognize that this study was basically an eXperimental study in which the dependent variable of work motivation was a self-report measure. The caution that must be exercised in generalizing from an eXperimental study is obvious and need not be elaborated upon here. The use of self-report motivation data, while consistent with the majority of past expectancy theory research, raises the very basic issue of whether the results obtained are method bound or, stated differently, whether self reports can be assumed to accurately reflect motivation. As past expectancy theory research has shown, there is apparent reason to question this assumption (compare columns 1 and. 3 in Table 1, page 22), and it is therefore important that future research be directed toward this issue. 96 Quite obviously, this research would be characterized by the collection of actual task behavior data. Measures of motivation could then be derived from this data by taking into account individual differences in ability. Hopefully, this research would also be characterized by the continued use of within-subject analyses, and even though eXperimental studies place greater restrictions on the generalization of results, it would probably be most beneficial if these studies were conducted in controlled settings. This would provide for greater insight into the fundamentals of moti— vation, which we still know little about, and it would also provide for the study of motivation under varying conditions of complexity, the value of which was discussed earlier. It is also important to recognize that the subjects in the present study came from a relatively homogeneous occupational group. While there is no a priori reason to suspect that the models describing the work motivations of middle managers are in any way different from those de- scribing the work motivations of members of other occu- pational groups, it is, nevertheless, necessary that due caution be taken when generalizing from the results for this particular sample. Finally, the reader is reminded that only one of the two composition rules contained in the expectancy theory model was tested in the present study-—the multi- plicative composition rule. No attempt was made to verify 97 the additive composition rule contained in Proposition 1 of the theory (V = XIV), and the question, therefore, re- mains as to whether the overall expectancy theory model adequately describes behavior in the presence of multiple behavior contingencies. Recognition of this limitation once again points to the value of studying motivation under more complex situations in the future. An Alternative to the Conjoint Measurement Approach The primary focus in conjoint measurement is the discovery of qualitative laws that govern the composition of several attributes. Measurement per se is of secondary importance. Inherent in the conjoint-measurement approach is the view that the importance of measurement (as distinct from other usages of numerical indices) lies in the qualitative laws in which it is based, and that the usefulness of numerical scales derives from the em- pirical lawfulness that they reflect. Accordingly, measurement is regarded as a consequence, or a by- product, of the validity of some qualitative laws, and major emphasis is placed on the study of these laws. [Krantz and Tversky, 1971, p. 166] In constrast to the conjoint measurement approach is the numerical approach to the study of composition rules. This approach, which characterizes the work of Thurstone and Jones (1957), Anderson (1970), and others, is based on the argument that it is more advantageous to study com- position rules in terms of numerical values than in terms of qualitative properties. The inapprOpriateness with 98 which this approach has been utilized in past expectancy theory research was, of course, one of the primary argu- ments for using the conjoint measurement approach in the present study. This is not to say, however, that the numerical approach need always be inappropriate, and it is, therefore, important that the reader be aware of the relative merits of the two approaches. As an aid in achieving this awareness, Table 9 has been prepared. As Krantz and Tversky (1971) point out, and as Table 9 implies, the relative strengths and weaknesses of these two approaches suggest that they can most prof- itably be used in a complementary nature. The merging of these two approaches in future work motivation research would therefore appear to be a worthwhile endeavor. 99 Table 9 A comparison of the conjoint (axiomatic) and numerical approaches to the study of composition rules Conjoint (Axiomatic) Approach Numerical Approach Major Discovery of qualitative laws, Analysis of empirical Emphasis which leads to construction of relationships based on measurement scales given numerical scales Provides powerful diagnostic Allows for fallible tests for distinguishing be- data EXISE alternatlve comp051tlon Standard statistical tests can be employed Allows for location of spe- cific sources of theory vio- lation Does not allows for fallible Allows for testing of data (Error variance poses overall goodness-of- a particularly difficult fit, but does not gen- problem)a erally allow for loca- tion of specific sources Standard statistical tests b of theory violation are generally inappropriate Critical tests for dis- Weaknesses tinguishing between models are not avail- able, and, in the pres- ence of fallible data, it may be difficult to distinguish between models on the basis of a measure of overall _goodness-of-fit When a specific composi- tion rule is not met by the data, it is often impossible to discern whether the composition rule is invalid or the numerical scales are inadequate 3The ramifications of this particular weakness of the con- joint measurement approach were most evident in the present study, where it was necessary to have the subjects respond to an inor- dinately long questionnaire in order to minimize the fallibility of the resultant rank orderings. ' b This weakness of the conjoint measurement approach was also evident in the present study, as witnessed by the necessity to establish arbitrary decision rules for the various single and joint- factor tests. BIBLIOGRAPHY BIBLIOGRAPHY Anderson, N. H. Functional measurement and psycholophysical “ judgment. Psychological Review, 1970, 11, 153-170. Arvey, R. D. Task performance as a function of perceived effort-performance and performance-reward contin— gencies. Organizational Behavior and Human Perfor— mance, 1972, 8, 423-433. Arvey, R. D., and Mussio, S. J. A test of expectancy theory in a field setting using female clerical employees. Journal of Vocational Behavior, 1973, l, 421—432. Behling, 0., and Starke, F. A. Some limits on expectancy theories of work effort. Proceedings, Midwest Meeting, American Institute of Decision Sciences, 1973. Coombs, C. H., Dawes, R. M., and Tversky, A. Mathematical Psychology. Englewood Cliffs, New Jersey: Prentice- Hall, 1970. Coombs, C. H., and Huang, L. C. Polynomial psychophysics of risk. Journal of Mathematical Ppychology, 1970, 1, 317—338. Dachler, H. P., and Mobley, W. H. Construct validation of an instrumentality-expectancy-task-goal model of work motivation: Some theoretical boundary condi- tions. Journal of Applied Psychology Monograph, 1973, £8, 397-418. Darlington, R. B. Multiple regression in psychological re- search and practice. Psychological Bulletin, 1968, 69, 161—182. Galbraith, J., and Cummings, L. L. An empirical investiga- tion of the motivational determinants of task per- formance: Interactive effects between instrumentality- valence and motivation-ability. Organizational Be~ havior and Human Performance, 1967, l, 237-257. 100 101 Gavin, J. F. Antecedents of effective job performance: A test of the Porter-Lawler hypothesis. Journal of Industrial and Organizational Psychology, 1974, in press. Georgopoulos, B. S., Mahoney, G. M., and Jones, N. W. A path-goal approach to productivity. Journal of Applied Psychology, 1957, ll, 345-353. Graen, G. Instrumentality theory of work motivation: Some - experimental results and suggested modifications. Journal of Applied Psychology Monograph, 1969, 88, 1-25. Hackman, J. R., and Porter, L. W. Expectancy theory pre- dictions of work effectiveness. Organizational Be— havior and Human Performance, 1968, 8, 417-426. Heneman, H. G. III, and Schwab, D. P. An evalution of re- search on expectancy theory predictions of employee performance. Psychological Bulletin, 1972, 18, 1-9. House, R. J. A path goal theory of leader effectiveness. Administrative Science Quarterly, 1971, l8, 321-338. Krantz, D. H. Measurement structures and psychological laws. Science, 1972, 175, 1427-1435. Krantz, D. H., Luce, D., Suppes, P., and Tversky, A. Founda- tions Of measurement. Volume 1. Additive and poly- nomial representations. New York: Academic Press, 1971. Krantz, D. H., and Tversky, A. Conjoint-measurement analysis of composition rules in psychology. Psychological Review, 1971, Z8, 151-169. Kruskal, J. B. Relationship of clustering to scaling and the interpretation of neighborhoods. Paper pre- sented at the Bell-Penn Workshop on Multidimensional Scaling, June, 1972. Lawler, E. E. III. A correlation-causal analysis of the relationship between expectancy attitudes and job performance. Journal of Applied Psychology, 1968, 88, 462-468. Lawler, E. E. III, and Porter, L. W. Antecedent attitudes of effective managerial performance. Organizational Behavior and Human Performance, 1967, 8, 122-142. 102 Lawler, E. E. III, and Suttle, J. L. Expectancy theory and job behavior. Organizational Behavior and Human Performance, 1973, 8, 482-503. Luce, R. D., and Tukey, J. Simultaneous conjoint measure- ment: A new type of fundamental measurement. Journal of Mathematical Psychology, 1964, l, 1-27. McCormick, E. J., and Roberts, W. K. Paired comparison ratings: 2. The reliability of ratings based on partial pairings. Journal of Applied Psychology, 1952, 18, 188-192. Mitchell, T. R. Expectancy models of job satisfaction, oc- cupational preference and effort: A theoretical, methodological and empirical appraisal. Psycho- logical Bulletin, 1974, 8l, 1053-1077. Mitchell, T. R., and Albright, D. W. Expectancy theory pre- dictions of the satisfaction, effort, performance and retention of naval aviation officers. Organiza- tional Behavior and Human Performance, 1972, 8, 1-20. Mitchell, T. R., and Nebeker, D. M. Expectancy theory pre- dictions of academic effort and performance. Journal of Applied Psychology, 1973, 82) 34-45. Nunnally, J. C. Psychometric theopy. New York: McGraw- Hill, 1967. Porter, L. W., and Lawler, E. E. III. Managerial attitudes and performance. Homewood, IllinEIs: Dorsey Press, 1968. Pritchard, R. D., and DeLeo, P. J. Experimental test of the valence-instrumentality relationship in job performance. Journal of Applied Psychology, 1973, ‘81, 264-270. Pritchard, R. D., and Sanders, M. S. The influence of valence, instrumentality, and expectancy on effort and performance. Journal of Applied Psychology, 1973, 81, 55-60. Rambo, W. W. The effects of partial pairing on scale values derived from the method of paired comparisons. Journal of Applied Psychology, 1959, 81, 379-381. Ross, R. T. Optimum orders for the presentation of pairs in the method of paired comparisons. Journal of Educational Psychology, 1934, 18, 375-382. 103 Schmidt, F. L. Implications of a measurement problem for expectancy theory research. Organizational Be- havior and Human Performance, 1973, l8, 243-251. Schuster, J. R., Clark, B., and Rogers, M. Testing por- tions of the Porter and Lawler model regarding the motivational role of pay. Journal of Applied Psychology, 1971, 88, 187-195. Schwab, D. P., and Dyer, L. D. The motivational impact of a compensation system on employee performance. Organizational Behavior and Human Performance, 1973, 8, 215-225. Snedecor, A. W., and Cochran, W. G. Statistical methods. Ames, Iowa: The Iowa State UnIversIty Press, 1967. Thurstone, L. L., and Jones, L. V. The rational origin for measuring subjective values. Journal of the American Statistical Assocation, 1957, 81, 458-471. Tversky, A. A general theory of polynomial conjoint measure- ment. Journal of Mathematical Psychology, 1967, 4, 1-20. _ Vroom, V. H. Work and motivation. New York: John Wiley and Sons, 1964. Wahba, M. A., and House, R. J. Expectancy theory in work and motivation: Some logical and methodological issues. Human Relations, 1974, 11, 121-147. APPENDICES APPENDIX A NARRATIVES USED IN WORK MOTIVATION QUESTIONNAIRE Narrative Number 5 12 16 32 APPENDIX A NARRATIVES USED IN WORK MOTIVATION QUESTIONNAIRE Narrative ++ -- ++ (E ,I ,V ) While you doubt whether much of anything of consequence will result from your unsuccess- fully performing this task, it is almost certain that successfully performing it will actually pre- vent you from receiving the promotion and sub- stantial pay increase for which you now appear destined. You feel your chances of successfully performing this task are good if you work hard. (E+ ,I--,V++) Even if you work hard you feel your chances of successfully performing this task are poor. You have little reason to suspect that anything of consequence will result from your performing it unsuccessfully. On the other hand it is almost certain that successfully performing it will actually prevent you from receiving the promotion and substantial pay increase for which you now appear destined. (E+ ,I++,V++) Even if you work hard you feel your chances of successfully performing this task are poor. It is almost certain you will receive a promotion and substantial pay increase if you successfully perform it. (E++,I++,V++) It is almost certain you will receive a promotion and substantial pay increase if you successfully perform this task. If you work hard you feel your chances of successfully performing it are good. (E++,I- ,V+ ) If you work hard you feel your chances of successfully performing this task are good. However, while unsuccessfully performing it is likely to be inconsequential, there is a fair chance that successfully performing it will actually prevent you from receiving the moderate pay increase for which you now appear destined. 104 Narrative Number 26,33 25 28 3O 20 105 Narrative (B+ ,1. ,V+ ) There is a fair chance that success- fully performing this task will actually pre- vent you from receiving the moderate pay in— crease for which you now appear destined, whereas unsuccessfully performing it is likely to be inconsequential. Even if you work hard you feel your chances of successfully perform- ing this task are poor. (E+ ,I+ ,V+ ) There is a fair chance you will re- ceive a moderate pay increase if you success- fully perform this task. You also realize that even if you work hard your chances of successfully performing it are poor. (EH-,1+ ,V+ ) If you work hard you feel your chances of successfully performing this task are good. There is a fair chance you will receive a moderate pay increase if you successfully per- form it. ++ + -- . . (E ,I ,V ) There 15 a falr chance that success- fully performing this task will actually lead to your being fired, whereas not much of any- thing is likely to happen if you perform it unsuccessfully. If you work hard you feel your chances of successfully performing this task are good. (E+ ,I+ ,V-n) Even if you work hard you feel your chances of successfully performing this task are poor. In addition, while it is unlikely that much of anything will happen if you per— form this task unsuccessfully, there is a fair chance that successfully performing it will actually result in your being fired. (E++,I ,V ) If you work hard you feel your chances of successfully performing this task are good. You are on the brink of being fired and there is a fair chance you can save your job by perform- ing this task successfully. (E+ ,I ,V ) You are on the brink of being fired and there is a fair chance you can save your job by successfully performing this task. You also realize that even if you work hard your chances of successfully performing it are poor. Narrative Number 9 11 27 29 14 24 31 106 Narrative (E++,I++,V--) It is almost certain that successfully performing this task will actually lead to your being fired, whereas not much of anything is likely to happen if you perform it unsuccess- fully. If you work hard you feel your chances of successfully performing this task are good. (E+ ,I++,V- ) Even if you work hard you feel your chances of successfully performing this task are poor. In addition, while it is unlikely that much of anything will happen if you per- form this task unsuccessfully, it is almost certain that successfully performing it will actually result in your being fired. ,++ (E ,I--,V--) If you work hard you feel your chances of successfully performing this task are good. You are on the brink of being fired and it is almost certain you can save your job by perform- ing this task successfully. (E+ ,I -,V--) You are on the brink of being fired and it is almost certain you can save your job by successfully performing this task. You also realize that even if you work hard your chances of successfully performing it are poor. (E++,I-_,V+ ) If you work hard you feel your chances of successfully performing this task are good. However, while unsuccessfully performing it is likely to be inconsequential, successfully per- forming it is almost certain to actually pre- vent you from receiving the moderate pay in- crease for which you now appear destined. (E+ ,I ,V+ ) It is almost certain that successfully performing this task will actually prevent you from receiving the moderate pay increase for which you now appear destined, whereas unsuccess- fully performing it is likely to be inconsequen- tial. Even if you work hard you feel your chances of successfully performing this task are poor. + ++ + , _ , . (E ,I ,V ) It 15 almost certain you W111 recelve a moderate pay increase if you successfully per- form this task. You also realize that even if you work hard your chances of successfully per- forming it are poor. Narrative Number 17 10 22 107 Narrative ++ ++ + (E ,I ,V ) If you work hard you feel your chances of successfully performing this task are good. It is almost certain you will receive a moderate pay increase if you successfully perform it. (E++,I‘ ,V++) While you doubt whether much of any- thing of consequence will result from your un- successfully performing this task, there is a fair chance that successfully performing it will actually prevent you from receiving the promo- tion and substantial pay increase for which you now appear destined. You feel your chances of successfully performing this task are good if you work hard. (E+ ,I- ,V++) Even if you work hard you feel your chances of successfully performing this task are poor. You have little reason to suspect that anything of consequence will result from your performing it unsuccessfully. On the other hand there is a fair chance that successfully performing it will actually prevent you from re- ceiving the promotion and substantial pay in- crease for which you now appear destined. + + ++ (E ,I ,V ) Even if you work hard you feel your chances of successfully performing this task are poor. There is a fair chance you will re- ceive a promotion and substantial pay increase if you successfully perform it. (E++,I+ ,V++) There is a fair chance you will re- ceive a promotion and substantial pay increase if you successfully perform this task. If you work hard you feel your chances of successfully performing it are good. (E++,I++,V- ) Although you doubt whether much of any- thing will result from your unsuccessfully per- forming this task, successfully performing it is almost certain to actually result in your being transferred to a less desirable job. You feel you have a good chance of successfully performing this task if you work hard. Narrative Number 19 21 13 18 23 15 108 Narrative + ++ (E ,I ,V- ) Even if you work hard you feel your chances of successfully performing this task are poor. You have little reason to suspect that much of anything will happen if you un- successfully perform it. It is almost certain that successfully performing it will actually result in your being transferred to a less desirable job. (E++,I‘-,V- ) If you work hard you feel your chances of successfully performing this task are good. Your transfer to a less desirable job, which appears all but certain at the present time, is something you can almost certainly prevent by performing this task successfully. (E+ ,I—-,V-) As things stand now it appears all but certain you will be transferred to a less de- sirable job. However, it is almost certain you can prevent this transfer by successfully per- forming this task. Unfortunately, even if you work hard your chances of successfully perform- ing it are poor. (E++,I+ ,V- ) Although you doubt whether much of anything will result from your unsuccessfully performing this task, there is a fair chance that successfully performing it will actually result in your being transferred to a less de- sirable job. You feel you have a good chance of successfully performing this task if you work hard. + + '(E ,I ,V- ) Even if you work hard you feel your chances of successfully performing this task are poor. You have little reason to suspect that much of anything will happen if you un- successfully perform it. There is a fair chance that successfully performing it will actually result in your being transferred to a less desirable job. (E++,I- ,V- ) If you work hard you feel your chances of successfully performing this task are good. Your transfer to a less desirable job appears all but certain at the present time and there is a fair chance you can prevent this transfer by performing this task successfully. 109 Narrative Number Narrative 2 (E+ ,I— ,V- ) As things stand now it appears all but certain you will be transferred to a less desirable job. However there is a fair chance you can prevent this transfer by successfully performing this task. Unfortunately, even if you work hard your chances of successfully per- forming it are poor. APPENDIX B NARRATIVE PAIRS DEFINING ITEMS IN WORK MOTIVATION QUESTIONNAIRE Item Number Narrative Pair APPENDIX B NARRATIVE PAIRS DEFINING ITEMS IN WORK MOTIVATION QUESTIONNAIRE Item Number Narrative Pair 1 2 10 ll 12 13 14 15- 16 17 18 19 Note: 10,26 24,12 14,22 16,20 8,29 10,27 12,25 14,23 21,16 19,18 33, 5 110 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 See Appendix A for definitions of numbered narratives. Item Number 39 4O 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57‘ 58 59 6O 61 Narrative Pair 111 Item Number Narrative Pair 24,16 18,22 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 30,13 15,28 17,26 19,24 22,21 Item Number 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102‘ 103 104 105 106 107 108 Narrative Pair 9, 5 11,3 13,33 15,31 29,17 19,27 25,21 5,10 112 Item Number Narrative Pair 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 13, 4 2,15 33,16 18,31 29,20 22,27 24,25 9, 1 11, 7 5,13 3,15 17,33 19,31 29,21 27,23 1,25 Item Number Narrative Pair 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 10, 1 12, 8 6,14 4,16 2,18 32,20 30,22 28,24 26, 1 10,11 113 Item Number 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 Narrative Pair 31,23 25,29 11,12 32,23 30,25 28,27 14,10 8,16 18, 6 20, 4 24,32 26,30 12,13 10,15 6,19 4,21 Item Number 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 Narrative Pair 33,24 31,26 31,28 114 Item Number 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 Narrative Pair 20, 8 22, 6 24, 4 115 Item Number Narrative Pair Item Number Narrative Pair 225 13,18 245 29, 4 226 20,11 246 2,31 ‘ 227 9,22 247 32,33 228 7,24 248 1,17 229 5,26 249 19,15 230 3,28 250 21,13 231 31,32 251 23,11 232 18,14 252 25, 9 233 20,12 253 7,27 234 10,22 254 29, 5 235 8,24 255 31, 3 236 6,26 256 1,33 237 4,28 257 18,17 238 2,30 258 15,20 239 17,16 259 ' 13,22 240 14,19 260 11,24 241 12,21 261 9,26 242 10,23 262 28, 7 243‘ 25, 8 263 5,30 244 6,27 264 32, 3 “111111111111