III IIIHIII ’ I I SEQ WWII“IINIJIJIIIIIII A COMPARATIVE STUDY OF THE PERSONALITY FACFORS ASSOCIATED WITH TWO DIFFERENT OPERATIONAL DEFINITIONS OF DISCREPANT ACHIEVEMENT Thu“ For I‘Im Degree of EJ. D. MICBISAN STATE UNIVERSITY Richard Bland Smith 1963 TH E513 This is to certify that the thesis entitled A COMPARATIVE STUDY OF THE PERSONALITY FACTORS ASSOCIATED WITH TWO DIFFERENT OPERATIONAL DEFINITIONS OF DISCREPANT ACHIEVEMENT presented by Richard Bland Smith has been accepted towards fulfillment of the requirements for Ed. D. , Education _____ degree 1n ______ Major professor Date ”7 Z/y’gj 0-169 LIBRARY Michigan State University A.A.-._.4s ‘m ._ ABSTRACT -A COMPARATIVE STUDY OF THE PERSONALITY FACTORS ASSOCIATED WITH TWO DIFFERENT OPERATIONAL DEFINITIONS OF DISCREPANT ACHIEVEMENT by Richard Bland Smith The purpose of this studyvuusto investigate the per- sonality factors of under- and over-achieving samples of eleventh grade students selected by two different operational techniques. .With the exception of the operational definition of discrepant achievers used, this thesis is a replication of an earlier study done by Taylor. .The present study in- ~volves a comparative investigation of the personality charac- ~teristics of individuals isolated as discrepant achievers in this and Taylor's study. .In the present study a personality instrument was constructed from items which previous research had found to 'differentiate between under- and over—achieving students. It was found that 16 female and 27 male items significantly discriminated between under— and over-achievers after cross validation. .The items found to discriminate between dis- crepant achievers in this study were compared with the dis- criminating items isolated by Taylor. ,The chi square test was performed to determine the significance of the overlap of items in the two studies. .The resulting chi square value failed to reach the .05 level of significance. .It was Richard Bland Smith concluded that the items found to discriminate between dis- crepant achievers in the two studies did not overlap to an extent greater than would have been expected by chance alone. The discriminating items in the present study were factor analyzed, and the resulting factors compared with the factors isolated by Taylor. Six male and five female factors were located. Taylor isolated seven male and six female factors. Four male and four female factors in the two studies were hypothesized as being related. The related male factors dealtwith themes of anxiety, compulsivity, conformity excitation, and authority relations. The related female factors were concerned with fantasy, excitation, organiza- tional need, and activity planning. A COMPARATIVE STUDY OF THE PERSONALITY FACTORS ASSOCIATED WITH Two DIFFERENT OPERATIONAL DEFINITIONS OF DISCREPANT ACHIEVEMENT By Richard Bland Smith A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF EDUCATION College of Education 1963 k. In ACKNOWLEDGMENTS Sincere appreciation is hereby expressed to Dr. William W. Farquhar for his guidance throughout the plan- ning, execution, and reporting of this research. The writer is indebted to Dr. Jean Lepere for her encouragement and critical comments which led to the com- pletion of this study. The other members of the guidance committee, Dr. Wilbur Brookover and Dr. Bernard Corman are thanked for their helpful suggestions. 11 TABLE OF CONTENTS ACKNOWLEDGMENTS. LIST OF TABLES LIST OF FIGURES. Chapter I. THE PROBLEM. Purpose of the Study Need for the Study. Theory. . The Nature of the Study II. DESIGN AND METHODOLOGY Instrumentation. . Sample Selection Based on Krug' s Technique Hypotheses Item Analysis Procedure Factor Analytic Procedures Assumptions . . Rotation of the Factors Summary . . III. ANALYSIS OF DATA Item Analysis Results. Reliability Estimates. Factor Analysis Results Interpretation of the Factors Summary IV. A COMPARISON OF RESULTS A Comparison of the Items Selected A Comparison of Male Factors A Comparison of Female Factors. Summary iii Page ii vii |_J WIDIDI—J IA 15 l8 18 20 21 21 22 23 23 2A 26 32 LII 42 11.2 A3 48 53 Chapter Page V. SUMMARY, CONCLUSIONS, RESEARCH IMPLICATIONS, AND SUGGESTIONS FOR FUTURE RESEARCH . . . . 54 Summary. . . . . . . . . . . . . 5A Conclusion. . . . . . . . . . . 56 Research Implications . . . . . . 59 Suggestions for Future Research. . . . . 6O BIBLIOGRAPHY . . . . . . . . . . . . . . . 63 APPENDIX . . . . . . . . . . . . . . . . 66 iv Table 2 wwwwwwwwwww .1 \OCDNIO .11 .12 .13 .14 .15 .16 LIST OF TABLES Sample Size for Validation and Cross— Validation Classification . . Reliability Estimates of the Factored Items and Total Scale . . . . . . Item Intercorrelations of Twenty—Three Male Items Used in Factor Analysis of the Human Trait Inventory Scale . . . . . Item Intercorrelations of Sixteen Female Items Used in Factor Analysis of the Human Trait Inventory Scale Rounded, Unrotated Loadings for the Seven Male Factors of the Human Trait Inventory. Rounded, Unrelated Loadings for Six Female Factors of the Human Trait Inventory Item Content of Male Factor I. Item Content of Male Factor II Item Content of Male Factor III Item Content of Male Factor IV Item Content of Male Factor V Item Content of Male Factor VI Item Content of Female Factor I Item Content of Female Factor II. Item Content of Female Factor III Item Content of Female Factor IV Item Content of Female Factor V . V Page 16 25 27 29 3O 31 33 34 35 36 36 37 38 39 39 40 41 Table Page 4.1 A Graphic Comparison of the Male Factors Isolated in the Two Studies . . . . . . 44 4.2 Male Factors, Items, and Loadings for Krug's Technique's Factor I, and Taylor's Related Factors. . . . . . . . . . . . . 45 4.3 Male Factors, Items, and Loadings for Krug's Technique's Factors II and IV, and Taylor's Related Factor . . . . . . . . . . 47 4.4 A Graphic Comparison of the Female Factors Isolated in the Two Studies . . . . . . 49 4.5 Female Factors, Items, and Loadings for Krug's Technique 8 Factors III and V, and Taylor's Related Factor . . . . . . . . . 51 4.6 Female Factors, Items, and Loadings for Krug's Technique's Factor II, and Taylor's Related Factor . . . . . . . . . . . . . 52 vi Figure 1.1 1.2 1.3 1.4 2.1 LIST OF FIGURES Graphic Presentation of Shaw and McCuen's Technique for Selecting Under- and Over- Achievers (Extended) Graphic Presentation of Winberg's Arbitrary Partitioning Technique Of Selecting Under— and Over-Achievers. . . . . . First Stage of the Two Stage Regression Model. Second Stage of the Two Stage Regression Model Graphic Presentation of Krug's Method of Selecting Under- and Over-Achievers vii Page 11 12 17 CHAPTER I THE PROBLEM Purpose of the Study Research studies in the area of academic motivation contain many conflicting results. It is hypothesized that these contradictory findings stem from the different ways of operationally defining over— and under-achievement. The effect different operational definitions of under— and over-achievement have on the results of motivation studies have not been adequately examined. .In a recent paper which compared the techniques used in selecting under- and over- achievers, Farquhar noted seven techniques representing four methodological categories which have been used to select discrepant achievers.l It was further demonstrated that the different operational definitions of over- and under- achievers resulted in the selection of relatively different individuals. .It is the purpose of this study to investigate the effect two different operational procedures have on personality item discriminations and subsequent factor struc- ture. lWilliam Farquhar, "The Comparison of Techniques Used in Selecting Under and Over-Achievers" (paper read at APGA, Denver, Colorado, 1961). Need for the Study The need for the study is basically derived from the lack of standardization of the operational procedures used in identifying discrepant achievers. This lack of standard- ization may have been the cause of inconsistent and uninter- pretable research findings in the area, and appears to have led to the selectibn of as many different samples as there are operational techniques.1 The characteristics of these different samples have not been adequately examined. It is the intent of this study to investigate the responses to a personality test of two samples drawn from the same popula- tion, but selected by different Operational procedures. Theory Human behavior theory is conceived of by Farquhar2 as functioning at the levels Of focusing, predicting, and inte- grating. The focusing level is concerned with the process of (l) eliminating seemingly plausible but irrelevant vari- ables, (2) the directing of attention to relevant variables. -In this stage the many nebulous theories and unrelated findings provide the basic tenets which are explored. .The second, or predictive level Of behavior theory, comes after previous studies and theorizing have provided convincing lIbid. 2Williamw. Farquhar, A Comprehensive Study of the Motivational Factors Underlying Achievement of Eleventh Grade High School Students, Research Project No. 8361 (8458) in cooperation with the U. 8. Office of Education, Washing- ton, D. C. 3 evidence that the direction of the alternative hypothesis can be specified. Integrating, the third level of behavior theoryyis concerned with the development of an interlocking system of laws and constructs. In this study attention has been focused on (1) the comparison of samples selected from the same population by two different operational procedures and (2) the isolating and comparison of traits related to academic motivation. Summary of Classification Techniques Farquharl prOposed that the many techniques for locating discrepant achievers be grouped into four general classifications. The first of these was by Central Tendency Splits. In this method, under- and over—achievement is deter— mined by dichotomizing a distribution of combined aptitude and achievement measures. The method used by Shaw and McCuen is typical.2 Here, under-achievers were determined to be those individuals who scored in the top 25 per cent in verbal ability based on the Pintner General Ability Test: Verbal VSeries, and who had an earned grade point average below the class mean. The method Of selecting over-achievers was not identified in the article, but it was confirmed by Farquhar lFarquhar, "The Comparison of Techniques Used in Selecting Under and Over-Achievers," op. cit. 2M. C. Shaw and J. T. McCuen, "The Outset of Academic Under-achievement in Bright Children," Journal of Educational Psychology, Vol. 51 (1960), pp. 103-108. 4 in personal correspondence with Shaw that over-achievers would be found by reversing the procedure. The Shaw—McCuen procedure is graphically presented in Figure 1.1. The second teChnique involved arbitrary partitions with the middle group eliminated. Here, discrepant achievers are determined by contrasting the extremes in achievement- aptitude distributions, and by eliminating a middle group. The arbitrary partitions with the middle-group eliminated- technique, with some slight modifications, was used by Shaw 3 4 and Brown,1 Shaw and Grubb,2 Drews and Teahan, Brookover, Frinkel,5 and Winberg.6 1M. C. Shaw and D. J. Brown, "Scholastic Under- Achievement of Bright College Students," Personnel and Guidance Journa1,Vol. 36 (1957), pp. 195—199. 2M. C. Shaw and J. Grubb, "Hostility and Able High School Under-achievers," Journal of Counseling_Psychology, Vol. 5 (1958), pp. 263—266. 3Elizabeth M. Drews and J. E. Teahan, "Parental Atti- tudes and Academic Achievement," Journal of Clinical Psy- chology, Vol. 13 (1957), pp. 328-332. uWilbur Brookover, "Identification of Self—Images and .Significant Others for Junior High School Students and Ex- ploration of the Relationship of Self-Image to Achievement in School Subjects," Cooperative Research Project, U. S. Office of Education and Michigan State University, 1959. 5E. Frinkel, "A Comparative Study of Achieving and Under-achieving High School Boys of High Intellectual Ability," Journal of Educational Research, Vol. 53 (1960), pp. 172-180. 6Wilma A. Winberg, "Some Personality Traits of Collegiate Under-achievers," Proceedings of the Iowa Academy of Science, Vol. 54 (1947), pp. 267-270. ,\ Over-//// ¢ Achievers D4 <5 / o a s m c w my (I) (D E: .‘E‘. 4—3 U) C a) 6 cd E H 8 0 Under- 3 Achiever .c 2 / Lower 25% in Mean Upper 25% in Ability Ability Aptitude Measure Figure 1.1. Graphic Presentation of Shaw and Mc— Cuen's Technique for Selecting Under- and Over- Achievers (Extended). 1William W. Farquhar, "The Comparison of Techniques Used in Selecting Under- and Over-Achievers" (paper read at APGA Convention, Denver, Colorado, March 1961, mimeographed). 6 ~Winberg's study is typical of the group and consisted Of acquiring the cumulative grade-point averages, American Council on Education (ACE) total scores and designating under— achievers, over-achievers, and normals as follows: (1) under- achievers were designated as those individuals who had ACE total scores at or above 100, but whose GPA's were below 2.00; (2) over-achievers, were identified as individuals having ACE's totals of 120 and below, but whose GPA was above 2.60; (3) normals were designated as individuals with ACE totals of 130 or above, and a GPA of 2.60 or above. Win- berg's method is graphically illustrated in Figure 1.2. The third method of classification proposed by Far- quhar was concerned with relative discrepancy splits. In this method grade-point average and aptitude predictors were ranked independently, and over- and under-achievement was determined by the discrepancy between the two ranks. Studies conducted using this technique include McQuary and Truax,l Diener,2 Mitchell,3 Baymur and Paterson,” and Duff and 1J. J. McQuary and W. E. Truax, "An Under—Achievement Scale," Journal of Educational Research, Vol. 48 (1955), pp. 393-399. 20. L. Diener, "Similarities Between Over-Achieving and Under-Achieving Students," Personnel and Guidance Journal, (1960), pp. 396-400. 3James V. Mitchell, "Good Setting Behavior as Function of Self-Acceptance, Over- and Under-Achievement and Related Personality Variances," Journal of Educational Psychology, Vol. 50 (1959), pp. 93-104. 4F. B. Baymur and C. H. Paterson, "A Comparison of Three Methods of Assisting Under-Achieving High School Stu- gengs," Journal of Counseling Psychology, Vol. 7 (1960), pp. 3- 9. ’ Cumulative GPA 4.0 -, 3.5 ‘ Over-Achievers Normal 3.0 - 2.5 ‘ 2.0 ‘r 1.5 ' 1'0 Under-Achievers 05 - i t i i i i i 1;. f 1r 50 50 7O 80 90 100 110 120 130 14 150 Aptitude Measure (ACE) Figure 1.2. Graphic Presentation of Winberg's Arbitrary Partitioning Technique of Selecting Under- and Over- Achievers.l 1William W. Farquhar, ”The Comparison of Techniques Used in Selecting Under- and Over-Achievers" (paper presented at APGA Convention, Denver, Colorado, March 1961, mimeographed). 8 Siegel.l Diener's approach, which illustrates this method, involved converting aptitude and GPA measures into "T" scores and defining the discrepant groups on the basis of plus and minus 15 "T" score units. Because of the varied locations Of these discrepant achievers in the scattergram no way was found of illustrating this method graphically. The fourth method of selecting discrepant achievers entailed the construction Of a regression line. Over- and under-achievers are designated as those individuals whose aptitude and achievement scores fall a certain degree above or below the regression line. The regression method is the only selection procedure which precisely determines the re- lationship between the aptitude and achievement measures. (For this reason, this study is primarily concerned with operational procedures which employ regression equations to predict achievement from aptitude measures. Twelve studies have used techniques of selection which would be classified under the regression model. Among these are Gerberich,2 Malloy,3 1O. L. Duff and L. Siegel, ”Biographical Factors Associ- ated with Academic Over and Under-Achievement," Journal of Educational Psychology, Vol. 51 (1960), pp. 43-46. 2R. Gerberich, "Factors Related to the College Achieve- ment of High-Aptitude Students Who Fail Expectation and Low- Aptitude Students Who Exceed Expectation," Journal of Educa— tional Psychology, Vol. 32 (1941), pp. 253—265. 3J. Malloy, ”An Investigation of Scholastic Over and Under-Achievement Among Female College Freshmen," Journal of Counseling Psychology, Vol. 1 (1954), pp. 260-263. 9 Fischer,l Owens and Johnson,2 Burgess,3 Gebhart and Hoyt,“ Krug,5 Jenson,6 Lum,7 Merrill and Murphy,8 DuBois,9 and Farquhar.lo Farquhar's two-stage regression technique is illustra- tive of the fourth procedure. 1R. P. Fischer, "The Role of Frustration in Academic Under-Achievement: An Experimental Investigation," Journal of the American Association of College Registrars, Vol. 18 (1943). pp. 227-238. 2W. A. Owen and Wilma C. Johnson, "Some Measured Per- sonality Traits of Collegiate Under—Achievers," Journal of Educational Psychology, Vol. 40 (1949), pp. 41—46. 3E. Burgess, ”Personality Factors of Over and Under— Achievers in Engineering," Journal of Educational Psychology, (1956). pp. 89-99. 4G. G. Gebhart and D. T. Hoyt, "Personality Needs of Under and Over-Achieving Freshmen," Journal of Applied Psychology, Vol. 42 (1958), pp. 125-128. 5R. E. Krug, "Over and Under-Achievement and the Edwards PPS," Journal of Applied Psychology, (1959), pp. 133—136. 6Vern H. Jensen, "Influences of Personality Traits on Academic Success,” Personnel and Guidance Journal, Vol. 36 (1958). pp. 497-500. 7M. Lum, ”A Comparison of Under and Over—Achieving Female College Students," Journal of Educational Psychology, Vol. 51 (1960), pp. 109-114. - 8R. M. Merrill and D. T. Murph , "Personality Factors and Academic Achievement in College,‘ Journal of Counseling Psychology, Vol. 6 (1959), pp. 207—209. 9P. H. DuBois, "0n the Statistics of Ratios," The American Psychologist, V01. 3 (1948), pp. 309. lOFarquhar, A Comprehensive Study of the Motivational Factors Underlying Achievement of Eleventh Grade High School Students, op. cit. 10 Stage I.——The first stage was devised to add stability by eliminating individuals with inconsistent aptitude scores. This stage consists of constructing a regression line from two aptitude measures:the California Test of Mental Maturity- Language (CTMM-L) and Differential Aptitude Test—-Verbal Reasoning (DAT-—VR). Two parallel lines were then drawn above and below the regression line at a distance equal to one standard error of estimate. Those individuals falling outside of these lines on the scattergram were then excluded from the study on the premise that their aptitude scores were unreliable. Stage II.--The aptitude predictor which correlated highest with the achievement criterion was used to build a regression line predicting achievement. The standard error of estimate was used to establish limits. Under-achievers were defined as individuals whose actual grade-point averages fell at least one standard error of estimate below the regres- sion line prediction of achievement. Similarly, over-achievers were designated as those individuals whose grade-point average fell one standard error of estimate above the regression line. A graphical representation of the two stage regression model 1 is reprOduced from the Farquhar study in Figures 1.3 and 1.4. lIbid. (with permission of the author). 11 .opspapa< comeHpmm manwpm o>mm 0:3 mHm56H>HUCH wchooaom mo . nonpoz .Hopoz coammopwom owwpm 038 03p Mo ommpm pmhfim .m.H opswam Am>-emflnoo Ucw upopc3 wCHpooHom mo moonpoz .Hopoz cofimmopwom ommpm oza esp mo owmpm pcooom swam mgo>0H£omuhonc3 II D H O mpo>oazomuho>o Am>-e4 ll m ll Selecting Under- and Over- Achievers. Normal Achievers; 0 = Over-Achievers; U = Under- Achievers. Regression Line l8 Hypotheses Five research hypotheses are investigated in this study. These hypotheses are as follows: Research Hypothesis I: The method of selecting over- and under—achievers designated by Krug will yield different individ- uals from those selected by the two stage regres-' sion model. Research Hypothesis II: The Human Trait Inventory contains items which will differentiate between under- and over-achieving students defined by Krug's technique. Research Hypothesis III: The items found to discriminate between under- and over-achievers will be dependent upon the operational definition of under- and over-achievement used. Research Hypothesis IV: Factor analysis of item intercorrelations will yield interpretable factors which will meet Thurston's criteria for a simple structure. Research Hypothesis V: Conceptionally, empirically extracted factors will differ between Krug's and Farquhar's operational- izing procedures. Item Analysis Procedure Chi-square tests of significance were used to select those HTI items which discriminated between under- and l9 over—achievers for both the validation and cross-validation samples. The response continuum of the HTI (never, sometimes, usually, always) was dichotomized to facilitate item analy— sis. Items were then directionally keyed. Items keyed in the direction of alternatives assumed to characterize the over-achiever became "l" and the under-achiever response became "O." Frequencies for every reSponse were obtained and entered into a 2 x 2 contingency table to determine the chi-square values.1 The level of significance was set by Farquhar and his associates at .20 (two-tail test) for validation of the items, and .10 for cross—validation (one-tail test). Those personality items which differentiated between under- and over-achievers at the .20 level of significance were used in validation in order to insure the selection of those items that discriminate. The level (.10) was used in cross- validation of those items in order to minimize the acceptance of items when they should have been rejected. Items which discriminated in the same direction, and met the signifi- cance levels established for both the validation and cross- validation groups were selected for use in the personality instrument. 1This analysis was accomplished by a high speed elec— tronic computer (MISTIC) at Michigan State University, by punching the observed frequencies for the chi-square on computer tape and analyzing it with the K6M program. 2O Factor Analytic Procedures Prior to factor analysis it was necessary to construct two inter-item correlation matricies (one for eachsex). The entire sample of each sex was used in constructing their reapective response matrix. When the over- and under— achieving males from both the validation and cross-validation groups were combined with their responses ("1" or "0") to the 23 items, a 23 x 142 matrix (23 items and 142 individuals) was formed. A similar procedure was followed for females, and produced a 16 x 138 matrix (16 items and 138 individuals). Cattell defends the use of the product-moment coeffici- ent by stating, Neither the product moment nor the principles of factor analysis assume or require a normal distri- bution. . . . As Thurstone points out (126), the nature of the factors . . . is remarkably immune to distorted distributions or crude coefficients.l These matricies were placed on a high speed computer and item intercorrelations computed.2 The correlation matricies were then analyzed by the Principal Axis Factor Extraction and Quartimax Rotation method. The principal axis method of factor analysis was used because it extracts all of the variance presented by a matrix of intercorrelations,3 whereas other methods leave residual 4 variance. 1Raymond B. Cattell, Factor Analysis (New York: Harper Brothers, 1952), pp. 238. 2This analysis was accomplished on a high Speed com- puter (MISTIC at Michigan State University, the K-11 program. 3Catte11, pp. cit., pp. 129—149. ”Ibid. 2l Assumptions The mathematics of the principal axis solution in- volves the assumption that the total variance demonstrated by the intercorrelations can be divided into independent sets.1 These independent sets of variance represent the number of factors necessary to account for a matrix of in- tercdrrelations.2 It is not required that either the cor- relations or the population from which these correlations are extracted be normally distributed. Rotation of the Factors The purpose of rotating factors is to arrive at a simple structure which Thurstone has said is the most widely practicable criterion for finding a uniquely mean— ingful position.3 Cattell states that: According to this axiom if we have several alterna— tive hypotheses, each fitting equally the given facts, we should decide among them by taking that which is the simplest, i.e., that which requires fewest conditions and least bolstering by supple- mentary hypothesis. .In terms of factor analysis, Thurstone argued, this means that any one test (in this case any one item) should have the simplest possible factor constitu- tion. . . . This means in terms of the factor matrix that every test (item) should have some zeros in it, i.e., that some factors should not load-it and that every factor should have some zeros in its column, i.e., that not all test (items) should be affected .by it. 1Ibid., p. 39. 2Ibid., pp. 129—149. 3Ibid., p. 67, citing L. L. Thurstone. 22 In a factor analytic solution rotated to simple structure there is actually a double application of the simplicity or parsimony principle. First we have represented many variables by a few common factors and secondly we have distributed these factors to giye the simplest explanation for that number of factors. Neuhaus and Wrigley devised the quartimax method of rotation in order to achieve the desired orthogonal simple structure.2 The selection of a method of rotation is sub- jective and will vary with the biases of the researcher. However, the quartimax method of rotation does seem to meet Thurstone's criteria and was used here. Summary Farquhar‘s Human Trait Inventory consisted of 125 personality items which had previously been shown to dis- criminate between under- and over—achieving students. This instrument was administered by Farquhar to 4,200 eleventh grade students. In this thesis a sample of male and female over- and under-achievers was randomly selected from the 4,200 eleventh grade students. The sample was then randomly divided into validation and cross-validation groups for each sex. Items were selected that discriminated between male and female under- and over-achievers after cross-validation. Twenty-three male and sixteen female items found to be most discriminating were factor analyzed by the principle axis method, and rotated in an attempt to isolate the personality factors of discrepant achievers. lIbid.,epp. 67-68. 2J. 0. Neuhaus and Charles Wrigley, "The Quartimax Method, An Analytical Approach to Orthogonal Simple Structure,‘ British Journal of Statistical Psychology, Vol 7 (1954), pp. 89-91. I CHAPTER III ANALYSIS OF DATA In this chapter an analysis and interpretation of the data are made. Item Analysis Results Criterion for Selection In order to diminish the probability of items being selected by chance, validation and cross-validation groups were established within each sex. To meet the criterion established, the items must: (1) discriminate between over- and under-achievers in the validation group at the .20 level of significance; (2) discriminate between over- and under- achievers in the cross-validation group at the .10 level of significance; and (3) items must discriminate in the same direction within both the validation and cross-validation groups. The following null hypothesis was tested: Null Hypothesis I: There is no significant difference in the proportion of choice alter— natives for under- and over-achievers. 23 24 Item Analysis Results From the original items, 16 of the female and 27 of the male items met the criterion for selection. 0f the items found to discriminate between under- and over-achievers, eight were common to both sexes. Reliability Estimates Hoyt's method of reliability was used to determine the internal consistency of the 16 female and 23 male factored items.l Estimates of the reliability for the under-achievers, over-achievers, a combined over and under sample, a random sample of the general population, and a sample of normals for each sex are presented in Table 3.1. The reliability of the 23 male factored items was then projected to give an estimate of reliability of the entire 27 item scale.2 The estimates are dependent upon the number of items in the scale. The uncorrected reliability estimates range between .57 and .71 and thus have a reliability of less than .80. It should be noted that the combined group reliabili— ties are most relevant to the factor analytic process. This is because both the validation and cross-validation groups were combined for factor analysis. As would be expected, leril J. Hoyt, "Test Reliability Estimated by Analysis of Variance," Psychometrika, Vol. 6 (1941), pp. 153—160. 2J. P. Guilford, Fundamental Statistics in Psychology and Education (New York: McGraw-Hill Book Company, 1956), p. 452. 25 because of the smaller number of items, the combined over- and under-achieving female reliabilities are lower than those of the combined males. TABLE 3.1 RELIABILITY ESTIMATES OF THE FACTORED ITEMS AND TOTAL SCALE Reliability Estimates Males N Factored Items Total Scale8 (23) (27) Generalb 66 .71 .74 Over 70 .64 .69 Under 72 .64 .69 NormalsC 50 .69 .72 Combined Over- Under-achievers 142 .70 .74 Factored Items Total Scale Females N (16) (16) Generalb 66 .62 .62 Over 72 .60 .60 Under 66 .59 .59 NormalsC 50 .60 .60 Combined Over- Under-achievers 138 .64 .64 aSpearman-Brown Formula. b Random sample from total population of 4200. 0Over- and under-achievers excluded, random sample from general pOpulation. Validity estimates were determined by correlating the total HTI score derived by Krug's method with grade point average for 200 male and 200 females separately. These CO- efficients were .35 for males and .46 for females, and 26 though low, are significantly different from zero at the .01 level of significance. Factor Analysis Results The item intercorrelations for the most discriminating items for each sex are shown in Tables 3.2 and 3.3. These intercorrelations were factor analyzed to determine if they would yield interpretable factors. The principal axis method normally extracts as many factors as there are items or variables. Thus the HTI (male) produced 23 factors and the HTI (female) 16. However, to be considered a factor the sum of the squares (eigen values) had to exceed 1.00. Seven male and five female factors sat- isfied this criterion. The rounded, unrotated loadings for those factors at or near 1.00 for male and female over- and under-achievers are presented in Tables 3.4 and 3.5. A further criterion was added demanding that each factor have at least two items loading highest on it across rows. If the criterion was not met, the factor was consid- ered uninterpretable. The factor was then drOpped, and another quartimax rotation performed. This was continued until there remained six male and five female factors which met the criterion of having eigen values (sum of squares) of 1.00 or greater, and at least two items loading highest on it across the rows. This required that the male and the female factors be rotated once. 27 TABLE 3.2 ITEM INTERCORRELATIONS OF TWENTY-THREE THE HUMAN TRAIT INVENTORY SCALE.* VALUES ARE POSITIVE UNLESS 11 16 27 37 44 5O 54 56 6O 62 63 11 1.00 02 33 10 16 -08 O2 1 20 -0 ll 16 1.00 06 18 l3 14 29 2 l3 0 l3 27 1.00 07 10 -08 2O O3 16 09 24 37 1.00 14 23 46 21 04 32 24 44 1.00 02 l6 13 20 23 08 50 1.00 26 lo 05 l3 16 54 1.00 18 28 37 32 56 1.00 14 ll 13 60 1.00 15 08 62 1.00 22 63 1.00 66 68 70 74 75 76 77 89 101 113 122 124 *Item numbers correspond to the numbers of the items on 28 MALE ITEMS USED IN FACTOR ANALYSIS OF (DECIMALS ARE OMITTED AND THE OTHERWISE INDICATED.) 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