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Factorial invariance and the construct validity of a school related self-concept measure

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Factorial invariance and the construct validity of a school related self-concept measure

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Content FACTORIAL INVARIANCE AND THE CONSTRUCT VALIDITY OF A SCHOOL RELATED SELF-CONCEPT MEASURE by Michael James Wilson A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (Education) June 1983 UMI Number: DP24958 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. Dissertation Publishing UMI DP24958 Published by ProQuest LLC (2014). Copyright in the Dissertation held by the Author. Microform Edition © ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code ProQuest' ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106- 1346 UNIVERSITY OF SOUTHERN CALIFORNIA T H E G R A D U A T E S C H O O L U N IV E R S IT Y P A R K LO S A N G E L E S , C A L IF O R N IA 9 0 0 0 7 This dissertationy written by Michael .James. Wilson under the direction of h..Ls . . . Dissertation Com mittee, and approved by all its members, has been presented to and accepted by The Graduate School, in partial fulfillment of requirements of the degree of D O C T O R O F P H IL O S O P H Y Dean Date. DISSERTATION COMMITTEE Chairman ABSTRACT The self-concept literature does not indicate whether black or white students exhibit higher levels of self-con cept, a number of investigations present conflicting re- jsults. It is possible that the direction of the difference | |has been unclear because of a lack of invariant response l I pattern in cross-racial self-concept measurement. In order to investigate a possible relationship bet- i ! ween level differences and construct invariance, a measure | i fof academic self-concept was developed along dimensions in !which previous research has indicated that blacks and i i iwhites have consistently shown level differences. The. I * I I method used in this study of invariance was factor analy- i I | sis. i j Previous studies have used exploratory factor analy sis, which is subject to indeterminacy problems, as well as i I limited potential for precision in the comparison of multi- ! pie group response structures. Simultaneous confirmatory factor analysis was used to compensate for these difficul ties. Besides being able to analyze two or more groups* iresponse patterns simultaneously, it also provided compara- tive tests of separate factor parameters and a likelihood ratio of fit between the original and the estimated factor j matrices, i The analysis of factor invariance was conducted on the responses of 351 Southern California junior high school students, 171 black and 180 white. The academic self-con- i i cept insturment contained five dimensions: Expectation/As- I piration, Locus of Control, System Blame, Anger/Aggression and Anxiety, i ; The results did not support the hypothesis that mean !level differences would be associated with structural dif-! ! \ i I | ferences, which, in turn, would have suggested a partial i I explanation for mean level inconsistency of cross-racial ! ! I I ! self-concept measurement, j ACKNOWLEDGEMENTS I would like to thank, first, my wife, Cathy, who per- servered through many hours without a husband, second, my children,Joshua and Megan, who loved me throughout my ab sence, third, my stepfather, John, who spent several hours i (editing, and finally the members of my committee, Doctors I and Cliff, who patiently guided me through i process, j Smith, Benson this learning iv CONTENTS ABSTRACT ...... ............................... ii ACKNOWLEDGEMENTS.................................. iv Chapter _P_age, I. INTRODUCTION ................... 1 Problem . .................................. 5 Purpose.................................... 6 Research Questions .................................. 6 Importance ............................................ 6 Organization of the Remainder of the Study . . . 8 II. LITERATURE REVIEW ........................................9 Studies Investigating Black/White Differences . 9 I Level Differences ................................ 9 Structural differences ...................... 12 Theoretical Dimensions of Black/White Level Differences...................................13 Expectation/Aspiration ...................... 14 -'■Locus of Control................. 17 System Blame .................................. 20 Anger/Aggression................... 22 Anxiety ..... ............................. 25 Relation of Dimensions to S E S ....................27 Confirmatory Factor Analysis , . ............... 32 III. METHODOLOGY ............................................ 34 Subjects...............................................34 Instrumentation ...... ................... 35' Procedure................. 38 Hypothesis........................ 39 Reliability..........................................40 Model Tested and Data Analysis....................41 Hypothetical model ........................... 42 L I S R E L ......................................... 44 Data analysis................... 49 invalidity and b i a s .........................49 v research question .......... 51 IV. FINDINGS AND DISCUSSION.................................55 Findings .......................... 55 Discussion............................................ 61 V. SUMMARY, CONCLUSIONS AND RECOMMENDATIONS .... 69 Summary ...... .......... 69 Purpose............................................ 69 M e t h o d ............................................ 69 sample..........................................69 statistical analysis ...................... 70 measurement...................................70 Findings..........................................70 Conclusions . . . . . . . ................. . 71 Limitations................... 71 ! Recommendations.................................. . 73 i j | REFERENCE ................................................ . 74 i I Appendix page A. ACADEMIC SELF CONCEPT INVENTORY .................... 81 'B. ITEMS USED IN HYPOTHETICAL FOUR FACTOR MODEL . . 84 LIST OF TABLES Table page 1. Reliability of Scales by Group and Dimension . . . 41 2. Organization of Hypothetical M o d e l ............... . 44 i i (3. Fit Indicies for Single Group Analyses ............. 56 (4. Standardized Factor Loadings by Group and Scale . . 57 5. Fit Indicies for Four Group Simultaneous Analyses . 59 ,6. Fit Indicies of Comparative Analyses to Detect Non- Invariance ............................. 61 t Chapter I INTRODUCTION Self-concept is a broadly defined construct which is thought to be multifaceted or multidimensional (Shavelson, Hubner & Stanton, 1976; Wylie, 1979). This suggests that jwhen the concept is measured, the measurement should con- jsist of separate dimensions. Of particular interest is the dimension of school related self concept and its relation I | to academic achievement (Tyler,1972). Bloom referred to this dimension of self concept as a !,student!s reporting ! .'something about himself in relation to learning, the school I and teacher and how he views his learning i ithe learning of of others." (1976, p.96) i The measurement of school related self ject to most of the difficulties inherent ment of self-concept. The major concern is ! the measurement. Shavelson et al.( 1976) I jlittle construct validation has been conducted in the area i jof academic self-concept. Self-concept studies have been conducted for generalization and comparison of self-concept without first establishing the foundation of an adequate in relation to concept is sub in any measure- the validity of noted that too 1 validation of the construct. Shavelson et al. recommended that construct validation studies be conducted so that re search on the utility of self-concept would be based on valid constructs. A major issue of construct validation is the compari son of constructs across different groups. An instruments constructs are the basis of interpretation of measurement j results. If the hypothesized structure does not apply to all groups, then neither the construct validity nor the in- l jterpretation would be consistent across all the groups. | i i * t I The construct of a self-concept instrument is embodied in : i I (theory; to the extent that the theory is not supported by! the observed response structure, it is invalid. J i In one particular area, the measurement of self-con-i t cept across groups of black and white school children, the ! !results are contradictory. Analysis of a number of studies I ! |does not portray a clear picture of blacks or whites res- | : I jponses to the comparability of self-concept measurement, j I i :One possible explanation for the lack of clarity is a dif- j I ference in black and white interpretation of self-conceptj items. Racial differences in interpretation would result! i i in structural differences across groups producing scores' that could not be compared since they would be the result of measurements of different dimensions. Differences in 2 scores would therefore be meaningless. The literature also suggests that these mean level differences are compounded by differences in the socioeconomic status. One possible result of the lack of structural invari- i ance in a measure of self-concept is structural bias. Cole (1980) in a discussion of bias stated that if scores in different groups yield different interrelationships when i •the data is examined, the measure is behaving in a way that ishould not be expected given the construct upon which it t i j jwas based. These differences in the pattern of responses j [across the groups being measured are suggestive of bias. t i Cole suggested factor analysis as a statistical proce- { j ! [dure that can assist in interpreting the meaning of mea- j 4 |surement structure. If the identified factors are in- 'terpretable as hypothesized, they should represent Jtheoretically derived dimensions of the construct. If, j jcounter to expectations, the factor dimensions are not com mon for the different groups, then bias may be present. J Factor analysis, according to Cole (1982), is useful | in observing the differences in the structural relation ships of the data. The most commonly used form of factor analysis is exploratory factor analysis. But exploratory factor analysis is susceptible to two basic problems of in- j i jdeterminacy (Kim & Mueller, 1978): 1) indeterminacy through rotation— given a specified number of factors, it is possi ble to have more than one set of factor loadings depending jon the rotation method used that equally reproduce the cor relation matrix; (2)indeterminacy through number of factors !— by changing the number of factors, the factor structure i |and its theoretical interpretation can change drastically i i jbut be equally as effective in explaining the correlation I Imatrix. In addition, exploratory analysis is a method used j j i |to search for underlying relationships, not to observe the jsuccess of hypothetical constructs but to explain the » ! structure of measured variables. Since construct validity ! I iis dependent on the confirmation of hypothetical relation- j iships, it is appropriate that the method of validating con- j | i i | jstructs tests the hypothesized relationships instead ofi i ! I supplying various structural alternatives. I I | Joreskog (1969) introduced a procedure which could be | employed to investigate hypothesized constructs. The ] i procedure, confirmatory factor analysis, allows the factorj t structure to be specified prior to the statistical analy- ‘ sis. Alternative structures can then be statistically com- | |pared with the use of a chi-square likelihood ratio test of i | fit. As a consequence, this method is capable of investi- i |gating whether an observed factor structure provides in terpretable results across diverse groups.. Shavelson et al. have identified self-concept as a mul tidimensional construct, therefore, it is appropriate to investigate possible differences in the dimensions of the construct. Confirmatory factor analysis appears particu larly well suited to the task of more clearly distinguish ing differences in the dimension of groups1 responses to self-concept measures and providing answers to questions about the construct validity across groups. I 1.1 PROBLEM I ; i i ! There have been a number of studies that have investi- i i 'gated the problem of whether blacks or whites have a higher) i I !self-concept. There is a strong indication that there are! i t )differences, but the direction of the difference has not) | I {been established. This lack of clear direction is a prob- | r j J lem that may be related to a lack of invariance across the j * i tgroups being measured. The problem investigated in the) [ i t present study is whether a lack of invariance across group jstructures might be associated with responses to a school related self-concept measurement in which there are obvious group mean level differences in the responses. 1.2 PURPOSE The purpose of this study was to determine whether the 'responses of four groups of students— -lower SES black, mid dle SES black, lower SES white and middle SES white— to a measure of academic self-concept could be explained by a common factor structure. The hypothesized structure would be invalid for the groups which did not respond with a| structure that supported the measurement1s constructs. The lack of a common structure across -the groups1 response pat- i |tern would be an indication of structural bias. I i I | i1.3 RESEARCH QUESTIONS j Is there a common structural pattern for academic j |self-concept measurement associated with mean level res-, Iponse differences across ethnic and SES status? i 4 I I 1.4 IMPORTANCE 1 ! Research in cross group validity of academic self-con- !cept is important because of what the understanding of aca- \ i Idemic self-concept represents to students, school adminis- i j trators and educational researchers as well as the nature j of the construct itself. First, a student1s self-concept I t is "valued as an educational outcome in its own right” i |(Shavelson et al., 1976 p.408). That is, it is important to attempt to understand and improve a student*s self feel ings in school because a good self-image is an important I [educational goal. Second, according to Bloom (1976), self-concept accounts for up to 25 percent of the variance of general academic achievement when both are measured with valid instruments. Therefore, on a scientific level, mea- I [ J surement of academic self-concept is of importance to the 1 ♦ ' I research community as a variable explaining or predicting ! i | !achievement differences. On a practical level, it is im- i jportant to those responsible for the education of particu- i j lar students. Self-concept is a useful idea but one must j | j j be aware of the context in which it is measured to inter- j i ! |pret its meaning. ! School related self-concept is seldom, if ever, mea- i | sured in populations that are composed of only one group. i !Therefore, the maintenance of construct validity in multi- i I group use of self-concept inventories is of primary con- i Icern. If groups* response level differences are associated jwith response structure differences, it is important to be !aware of the association. If the measure of a construct is not applicable across groups, then using it on the groups' responses would needlessly bias the interpretation. Inval idity and structural bias are, therefore, problems to be aware of and controlled when measuring self-concept. 1 .5 ORGANIZATION OF H I REMAINDER OF TH£ STUDY A brief review of the research comparing black and jwhite school children on levels of self-concept is present ed at the beginning of Chapter II. The only study found that compared the more general area of self-esteem as a construct across black and white students is reviewed. The Weaknesses of the study are discussed and changes are pro- i !posed that would improve the comparison of factor struc- I ! jtures. The remaining portion of the chapter is a review of ! jthe racial comparative literature which indicated the areas |of difference between the lower and middle SES black and ! White students. This last section is organized to coincide with the dimensions that were interpreted into the the aca- jdemic self-concept measuring instrument used in the present! jresearch. In Chapter III, information pertaining to the i imethods and procedures that were followed is presented. !The measure, its development and the sample obtained are i jdescribed. Then steps in the analysis are described se quentially, and their nature explained and justified, jChapter IV presents the empirical findings and a discussion !of the success of the analysis and possible bias in the in- i i strument are presented. Chapter V is a short summary of the investigation, its major conclusions, limitations and recommendations. Chapter II LITERATURE REVIEW 2.1 STUDIES INVESTIGATING BLACK/WHITE DIFFERENCES 2.1.1 Level Differences A number of studies comparing black and white school children on self-concept were reviewed. The review did not !show consistent results. One group of studies found lower I [self concept among blacks than among whites (Wy lie ,1963;McDonald & Gynther, 1965; Long & Henderson, 1968; I jHauser, 1971; Samuels, 1973; Osborne & LeGette, 1982) *another set of studies found no difference between the self i ] |concept of blacks and whites (Rosenberg, 1964; Henderson, Goffeney & Butler, 1969; Hodgkins & Stakenas, 1969; White & Richmond, 1970; Davids, 1973; Calhoun, Kurfiss & War ren,1976; Kuhlman & Bieliauskas, 1976; Cicirelli, 1977), and a third set of studies found that black students had higher self concept than white students (Soares & Soares, i J1966; Baughman & Dahlstrom, 1968; Hartnagel, 1970; Baugh man, 1971; Rosenberg & Simons, 1971; Dales & Keller, 1972; Greenberg, 1972; Trowbridge & Trowbridge, 1972; Hurtsfeld, 1978) In the above studies, the Piers Harris self-concept i t I 9 measure was used twice, one of the studies reported that the white students were higher and one that the black stu dents were higher. The Coopersmith was used five times, two of the studies reported that the white students were higher, one that the black students were higher and two re ported no difference. In six of the studies, self-concept , i measuring devices were used that had been used in previous j studies. The six measures were the Carolina Picture Ser- ! I ies, Tennessee Self Concept Scale, Bill!s Index of Adjust ment and Values, the Purdue Self-Concept Scale, the Draw a 'Person Test and the Measure of Self and Ideal Self. In the ! t 4 I six studies there were four non-significant differences re- i I I ported and two in which the black students were reported j I with higher self-concept. In thirteen of the studies, j I f * !self-concept measuring instruments were used that were ori- t i [ginal to the study. In these studies, four reported that white students were higher, five reported the black stu- i jdents higher and four reported that there were no signifi- j *cant difference between the black and white student's! t self-concepts. Eleven of the above studies were conducted j on elementary students and fifteen on junior high through J college students. Of the elementary student studies five j jshowed the white students higher, three showed the blackj [students higher and three showed no difference. Of the I ! i i i 10 junior high through college studies, four of the studies showed the white students to be higher, six showed the black students higher and five showed no difference between the two groups in self concept. Among the measurements used in the studies, 23 of the instruments contained one or more school related dimensions. The mixed results in the preceding studies could be attributed to any number of problems. Because most of the jstudies mentioned above contained evidence of differences (between black and white children in self-concept, it is | 'possible to argue for a difference in the level of self- j I concept between the two races. However, there is a nearly leven division between studies with higher black and and i i |those with higher white self-concept. One possible exlana- i I J I 1 (tion for the apparent confusion with respect to which group !is higher is a lack of common structure across groups. A i i i lack of a common structure of the response pattern, of i (course, would make interpretation and comparison of the Imultigroup responses to self-concept instruments impossi- I ible. 2.1.2 Structural differences Burbach and Bridgeman (1976) found structural differ ences between black and white students using exploratory factor analysis. In their research, the Coopersmith Self Esteem Inventory (CSEI) was administered to a group of fifth grade black and white students. The authors then factor analyzed the results and obtained a five factor so lution for black subjects and a six factor solution for the Iwhite students based on a scree test of an initial princi pal components solution. The black students responded along the dimensions of good and bad, caring and not car ing, success and failure. The structure of the white popu lation responses agreed with the measure's hypothesized di mensions of home, school and peer relations. The analysis ! I j I ; indicated a lack of a common response pattern to the CSEI j ; by the two groups. The authors concluded that black stu- j 'dents did indeed respond with a different pattern than did j | I jwhite students and therefore a single interpretation of the | j | jmeasurement outcome did not adequately explain the respons- ! jes of the two groups. J i i The Burbach and Bridgeman data analysis, however, was j subject to the problems inherent in the use of exploratory factor analysis, indeterminacy of factor number and factor interpretation, discussed in the first chapter. As sug 12 gested, confirmatory factor analysis developed by Joreskog (1969) is capable of investigating the identified problem. 12.2 THEORETICAL DIMENSIONS OF BLACK/WHITE LEVEL DIFFERENCES In a confirmatory factor analysis, the number of fac tors and the dimensional relationships between factors and j i ! jitems can be prespecified. Since the problem dealt with in [this study is to determine whether level differences might j be associated with dimensional differences, the dimensions in which level differences occur must be specifically deli- neated. The following pages contain a review of black- j 1 iwhite comparative literature that provides suggestions of I [areas in which blacks and whites in lower and middle socio- j I- I -economic status (SES) exhibit level differences. There! r I I j jwere five dimensions that were reviewed because the litera- j jture evinced significant differences in these areas: Expec- j | tation/Aspiration, Locus of Control, System Blame, Anger/ j 1 l (Aggression and Anxiety. \ i I Much of the present review of the literature contains j 'studies that deal with adults instead of children. The re- I j porting of these findings was deemed reasonable on the ba sis of the information provided by Langner and Michael. According to Langner and Michael (1963), the parents1 child rearing techniques which vary with socio-economics status, 13 affect the development of the children's sense of individu ality and identity. Their investigations indicated that parental feelings of self transfer to the child as the jchild identifies with parent so that childrenfs general self concept closely matches their parents1 self-concept. i i j t I t 12.2.1 Expectation/Aspiration ! | i The first of the five dimensions was labeled Expecta- { i I I tion/Aspiration. According to Baughman (1971), blacks ex- j i i Iperience lower levels of Expectation/Aspiration because |their goal oriented behavior is often frustrated by race loriented restrictions. Baughman noted that the same level j ! i [of frustration is not experienced by white youngsters. Be- I i !low are several studies that support Baughman1s ideas about ' i 'expectation and apiration. ! ; i i j | Rosen (1959) was interested in the degree of differ- ! i I ence in maternal aspiration for offspring across races. He | i stated that | I "Negroes who might be expected to share prevalent Am erican emphasis upon education face the painfully ap parent fact that positions open to educated Negroes i i are scarce. This fact means that most Negroes, in all liklihood, do not consider high educational aspiration realistic" (p. 123). 14 Rosen noted that a result of lower aspiration was a higher drop out rate from high school for blacks in comparison to the white population. He asked mothers to rank vocations then indicate which vocations and educational levels were i Jacceptable. Black mothers accepted occupations signifi cantly lower than the white groups that were studied. But these same mothers wanted just as high or higher education al levels for their children as any of the other groups. ' Connors (1965) investigated the occupational interest i !of black and white adolescent boys that lived in Washington i ;D.C.. The two groups were matched on three variables: in- i i I jtelligence, age, and socio-economic level. The instruments j used were the Geist Picture Interest Inventory and a ques- f jtionnaire that elicited occupational aspirations and expec-) itation. There was no difference in job aspiration between; ! i | the two races. However, the blacks were lower than whites I I j in job expectations. | Wylie and Hutchins (1969) looked into the influence of ;cultural learning on self-concept and aspiration. Questi- I onnaire data were received from a sample population of 4,245 students in grades seven through twelve in three jtowns in Pennsylvania and Illinois. The questions that ! 'were asked included self perception of school ability, in- i * jtelligence, desire to attend college, plans to attend col- I 15 lege, friends’ attitudes to trying hard and career aspira- [tions. The results indicated that effort for high grades I jwas higher for whites than for black high school students. Hurley’s (1973) study found a relation between race and occupational aspiration. He studied a sample of 182 black and white tenth through twelfth grade students in t (four urban areas of New York state. He expected to find a relationship between membership in a nuclear or fatherless family and a number of other variables. The instruments i jused were the New York University Study of Occupational !Scale for rating socio-economic status, a Work Values In- iventory, and the Semantic Differential for Self-Esteem. jThe findings showed a significant (p<.05) relationship bet- ! 'ween race and the (a) level of occupational aspiration, (b) i disparity between level of occupational aspiration and oc- i cupational expectation and (c) aspiration to and expecta tion of professional occupations. I ; Brown (1974) investigated the influence of racial group membership on occupational aspiration, educational intention, and occupational interest. He used a sample of 163 male eleventh grade students in an eastern U.S. city. I jThe instruments administered were the Hollingshead Two Fac tor Index of Social Position, Educational Planning Questi- 1 jonnaire of the National Educational Development Tests, and 16 the Kuder Occupational Interest Survey. The results indi cated that occupational aspiration and educational inten tions were significantly affected by racial group member ship, It also indicated that white male adolescents had significantly higher occupational aspirations and educa tional intentions than black male adolescents. In all of the studies above, blacks were consistently i (different than whites in expectation though not in the lev- ! { - | | el of aspiration. An Expectation/Aspiration dimension; would measure the students views of the foreseeable future. | An Expectation/Aspiration dimension is distinct from the i (following Locus of Control dimension. Expectation/Aspira- j i ( 1tion is related to feelings of desire and control over fu- j * t I ;ture occupational and life style choices, whereas Locus of; I jControl relates to feelings of control over the immediate land real environment. } I ! f I 2.2.2 Locus of Control i Gordon (1977) has stated that the black child runs jinto difficulty when he is forced to confront and deal with white societyfs opinion of blacks. This is the point at which the young black child realizes there is racial dis crimination, segregation and other forms of overt and co vert racial prejudice. Because the prejudice is based on 17 something over which he has no control, the black child be gins to develop a general sense of lack of control. Gordon felt that this feeling of lack of control is a major dif ference between the black and the white individual. A num ber of research studies have been completed that confirm this point of view. Coleman (1966) reported in his Equality of Educational ! I Opportunity study that blacks expressed a much lower sense i ! , j !of control over the environment than did white children in' ( i his sample. j i Jacobsen (1975) investigated locus of control cross | racially using Rotter!s Introversion-Extroversion Scale, j Jacobsen*s sample included 36 black and 91 white North Ca- ' i rolina high school students. The blacks scored signifi- J i ; ]cantly more externally than did the whites in the study. j Gurin and Epps (1975) hypothesized that locus of con- jtrol was composed of three dimensions: (1) control ideolo- i gy, (2) a sense of personal control and (3) the extent to i social | i Gurin dimen- white scores Howev- which the individual blames either himself or the system for whatever lack of control that he feels, and Epps designed an instrument with the above three sions and administered the instrument to black and elementary school children. They noted that black were like white scores on the the first dimension. er, the black scores were lower than the white scores on the second and third dimensions. That is, they had a lower sense of control, as well as, a higher level of blame of the society for the lower feelings of control. Gurin and Epps concluded that obstacles experienced by blacks, e.g. j racial discrimination, operate systematically and reliably. jThey also felt that black feelings of external control are irelated not to a passive belief in chance or fate but in- Jstead in an active use of blame of the socio-econmic system jto which the blacks could attribute the cause of their lack jof upward economic or social mobility. ! ! i i All of the above studies agreed that black locus of f i ! |control is more external than that of the white population, j iLocus of control indicates a persons feelings of ability to : ! * jchange and shape his own environment. The last articlej |suggested a connection between locus of control, expecta- : ition/aspiration and system blame which is the next dimen-! j 1 sion discussed in this chapter. The Locus of Control di mension measures feelings of the individual in relation to authority and its representatives. 2.2.3 System Blame It has been theorized by several people (Baughman, 1971 & Yancy and McCarthy, 1972) as well as Gurin and Epps in the previously cited study, that blacks use system blame to defend against perceived attacks on his self esteem. The system blame mechanism refers to a blaming of the soci o-economic system and whites, whom blacks associate with l * the system for their poor performance. Poor grades, low j i i jlevels of school acievement or low levels of vocational at- i t jtainment are some of the problems that blacks blame on the Iwhite controlled socio-economic system. Baughman theorized * 1 1 (that when the black child discovers that he does not mea- I ! ' I (sure up well in interactions with whites, psychologically! 1 | :he can move in one of two directions. He can view his ex- | I perience as evidence that he is in fact less adequate thanj I he had been led to believe, or he can blame the system for j I I {having discriminated against him by providing him with in ferior preparation. The black has the choice in other words of looking inward and finding that he is insufficient j or he can look outward and find the inadequacy in the so ciety. Baughman felt that the black choses the second path more often than the first because there is ample evidence to support that choice, that is, the system does discrimi nate against black people, and blacks have been encouraged 20 to find external blame by influential voices of many promi nent blacks and whites alike. Wendland (1967) investigated expressions of cynicism by black and white children. He found that black children tended to be more cynical and blame the socio-economic sys tem for their problem more than did the white children Wendland conducted his study on 685 black and white junior high school students. The students came from one large and one small town in North Carolina. The children were all! * t administered the Tennessee Self Concept Scale and a measure of their feelings of estrangement from and degree of cyni- t j cism toward the social environment. In addition, each sub ject filled a questionnaire to provide personal information about himself and his family. Special precautions were taken to ensure that limitations in a child’s reading abil ity did not invalidate responses to any of the three sca les. The differences on the Tennessee Self-Concept Scale indicated that the white children were more inclined to find fault with themselves. The black children found fault with their environment rather than seeing academic defi ciencies in themselves. Pierce-Jones, Reid and King (1959) investigated criti cal orientation toward society in black and white adoles cents. The sample was randomly selected from a population 21 of approximately 1600 seventh grade pupils involved in the Human Talent Research Project at the University of Texas. All subjects were administered the Texas Cooperative Youth Study Scales. Critical orientation to society and criti cism of education were measured. The authors found that blacks had the most critical orientations in comparison to the other two groups. System blame appears to be two things. It is a useful ! ;defense mechanism, as well as an often realistic portrayal i | of a society that first made blacks slaves, then second class citizens, segregated them and made it generally dif ficult to achieve social and economic parity with the domi- I nant white race. The next dimension reviewed, Anger/Ag- i Egression, is also in reaction to social and economic reality. But instead of being a defending mechanism, it is jan emotional response to the social and economic disparity ! between whites and blacks. 2.2.4 Ang er/AEgression Grier and Cobbs (1968) theorized that because of cen- i jturies of physical and psychological abuse, blacks have de veloped feelings of anger toward white society. Physical- i ly, the blacks have been slaves then second class citizens relegated to the poorest parts of municipal and agricultur- al areas. Psychologically, the blacks have been told they are inferior intellectually and developmentally. According to Grier and Cobbs theory, angry feelings are manifested in feelings of rage that are directed towards the white, race and white dominated institutions. Grier and Cobb asserted that anger and its overt manifestation, aggressiveness, (have contributed to a proportionately greater incidence of I .violence being committed by members of the black than the i I iwhite race. They suggested that the black militant move- \ I ! jment is a manifestation of the huge amount of anger con- ( ! ;tained in blacks. The following studies support the theory; i i ideveloped by Grier and Cobbs. ; i I j In 1953, Hammer investigated feelings of aggression in j school children. He collected data from 400 semi-rural and ; ; I semi-urban elementary school children from Virginia. Each j i ! ! child was asked to make three drawings, one of a house, a ; i < jtree, and a person. Then, with the aid of six independent! i | iclinicians, the drawings were evaluated for their degree of! I laggression without the knowledge of which drawings were j i done by black or white children. The black children re ceived a significantly (p<.05) higher agression rating than did the white children, Lefton (1968) in a study of black and white anger to ward the social system sampled 155 autoworkers. Of the sample, 83 were white and 72 were black. The black sample scored significantly higher on frustration and anger than did the white sample. Karon (1978) compared black and white responses to the Tomkins-Horn Picture Arrangement Test. A sample of 150 respondents was randomly selected from across the United i States. Among other things, Karon found that blacks have a jhigher general aggressive press than do whites and a higher Igeneral need to use aggression whether in a delayed or ne- •gative manner than do whites. The first finding indicated | to Karon that blacks are more likely to feel that people are angry at him and that they are going out of their way ! to make trouble for him. This feeling is a justification jto feel angry towards others. The second finding suggested J to Karon that blacks have a greater need than whites to t Jreact to aggression by being aggressive. He explained that i these feelings of aggression are a result of a higher level iof fear and anger at being aggressed against. I i The above articles indicate that within the black i |psyche there exists a higher level of anger and need to ex- 'hibit aggression than exists in the white population. This i ! anger according to Grier and Cobbs is the result of a his- j ! tory of social injustice in the United States that has its I jroots in white instituted slavery. The following dimen 24 sion, Anxiety, is based on reaction to many of the same pressures associated with anger and aggression, the domina tion of white society. But while anger and aggression are overt and demonstrative attitudes, anxiety is usually in ward and kept to ones1 self. I I (2.2.5 Anxiety l \ I Baughman (1968) hypothesized in his study of the black I f ! psyche that black children perceive their environment as a i I Imuch more threatening place than do white children. Baugh- i (man suggested that the more a person perceives an environ- i I ; ment as threatening, the more the person will be anxious I ; i j when in that environment. The following investigations !confirm the above hypothesis. j Convey and West (1979) hypothesized a higher level of; * j academic anxiety and fear of failure in blacks than in whites. The investigation developed the Academic Pressures j Scale for Adolescents (APSA) to measure stress, pressure or !anxiety felt by adolescents in the inner city environment. I i i jThe subjects were 179 black and white adolescents from in- I i ner city schools. The results of the analysis suggested I blacks experienced significantly (p<.01) higher levels of i j pressure to succeed in school and fear of failure in I |school. Generally, in all the scales of APSA, blacks re- j jported higher levels of stress, pressure and anxiety. 25 Clawson, Firment and Trower (1981) investigated the possible differences and their implication in the compari son of anxiety levels in black and white students. The in vestigators studied 150 ninth and 112 seventh grade stu dents from Northeastern Florida, 23 percent were black. The students all took the Test Attitude Inventory (TAI) which measured level of emotionality and cognitive con- i cerns. The two subscores added together produced the ove- | i rail test anxiety of the respondents. Among other things, ! ! i |the results indicated that the black students were signifi- 1 |cantly more anxious on all of the scores in the TAI, an ^analysis of the data also suggested that the black respon- j ; i !dents had higher test anxiety. ! The anxiety described here is a reaction of individu als to instances in a school routine when he or she is most vulnerable to failure. Anxiety is similar to system blame in that they are both reactions to points of injury to the self-concept. Anxiety is generalized fear or discomfort in response to a stimulus, whereas, system blame is used to cover up or avoid feelings of failure or inadequacy con nected with an event or series of events. The levels of the above dimensions affected by race are also subject to the effects of socio-economic status (SES). Wylie suggested that the effects of race were com 26 pounded by the effects of SES in the comparison of blacks and whites A review of the literature also supports the no tion of the complicity of the effects of race and SES on self-concept. The following section contains a review of the effect of SES to the identified dimensions with mean level racial differences, 2.3 RELATION OF DIMENSIONS TO SES Boocock (1972) has noted that school related attitudes {are affected by racial differences which are in turn relat- : l ; |ed to SES differences. Kohn and Schooler (1969) reported a* ! ' i isignificant but low correlation of .19 (p<,01) between j socio-economic status and self-esteem. Coleman (1966) ' i |found that school related self-feelings closely divide I j I jalong racial boundaries. The above statements lend support, j ' to supposition that many of the manifestations of differ-! i ! ■ i i ences in black and white attitude are related to a general- 1 i j ly lower black socio-economic status. i External locus of control may be an effect of low SES j as indicated by the following theory. Langner and Michael | ( 1963), Kohn (1963) and Pearlen and Kohn (1966) have all! hypothesized that parents from different socio-economic :levels hold different values for themselves and their chil- |dren. Kohn (1963) proposed that self direction and self 27 control are valued by middle class parents whereas lower SES parents are more concerned with conformity to external rules and standards with much less concern for the internal feelings of their children than is found in the middle I class parent. Wylie (1979) hypothesized that the members of the low est socio-economic levels have stronger reasons to blame the socio-economic system for their problems. Because of 1lower acceptable standards of behavior by social institu- I i ;tions such as school, lower SES individuals do more poorly ; i land consequently have lower self evaluations. With regard I I I t |to Aspiration/Expectation, Kremnitzer (1973) investigated! ! I the relationship of personal, sociological and demographic | I [Characteristics to anticipated mobility of 465 black and | i 'white young men and women. Anticipated mobility was de- j ! ■ fined by Kremnitzer as deviation from the expected occupa- I ! i Ition of a primary wage earner on the Hamburger scale. Data j i j |on occupational status, race, sex, grade in school and oth- ! i i jer characteristics were collected by a self-reporting re- J j I search questionnaire devised by the investigator. It was j found that while race did not successfully predict antici- I I i ipated occupational status, SES level did. | In relation to locus of control, Gruen, Kort and Baum :(1974) were interested in the variation of the locus of * I 28 control among different SES levels of several racial groups. The investigators used the Stephans Internal-Ex ternal Scale, a measure of locus of control with 1,100 sec ond, fourth and sixth grade children. There were 155 chil dren classified as affluent. The rest of the children were considered lower SES. Gruen, et al., found that the affl- iuent white children were more internal than the disadvan- i i staged white children and black children. With locus of control differences in mind, Middleton (1972) compared measures of alienation across race and edu- ; 'cational levels. He used a measure of alienation that was ] i :nested within a larger measure of attitudes. The sample I ! I jwas 107 white and 99 black students who were randomly se- I jlected. Middleton found that SES was related to the degree; ! I (of powerlessness felt, for example, l!there is not much that ■ I can do about most of the important problems that we face |today.” The findings showed higher levels of external con- I ! trol feelings for the lower class whites and blacks than |for the other respondents. i i j In a review of black locus of control literature, Gu- jrin,Gurin, Laos and Beatie (1969) noted that low income t i blacks experienced more external obstacles than the middle income blacks. This meant more layoffs, transportation difficulties and racial discrimination that were job relat 29 ed in addition to other types of discrimination. Gurin, et al., argued that these pressures are the basis for blacks1 i i feelings of being controlled, and the reason blacks have low internal locus of control. They also suggested that because of these experiences lower SES blacks become more I apt to blame society for their position in life. ; System Blame is used by blacks to explain failure within the social and economic systems. Gurin, et al., jnoted that "The internal alternative... means resting the iburden for failure on Negroes thenselves, specifically on j I : Itheir lack of skill, ability, training, effort or proper ! I 1 ' I ibehavior. In contrast, choosing the external alternative; t » ;means attributing the responsibility for the failure to the social system because of lack of opportunities and racial ; i [discrimination1 1 (p.300). It would follow that the less; I I * I success a black has attaining middle level SES, the more | ! ! i • i :system blame would be used. | i | j Gurin and Epps (1975) in an effort to explain the re- ! j lationship between SES and locus of control and anxiety, 1 :studied a samples of 966 blacks jjunior high schools. The lower Iternal (p<.001) than the higher north and the south. The lower er test anxiety (p<.001) than from northern and southern income blacks were more ex income blacks in both the income group also had high- the higher income group. Epps concluded from his study that low SES was strongly re lated to perception of limited opportunity and need for conf ormity. In an investigation of anger/aggression, Abeles (1976) studied the relationship between improvements in the socio economic condition of blacks and the rise of the civil ;rights movement and urban riots of the 1960fs. The find- i *ings were based on data from a randomly selected group from Cleveland and Miami. All respondents were black. Abeles theory that blacks desire for higher levels of SES would increase as their SES increased, was confirmed the higher j the SES of the individual, in both areas, the more militan- ! icy against and anger towards the socio-economic system in- » j 'dividuals exhibited. I i I Lefton (1968), also interested in middle class blacks, | 1 ! !found that contrary to his expectations, economically ad-j ivantaged blacks scored significantly higher than blacks with lower seniority and pay status on anomia, a term used by Lefton to indicate a feeling of separation between what respondents had and felt they should have. Lefton inter preted the data as indicating that anomia functions as an indication of frustration as well as despair. Lefton sug gested from his findings that as civil rights struggles in tensify, middle and upper middle class blacks will exhibit 31 militancy and anger that will exceed that of the economi- i Jcally lower status members of the racial group. The material contained in the previous sections was reinterpreted into the dimensions of a self-concept instru ment, the responses to which were analyzed using a confir matory factor analysis procedure found in LISREL. LISREL ! jand related literature is briefly reviewed in the following | section. I |2.4 CONFIRMATORY FACTOR ANALYSIS i 1 The present investigation used a computer program, LISREL V, developed by Joreskog and Sorbom (1981). LISREL, ! (linear structural relations) is a method of observing the I ! f delations between measured and latent variables. The t ;procedure requires that a model be prespecified to the ana lysis of the observed variance-covariance matrix. LISREL I can perform a confirmatory factor analysis on one group at ;a time or simultaneously on more than one group. The literature contains several studies that support the use of LISREL to simultaneously factor analyze the data of more than one group: for instance, McGarvey (1981) in- i j vestigated the structure of the Self-Rating Depression Sca- ; le by simultaneously factor analyzing three different age level groups using LISREL; Lei and Skinner (1982) investi- gated the structure of the Personality Research Form by us ing LISREL to simultaneous analyze the data from two lan guage groups. Several studies, in addition to the cross-structural equality of groups responses, have used LISREL to conduct analysis of invalidity or bias in affective instruments. jBenson, Hocevar and Cohen (1982) compared the effect of po- j I I jsitive and negative item phrasing of a measure developed to j ! i ;assess integration objectives at the fourth through sixth | 'grade levels. They investigated the effect of item phras- i ling on the validity of the measure by using a simultaneous jconfirmatory factor analysis to determine the degree of si milarity between three forms of the instrument. Benson (1982) used confirmatory factor analysis to investigate the jpresence of bias in a self-concept measuring instrument. A sample of responses was taken from a multiracial group of I i jeighth grade students. Benson defined bias as differences l » in factor structures in different groups. She used item ■statistics from LISREL to indicate whether an item was sig nificantly loading on the factor structure or contributing to bias in the structure. The chi-square difference test | !was also used to compare the success of competing models. I ;These studies suggest the applicability of LISREL as a j jmethod to investigate possible invalidity and bias due to I structural differences. 33 \ \ I Chapter III i METHODOLOGY Is there a common structural pattern for of self-concept associated with response level iacross racial and SES status? The following I [was developed to answer this question. i 3.1 SUBJECTS j The data was collected from two junior high schools in {Southern California. The academic self-concept measure was \ i {given to all black and white students present on the days ; i that the measure was given. The respondents whose parents; were either professionals, managers, execu tives , semiprof essionals , clerical workers, sales workers, I technicians, skilled workers or semiskilled workers were ! {designated as middle SES. The respondents whose parents 1 i iwere either unskilled or on welfare were designated as low- ! er SES. The definition of middle and lower socio-economic I |status (SES) was based on school counselor recommendations ]and administrative policy. Administrative policy broke the |groups into lower and middle SES groups to facilitate the j ! 34 measurement differences f methodology selection of free lunch recipients. Students in the lower group received the free lunch, the others did not. The ra cial designation was based on a combination of school re cords and self designation. Each student was asked to res pond as either black, Hispanic, white or other. There was a 96 percent agreement between the sources of racial desig nation. Cases in which there was disagreement as to race i ior SES sources were eliminated. A total of 351 acceptable responses were collected, 171 black and 180 white. Using the above categorization, there were 89 lower SES blacks, 82 middle SES blacks, 90 lower SES whites and 90 middle SES whites. The sample contained approximately 54 percent male students and 46 percent female students. All of the res- pondents were seventh or eighth grade students. <3.2 INSTRUMENTATION I Self-concept item examples upon which to base the items used in the hypothesized dimensions of the scale were j chosen from the following inventories: The Dimension of |the Self Concept (Michael & Smith, 1976) The Self-Esteem jlnventory (Coopersmith, 1959), the Piers-Harris Childrens !self Concept Scale (Piers & Harris, 1969), Self Concept of (Ability and School (Brookover, 1967), and the School Self I (Attitude Scale (Barker-Lunn, 1971). 35 The developed measure contained 79 items and was pi loted on a group of 58 seventh graders. Four percent were black, 12 percent were Hispanic and 84 percent were white. The piloted scale had a reliability of .73. Items that contributed to the scale reliabilities were kept, those that did not were deleted. I i ^ After piloting, the instrument contained 4 4 ^ terns with ! r ° t , r - im nl~'...... — H.H.I.U 1 Jan internal consistency reliability of .89. The academic i .- --- .. .... . . 9 0 ^ self-concept measuring instrument was then administered to | the^sample of junior high school students described in the j Jprevious section. The number of items in the instrument ' i i jwas further reduced in an effort to maximize the internal I j j •'consistency reliability of each dimension1 s scale among alii j i four groups. Items that contributed to the scale reliabil- | ; I ]ity in all of the groups were retained, those that lowered f i ! ; the reliability in any one of the groups were deleted. j ! i j The final form of the scale contained 26 items measur- ! j j ling five dimensions. The scales that correspond to the di- | f |mension described in Chapter II and the number of items per | :scale are described below. The items of the scale are f | shown in Appendix B. The dimensions relate to the affec- I | tive areas in which whites and blacks, according to litera ture, have exhibited mean level differences. 36 The Expectation/Aspiration scale consisted of five items. The aspiration items were developed to measure de gree of desire to perform well academically. The expecta tion dimension items were developed to measure to what ex tent the respondent felt that the aspiration would be fulfilled. The literature indicated that blacks aspire to the same level of vocational attainment as whites do but expect to attain lower levels than those expected by i Iwhites. ; j ! The Locus of Control scale consisted of six items. ' ; I . t This scale consisted of items that were designed to indi- [ i jcate whether the respondent felt able to exert some control j ■ l jover the school environment; whether there was a feeling of | ! ! having sufficient power to effect needed changes. The lit- i j ‘erature indicated that blacks exhibited greater feelings of j (external control than whites. j I i 1 i | The System Blame scale, consisting of six items, con- , I i I jtained items that were designed to measure blame of the | jschool and its personnel for troubled self feelings, for ! i i (example, blaming the school and its faculty for low grades i (rather than accepting responsibility or blame. 1 The Anger/Aggression scale consisted of four items. This scale contained items that were designed to measure feelings of self in the academic environment that relate to anger or instances of aggression. The literature indicated that the black tended to respond with more anger and had a !need for more aggressive behavior than the white individu- ! al. The Anxiety scale contained five items. The items in this scale were developed to measure feelings of stress or discomfort at points of interaction with school personnel or evaluation of progress in school. The literature indi- I Icated that black students experienced more anxiety in |stressful situations in school, such as testing or dealing Iwith authority, than did white students. I [ 1 \ ; i i i 13.3 PROCEDURE , | The 44 item academic self-concept , instrument , was ad- 'ministered to the students by the classroom teacher.^ Be fore being asked to respond to the instrument, the students were given four instructions. The first instruction was that the measure would not be graded; second, that there were no right or wrong answers; third, that it was impor tant to respond with honest feelings; and fourth, in every .case, to choose the answer closest to your own feelings^/ jWhile the students were responding to the inventory, the i \ teachers and counselors recorded each student’s SES level. I 38 ^ 3.4 HYPOTHESIS It was hypothesized that the measurement device which was constructed with dimensions in which blacks and whites exhibited mean level differences would contain two struc ture related problems. The first was invalidity, in which group response patterns do not support the hypothesized 1 ( jfactor structure. The second was bias, which occurs when isome aspect of the instruments response structure is not ! (common to all the groups involved and the construct indi cates either it should be common or does not indicate it j should be different. Invalidity and bias are, therefore, j t two aspects of the same problem: both occur when there are j structural discrepancies in relation to an instruments hy- j I I pothetical constructs. Invalidity results when the form is j i 'not as hypothesized and bias when there is invalidity m ; ;one group and j consistently i bias is not a the measure. i does not cor when a single not in another. That is, if the structure is J valid or invalid across all the groups then I I factor. Both relate to the interpretation of j i Invalidity occurs when the interpretation I respond with the underlying construct, bias interpretation is not common to all groups. 3.5 RELIABILITY Internal consistency reliability was an important con sideration, since it is the variance which is not associat- jed with error, the common variance, upon which the factor i structure of an instrument is developed. Cronbach's Alpha was used to compute the scale reliability. If a scale was deemed to be too low in reliability (.5 or less) in any one i jof the four groups scales, the scale was eliminated. The j 'low reliability scales were discarded because Kelly (1927) ! < i i l (recommended a minimum reliability coefficient of .50 for a j » I jmeasure to be useful in detecting group differences. Be- Jcause of a limited number of responses, the reliability i [analysis was conducted on the same responses on which the ; i 'subsequent analysis would be conducted. The listwise dele- ! i ' 1 i .tion of missing data was used in the analysis. The analy- | t ! |sis was accomplished on each separate scaled dimension us- * j ing raw data. \ The results showed that the groups were not responding with equal reliability to the five scales. The System i ! 'Blame dimension items had the highest average reliability! I [cofficient. The next highest average coefficient was ob-j I j served in the Anger/Aggression dimension items. The lower t white group had the highest average reliability coeffi cient, and the middle black group had the lowest average ( 40 reliability coefficient. The groups' reliabilities are shown in Table 1 : TABLE 1 Reliability of Scales by Group and Dimension Dimensions(item#) Black White Lower SES <n=87) Middle SES (n=80) Lower SES (n=87) Middle SES (n=86) Expctn/Asprtn (5) .54 .62 .65 .67 Locus of Cntrl (6) .67 .61 .71 .68 System Blame (6) .72 .68 .81 .73 Anger/Aggrssn (4) .68 .67 .82 .60 Anxiety (5) .38 .36 .53 .49 i The Anxiety scale was not used in any further analysis i jbecause of low reliability. i •3.6 MODEL TESTED AND DATA ANALYSIS I | Four groups were used;iWin^tte^an.alvsis: lower black, [middle black, lower white, and middle white. These groups were selected becajuse a review of the literature suggested these subgroups .wjdu 1 d.„jdIf. f _er_.in .the P£ r ceived„_sej,f-.coneept dimensions. 41 3.6.1 Hypothetical model The confirmatory analysis in the present investigation was accomplished with the LISREL computer package. In IlISREL, the factor model is specified by fixing or con- l jstraining the elements in three matrices, similar to the i [matrices encountered in an exploratory factor analysis. i jThese matrices are: (1) a matrix of factor loadings; (2) a ! jmatrix of factor variance-covariance, that indicates the j |relationships among the hypothesized factors; (3) a matrix; ; I ;of error/uniqueness, which provides information similar to j ! i I the communality estimates in the exploratory factor analy- t sis. The hypothetical model examined in this study is ishown in Table 2 . This table illustrates parameter pat- ! i terns to be estimated by LISREL in the factor loadings ma- | I t ; i ;trix and the factor variance-covariance matrix. The L’s i Jrepresent factor matrix parameters that were estimated, the i ;P’s represent variance-covariance matrix parameters that i i jwere estimated. The 1.0 values represent reference varia bles. The reference variables set the metric of the analy- sis. In exploratory factor analysis, the metric of analy s t sis is set to one with the ones in the diagonal of the t 'factor variance-covariance. Therefore, the factors1 rela tionships are portrayed in a correlational form rather than i twith a true score variance metric. In the basic hypothes- 42 |ized model, the metric was set by the reference loadings in I Ithe factor matrix. This allowed the diagonal of the vari- jance-covariance matrix to be estimated and to represent the i true score variance of the factors. Since the true score variances of the factors may differ from group to group or factor to factor, the use of variance-covariance, instead of correlation, is a generally accepted practice in simul taneous analysis of multigroup structures. The zeros indi cate the factor matrix parameters that were fixed to zero ! iin order to represent a simple structure model. The hy- | ipothetical model contained a total of 26 measured variables i ! tand five factors, as illustrated in Table 2 : j f I 43 TABLE 2 Organization of Hypothetical Model Factor Matrix Factors Var- Covar Matrix Factors F1 F2 F3 F 4 F1 F2 F3 F 4 Ex/ Loc Sys Ang Ex/ Loc Sys Ang Items Asp Ctl Blm Agg Fctrs Asp Ctl Blm Agg 1 L 0 0 0 FI P 2 L 0 0 0 F2 P P 3 1 .0 0 0 0 F3 P P P 4 L 0 0 0 F 4 P P P P 5 L 0 0 0 6 0 L 0 0 7 0 1 .0 0 0 8 0 L 0 0 9 0 L 0 0 10 0 L 0 0 11 0 L 0 0 12 0 0 L 0 13 0 0 1 .0 0 14 0 0 L 0 15 0 0 L 0 16 0 0 L 0 17 0 0 L 0 18 0 0 0 L 19 0 0 0 1 .0 20 0 0 0 L 21 0 0 0 L 3.6.2 LISREL Using a hypothesized model as a guide, LISREL is pro grammed to minimize a maximum likelihood loss function which is based on differences between the original covari ances and that reproduced from the fitted model. By so do 44 ing, the LISREL solution is said to explain the structure J |contained in the observed variance-covariance matrix. To indicate the degree of success encountered in the solution jusing the hypothesized model, a chi-square statistic, representing a log-liklehood ratio of fit is produced. LISREL can be used in either the single group or the multi- j group case, in which two or more groups’ matrices can be | simultaneously tested for fit to the same model. The hy- | ! jpothesized model is specified with the three matrices list- j I 1ed earlier: the factor, variance-covariance and error/uni- I j jqueness matrices. They can either be constrained to i ^equality across the groups or estimated independently for jeach group while LISREL fits a model to two or more matric- i ;es simultaneously. If the resulting chi-square is nonsig- i |nificant, the matrix has produced a satisfactory fit to the iobserved data. If the chi-square is significant, the mo- I | ! jdel’s fit of the data is unsatisfactory. i | Chi-square is additive and, as such, chi-square values i [that are derived from nested models can either be added or [subtracted to observe the data fit of different combina- I I jtions of models. Using the property of additivity, Bentler and Bonnett (1980) developed a chi-square difference test of nested models. The test is used to compare two chi- square values to determine which of two nested models is 45 jmore successful in explaining one or more data matrices. ! In the test, the df and the chi-square values of each solu- j i tion are subtracted from one another. The resulting dif ferences are used in a chi-square test that produces a probability indicating whether or not the model is provid ing a better explanation of a particular observed data ma- i ;trix. The chi-square is a useful tool, but it presents the j i I ;user with some difficulties in its interpretation. j I t j The chi-square used in LISREL has two problems. It is j affected by the size of the population and the complexity I of the problem. If the population is very large, the chi |square will nearly always be significant. Next, if the (problem has a large number of estimated variables, the chi ■square is likely to be significant. Therefore, problems! : i ; that are very complex and that are analyzed with a large | number of observations are almost always associated with ;significant chi square values. Conversely, simpler prob- !lems, with fewer observations seldom receive a significant t i I j chi square. For the reasons just presented, it is unwise | j to accept a LISREL chi-square value by itself or use it as the sole basis for decisions about the data. An index commonly used to to assist in the interpreta tion of LISREL generated chi-square values is a ratio of the chi-square to the degrees of freedom (Schmitt, 1978). I I I i j 46 t_____________________ _ The ratio can also be used with the chi-square difference test to produce a chi-square difference/df ratio. The in terpretations of the two are slightly different. In the chi-square/df ratio, a finding of difference indicates that the model does not provide a satisfactory fit of the ob served data matrix. The chi-square difference/df finding of difference indicates that one of the two models is pro- I | viding a better fit of the model than the other. In both, i the degrees of freedom is a function of only the number of j variables in the problem, i.e. the size of covariance ma- j j i itrix and the number of variables to be estimated. The lar- j I ’ Iger the df, the larger the chi-square. The chi-square is a I •function of complexity and number of responses. Therefore, !the chi-square/df is a ratio of complexity plus population i ♦ 1 , over degree of complexity, which is not influenced by com-! I plexity but is still influenced by size of population, j I j i jWhen the population is small, as in the present investiga-| ' ! jtion, a generally accepted ratio of 2.0 can be used as a |point at which difference occurs (Marsh & Hocevar, 1983). Ratios below 2.0 are acceptable indications that the model being tested is providing a successful fit of the covari ance in the data, the larger the ratio above 2.0, the greater the likelihood that the chi-square represents dif ference . 47 Another statistic used to aid in the interpretation of the LISREL chi-square was provided by Bentler and Bonnett (1980). It is an index based on the comparison of covari ance explained by a model and the amount of covariance available in observed data. The method produces a ratio called a delta coefficient. A delta is computed by sub tracting a null model's chi-square from the chi-square of the model being compared and dividing the results by the jnull model's chi-square value. The null model is one which i ! • ! contains no covariance. The more covariance contained m j j i the observed data, the worse the null model's fit of the ! idata. The ratio ranges from 0.0 to 1.0, the higher the ra- I . t i !tio, the more success the model being tested is having in !explaining covariance. Delta is free of the effect of sam- \ i | pie size unlike the chi square/df ratio but not of the ef- i j feet of model complexity. Also, if the covariance of the groups is not homogeneous or is low, it is difficult to in terpret the delta coefficient, | Neither of the alternative indices nor the chi-square | are completely satisfactory indicators of goodness of fit. I |This fact undermines what appears to be, at first glance, a I jrigorous approach to testing the fit of hypothetical struc- ! ture to data. Each index is subject to influences other f 'than the success or failure of model to data fit. The I ; 48 I L _ _ chi-square probability was used not so much as an absolute determiner of difference but as an indicator of degree of probable difference. Hence, the ,05, .01 and .001 levels of significance instead of being decision points, were used as gauges in combination with other indicators of differ- jence. Because of the nature of the LISREL chi-square and jchi-square difference tests, one must be wary of making ^either type I or type II errors depending on the chi-square i I : in use. The chi-square difference and corresponding ratio i i i would be associated with type I error because they are used j to suggest differences between models. The chi-square and j i corresponding ratio, however, would be associated with type j i II error because they are used as indicators of degree of ! similarity between an observed and model developed solution i ' i matrix. Because the chi-square probabilities and related j indices are both influenced by factors other than the de- 1 ! I ;gree of difference of the models being tested, the two ind- j iices and chi-square tests were used in a suggestive fashion j ! i ito answer the questions posed in this investigation. 3.6.3 Data analysis '3.6.3.1 invalidity and bias Measurement in which the observed response structure jof an instrument does not coincide with the hypothesized 49 ____ _ structure is not construct valid. Measurement, in which dimensional dissimilarity occurs for different groups that i | is counter to expectation, is biased. If a construct indi cates that dimensions are to manifest similar structural i jrelationship for all groups, invalidity that occurs incon sistently across groups* response structures is an indica- ! tion of structural bias. Therefore, structural bias is a special case of construct invalidity that occurs in rela- ! tion to multigroup measurment. j j ! j The analysis for invalidity or bias was developed in itwo parts. The results of both parts served as indications I j jof invalidity and bias. The first part was to determine ifj ' i ; the structure of the hypothesized factor model satisfacto- ; i ■ rily explained the covariance of all four groups and the ; i second was to determine whether or not the four group*s ob- \ ,served response structures contained invariant factor pat terns. The first part checked each group*s observed covar iance matrix for fit to the hypothesized model. The test |did not compare the factor structure for invariance but i [merely established that the group*s response structures ! |could be satisfactorily explained by the hypothesized fac tor structure. This test is general, but unless it is es tablished that the four factor structures can be described by roughly the same parameters, it makes no sense to com 50 pare those structures for invariance of structural parame ters. The second part of the analysis tested the factor, i variance-covariance and error/uniqueness matrices for in variant parameters using two sets of analyses. In the i I first set, a series of four group simultaneous analyses i tested separate factor matrices for invariant parameters, !If any non-invariance was observed in the first set of ana- jlyses, the matrices that were responsible for the invari ance were examined in the second set to establish which f 'groups were responsible for the non-invariance. J Structural differences not common to all groups in ; ; either the first or the second part of the analysis could be considered indications of invalidity and bias. The ana- j Jlysis represents a two part probe of a measure1s observed i •response structure, first of the shape of the structure and i 1 then of the individual elements of the structure. t : I * i i :3.6.3.2 research question i j Question : 1 s there a common structual pattern for academic < self-concept associated with response level | differences when measured across ethnic and SES status? In the first part of the analysis, the fit of the hy pothesized factor structure to each of the four groups ob- i ! served variance-covariance matrix was tested. The result- t ing chi-square values were analyzed using two of the indic es described above, the chi-square/df ratio and the Delta coefficient. The separate analyses were used to determine whether the hypothesized model provided a satisfactory fit j of each group’s structure. This test did not provide the j i i 'more specific comparisons of the matrices parameters whichj I I I required a simultaneous analysis of the group’s matrices. j i j Whereas in the first part the fit of each group’s ma trix to the hypothesized structure was tested, the second i ! part of the analysis provided a more restricted test of I 'the equality of the factor matrices’ parameters. In this! j t .part, LISREL simultaneously compared the parameters of thej » * :four groups’ observed variance-covariance matrices for in- ivariance. The test for invariant parameters was conducted) ! i |With two sets of analyses. The first set was a four group | [Simultaneous analysis and the second was a post hoc analy- i Isis performed to establish which group was responsible for ♦ I jthe lack of invariance, if any became apparent in the first | set. 1 i j In the second part of the analysis, the first set of |tests simultaneously fit a series of models to all four groups' observed data. The observed data matrices were fit to the hypothesized model with various constraints on the factor loading, variance-covariance and error/uniqueness matrices, A model without any constraints was also gener- ated by summing the chi-square and degrees of freedom va lues from the part one analysis. In the first simultaneous analysis, the factor matrix was constrained to invariance across all four groups while the other two matrices' param- eters were allowed to be estimated without constraint. In the next model, the factor and the variance-covariance ma trix parameters were constrained to invariance. Then, the factor and the error/uniqueness matrix parameters were con- l strained to invariance. Next, the chi-square difference of i each model comparison was determined by subtacting a mo- ■del's chi-square from the chi-square of the model with one i jmore constrained matrix: the chi-square of the non-con- strained solution was subtracted from the factor matrix constrained solution, then the factor constrained chi- square was subtracted from the factor plus variance-covari ance constrained and the factor plus error/uniqueness con- I l |strained chi-squares. The chi-square differences were i j compared using the chi-square difference/df ratio to det ermine whether or not the parameters of the lambda, psi or theta epsilon matrices were invariant. By comparing each 53 \ . matrix in this successive manner, the chi-square differ- ence/df ratio provided an indication of the degree of simi larity of the four group1s response structures across the the factor loadings, variance-covariance matrices and er ror/uniquenesses. Any matrix found to contain non-invariant parameters was subjected to further analysis. Each group*s non-invar iant matrices were compared with those of every other group to determine which group*s matrices were responsible for the lack of invariance. Each group was compared against all other groups to determine the source of the lack of in- j r [variance. In each comparison, the observed matrices were; i J jfit using two forms of the hypothesized model. In one mo-j idel, the matrix parameters that were found to lack invari-j i • - ! i i | ance in the previous set of analyses were constrained to j i i [invariance. In the other model, the matrices* parameters! I j [were estimated without the invariance constraints. Thet t 'chi-square values of the two models were then compared us- !ing the chi-square difference and the chi-square differ- I 'ence/df ratio. Chapter IV FINDINGS AND DISCUSSION 4.1 FINDINGS In the first part of the answer to the research ques tion, four separate confirmatory factor analyses were * com- j iputed to determine the fit of each of the four groups1 var- j J I i j iance-covariance matrices to the hypothesized factor jstructure. The resulting chi-square values for each group i were analyzed with the chi-square/df ratio and the delta • i i / |coefficient. The Delta coefficient is a ratio of the chi- j i i i !square value of a model to data fit over the null model fit , i of the same data. In the null model, each measured varia-j | ble is specified as representing a single factor none of iwhich covary. The error/uniqueness terms for each measured i variable are also specified without covariance. Table 3 contains the results of the analyses. TABLE 3 Fit Indioies for Single Group Analyses Group Matrix Chi- Sq (df=183) Chi- Sq/df Ratio Delta Coeff Low SES Blacks 239.15** 1 .31 .6 Middle SES Blacks 234.80** 1 .28 .5 Low SES Whites 270.84** 1 .48 .7 Middle SES Whites 100.66 .55 .8 *p<.05 **p<.01 ***p<.001 ♦ All of the chi-square difference ratios were less than ! i 2.00. Both of the white groups* delta coefficients were j jhigher than the black groups* delta coefficients. The mid- Idle white group had the only non significant chi-square, as well as, the only chi-square/df ratio below 1.0. To provide a visual comparison of the success of the j jhypothesized factor structure in the description of the !four groups covariance matrices, table 4 was provided. The significance level of each of the loadings was based on t- i |tests which LISREL computed for each item to indicate !whether or not the loading was significant. 56 TABLE 4 Standardized Factor Loadings by Group and Scale Scale Items Groups Low Blk Mid Blk Low Wht Mid Wht Exp/ 1 .34 .18 .21 .26 Asp 2 .1 2# .24 .29 .36 3 .30 .18 .33 .39 4 .29 .35 .65 .36 5 .25 .18 .43 .31 Loc 6 .23 .07# .32 .24 Cntl 7 .22 .18' .37 .29 8 .46 .41 .27 .36 9 .30 .28 .18 .37 10 .42 .29 .23 .28 11 .14# .32 .26 .29 12 .20 .21 .38 .34 Sys 13 .44 .39 .50 .33 Blm 14 .42 .18 .52 .36 15 .42 .32 .42 .47 16 .28 .41 .55 .42 17 .37 .38 .56 .36 Ang/ 18 .16 .27 .48 .43 Agg 19 .68 .41 .34 .36 20 .15 .36 .36 .31 21 .18 .17 .24 .21 one of #p>. 05 the loadings in the middle black not significant (p<.05) and two of the loadings in the low er black group were not, all the other factor loadings were significant. 57 Using the hypothesized model, three simultaneous con firmatory factor analyses across all four groups were com puted in the second part of the answer. A non-constrained model's chi-square was generated by summing the four chi- square values and degrees of freedom from Table 3 . Each simultaneous estimate used the hypothesized model with a different combination of invariance constraints on the es timated factor parameters. Three chi-square differences were then computed by subtraction: first, the model with- i out invariant constraints from the the factor matrix con- j strainedmodel, next, the factor matrix constrained model j I from the model with the factor plus variance-covariance ma- ; trices constrained, and finally, the factor matrix con- | strained model from the model with the factor plus error/u- i |niqueness matrices constrained to invariance, as shown in j !table 5 : 58| TABLE 5 Fit Indicies for Four Group Simultaneous Analyses Invariant Parameters Chi- Sq (df) Delta Chi- Sq Diff (df) Chi- Sq Diff/df Ratio None 845.45 (732) . 6 M l — M l M l M l Factor 920.08 (783) . 6 74.63* (51 ) 1 .46 Fetor + Var-Cov 950.28 (813) .6 30.28 (30) 1 .01 Factor + Uniquenss 1062.61 (846) .5 142,53*** (63) 2.26 *p<.05 **p<.01 ***p<.001 : All of the four group LISREL estimates observed had a I ! | j delta coefficient of less than .7. All of the chi-square |difference ratios were less than 2.00 with the exception of the ratio of the comparison between the factor loading and | the factor loading plus error/uniqueness constrained ma- i trices. The chi-square significance and the size of the chi-square/df ratio indicated that the error/uniqueness ma-1 [ trix had the greatest likelihood of containing non-invari- ance among the four matrices. Therefore, further analysis was conducted to determine the source of the possible non invariance, To accomplish this part of the investigation, 59 comparisons of the error/uniqueness parameters were gener ated across all the groups. The comparisons used two sim ultaneous confirmatory factor analyses of all possible paired combinations of the groups, one of which contained a model in which the factor matrices were constrained to in variance and the other a model in which the factor and the ! error/uniqueness matrices were constrained to invariance. j A n indication of the degree of similarity of the error/u- ^niqueness matrix parameters was provided by the chi-square i ;difference comparisons shown in table 6 . 1 1 i ; The comparison between the lower black and lower white j igroups exhibited the least amount of difference between the [ I ! !factor constrained and the factor plus error uniqueness : ‘ i | constrained matrices, the chi-square probability was great-! i ] er than .05 and the chi-square/df ratio was the lowest of ! the six comparisons, well below 2.0. The comparison bet- i i iween the lower white and middle black groups exhibited the I : largest and the comparison between the lower black and mid- i Idle black groups exhibited the second largest indicators of f error/uniqueness non-invariance, these two comparisons had the lowest chi-square difference probabilities and the largest chi-square difference ratios. The other three com parison exhibited nearly the same levels of error/unique ness, all of which had ratios close to 2.0 and chi-square difference probabilities of less than .01. 60 TABLE 6 Fit Indicies of Comparative Analyses to Detect Non-Invariance Group Pairs Factor Constrnd Chi-Sq (df=383) Factor Uniqnss Constrnd Chi-Sq (df=404) Chi-Sq Diff (df=21) Chi- Sq Diff Ratio mid low blk wht 529.21 612.32 83.11*** 3.96 low mid blk blk 500.32 553.04 52.72*# 2.51 mid mid blk wht 351.97 395.95 43.98* 2.09 low mid wht wht 385.91 426.50 40.59* 1 .93 low mid blk wht 367.74 406.71 38.97* 1 .86 low low blk wht 540.16 569.45 29.29 1 .39 I *p<.05 **p<.01 ***p<.001 i I t 4.2 DISCUSSION Part one results of the analysis appeared to support! the fact that the four groups’ observed covariance could be explained by the hypothesized factor structure. Although i three of the four chi-square values were significant, all i ;of the associated chi-square/df ratios were well below 2.0 I i jand close to 1,0 which according to Schmitt (1978) could be ♦ i 1 t 61 used as a lower limit for the indication of a successful model to data fit. Schmitt suggested that ratios of less than 1.0 were excessively low and could not be relied on to remain stable in future replications. The middle white data model to data fit appeared to be excessively low alt hough the delta coefficient indicated there was still co- j variance unexplained and the the factor matrix shown in ta- i ble 4 did not indicate unusual factor loadings. Table 4 also supported the conclusion that the hypothesized model adequately described the observed covariance in the other j groups because all factor loadings were fairly successful i I in the middle and lower white groups and only one in the j I I !middle black and two in the lower black were particularly! i poor with loadings at greater than the .05 significance; i ' |level. Although the results suggested that the hypothes-j ! I i I ized factor structure provided a satisfactory explanation of each group’s pattern of response, they did not indicate whether the different matrices1 parameters were invariant across the different groups. A common factor structure is i a logical first step to the examination of invariant factor ! patterns because if the item factor relations are dissimi- jlar from group to group, then parameter estimates cannot be comparable, much less invariant. In the second part of the answer, two sets of compari sons were used. The first set was a series of four group simultaneous confirmatory factor analyses in which diffe rent combinations of invariance constraints were placed on the factor models tested. In the second set, the model to ■ data fit of the error/uniqueness matrices of all groups was examined in groups of two. In each of these sets of com- Iparisons, there were two models tested, one with factor ma- jtrix constrained and the other with the factor plus error/ i (uniqueness matrices constrained to invariance. I In the first set, the chi-square difference/df ratio, ] |2.26, suggested that the error/uniqueness matrices were the (most suspect of any of the matrices. In addition, the i !chi-square difference test between the factor and the fac- ; tor plus error/uniqueness matrices was a good deal more (significant than the other two comparisons. For this rea- j Ison, the error/uniqueness matrices had the greatest prob ability of non-invariance, which ran counter to a hypothes- i I I ized lack of invariance indicating invalidity and bias. !Also, the comparisons did not provide an indication of | jwhich group comparisons were responsible for the non-invar- t Iiance. i j The source of non-invariance was investigated in the ! second set of analyses by comparing each group with every i other group using a two group simultaneous comparison of the factor parameters. Two comparisons, one between the middle black and the low black and the other between the middle black and the low white error/uniqueness matrix par ameters showed higher chi-square difference/df ratios than ithe other group comparisons. These results indicated that ! jthe greatest probability of non-invariance was located pri- I 'marily in comparisons between the middle black and the low er black and white error/uniqueness matrices. The compari- i * son between the two lower SES groups, on the other hand, ! showed the greatest probability of invariance. It was hypothesized that differences in black and Jwhite students mean response levels to school related jself-concept measurement would be associated with differ ences in response structure; these differences would be in- i jterpreted as invalidity for groups with response patterns : that were not as described by the theory, and bias for i (groups with response patterns that were not common to all ithe groups involved in the measurment. i ! Contrary to the hypothesis, however, the greatest !probability of structural dissimilarity was not associated i 'with invalidity and bias, both of which are dependent on !structural dissimilarities in the factor loadings and vari- i i Iance-covariance matrices. The results of the analysis sug- 64 gested that the lack of invariance was associated primarily with the shape of the error/uniqueness matrices among the middle black and two lower SES groups. Such non-invariance could indicate that although the factor loading pattern and |and parameters were common to all groups, the communalities j from which the factor loadings were estimated were not com mon among the groups. Hence, the lack of invariance was not as hypothesized. Consequently, the results did not j support the hypothesized existence of invalidity or bias as j l explanations for the contradictory results discussed in the ♦ first part of this report. The measurement was neither in valid nor biased because a single set of factor loadings could be used to interpret the responses of all four groups, but the finding of a common and invariant structure Jwas based on what appeared to be error/uniquenesses that jlacked invariance. i ♦ I Although failing to support the hypothesized structur al differences, the results to both parts of the question must be looked at in light of the cross group differences that were apparent. In terms of race, the black groups ex hibited the lowest relibilities and lowest delta coeffi cients but comparatively good chi-square ratio indications of model fit. In terms of the SES levels, the structural differences appeared greatest between the middle black and 65 the two lower SES groups. The middle white comparisons were based on data fit that was spuriously close and there fore the fit statistics related to the middle white data were probably not as stable as those of the other three groups. The comparison between the two lower SES groups showed the greatest amount of similarity. The reliability and the delta coefficients, both indications of the amount of covariance available to the analysis, may very well be related to the piloting of the instrument which was based i i i jalmost entirely on the responses from a sample of middle [white junior high school students. The differences in the i (reliability and delta coefficients point to cross-racial; ] factors while the LISREL simultaneous comparisons point to iSES influences. Stability of factors in replication and | ; i Expansion or change of factor scales are dependent on i !equality in the error/uniquenesses or one minus error/uni- ! jqueness which is communality. Since the different groups1 j | j factors were based on different amounts and shapes of com-I munality, it is likely that such differences would result! in unstable factors in any future replications. ! i ! The black, and particularly the middle black, respons- Jes to the instrument seemed subject to the greatest differ ences: the lower reliability and delta coefficients showed I I that the two black groups responses contained less covari- i i { I 66 ance than the white groups. The middle black group exhi bited the greatest differences in the shape of the error/u niqueness matrix parameters. The explanation for lower and differently shaped covariance may be found in the black group itself. The black population today is struggling to achieve self identity. Much of that struggle is reflected in black self-concept. The middle blacks in particular are i j jinvolved in this struggle, because of their relatively new j ! socio-economic status. The Black Panthers, black pride, ! i 7 | j"black is beautiful," and "Roots" are just a few of the ex- Iternal manifestations of the drive to enhance the black*s i I * jself image. Much of this drive is focused on black school |children. Perhaps, the black groups’ responses to the in- I l !ventory were influenced more by the emotion and turmoil of i |their environment than by the content of the academic | 'self-concept items. If the blacks, and particularly middlej iblacks, are involved in more turmoil than the other groups, j :then it is possible that the turmoil would be reflected in i :their responses to an academic self-concept instrument. I Whatever the underlying reasons of the differences, the (findings must reflect on the original hypothesis of the in- I Ivestigation. i It was hypothesized in Chapter I that inconsistency in black/white mean level responses to self-concept instru 67 ments might, in academic self-concept, be related to prob lems of interpretation of cross racial measurement. The findings of this investigation, however, did not support * this hypothesis, but suggested instead other possible ex- | i planations. First, they suggested that inconsistency of jmean response level might be associated with the error/uni- i jqueness structure and, therefore, different amounts of com- jmunality upon which the factors were based. Varying commu- jnality might certainly have an affect on the stability of a (measure particularly when items are added or deleted or the I ■inventory is changed in some other fashion. Second, the ,comparisons of error/uniquenesses suggested that the great- i t ! I |est differences occurred not cross racially but across SES levels, that is, the middle black when compared to both the lower SES groups showed the greatest likelihood of non-in- j variance and the two lower SES groups showed the greatest i i |degree of similarity. These effects of SES and error/uni- i queness on the structure of academic self-concept need to be investigated in future research and more thoroughly un- l iderstood, to improve the interpretation of self-concept ;measurement. 68 Chapter V SUMMARY, CONCLUSIONS AND RECOMMENDATIONS i t 5.1 SUMMARY 5.1 .1 Purpose j The purpose of this investigation was to determine i whether or not there was a common response pattern in the observed covariance matrices of black and white students to a measure of school related self-concept. The measuring I > instrument was developed based on dimensions that had been j previously indentified as containing black, white response j j level differences. The extent of the invariance of the I 1 different groups structures was examined in order to ob- !serve the relationship between a measure that designed to ! contain level difference and the extent of invalidity and j jbias in such a measure. j j I I |5.1.2 Method l |5.1.2.1 sample A total of 351 junior high school students, 171 black and 180 white responded to the inventory which measured academ ic self-concept. There were 89 lower SES and 82 middle SES blacks, and 90 lower SES and 90 middle SES whites. 69 5.1.2.2 statistical analysis The data was examined with single group confirmatory factor analyses to determine whether the observed covari ance was satisfactorily explained by the hypothesized mo del. The data was then analyzed with simultaneous confir matory factor analyses to determine whether or not the matrices* parameters were invariant, and, if any, which groups were responsible for the lack of invariance. 5.1.2.3 measurement A self-concept measuring instrument was developed with five dimensions based on affective areas that had been shown to contain significant level differences between .black and white responses. Self-concept items were devel- j I i » t | oped to conform to the dimensions. j |5.1.3 Findings i <1. The hypothesized factor pattern itself was found to ade- t Iquately explain the covariance in each of the four groups I [response structures. I l 12. The four groups* factor and variance-covariance matrix t 'parameters were found to be invariant, but the error/uni- I |queness matrix was not. Upon further analysis, the proba 70 ble lack of invariance was shown to be contained in the comparisons between the middle black and the lower black and lower white matrices. 5.1.4 Conclusions It was concluded that the existence of invalidity and bias in relation to black/white differences in academic self-concept measurement was not confirmed by the analysis; jthe greatest likelihood of a lack of invariance occurred in I the error/uniqueness matrices, which does not relate to the ! i ) 'shape of the factor structure but to the shape of the er- t ( l ♦ t !ror/uniqueness or common variance underlying the factor! ' i ' t !structure. Hence, the non-invariance did not indicate in- ( ! i validity or bias because both the factor matrices and the | ;variance-covariance matrices upon which interpretation of |the measurement results were based, appeared to be invari- ! |ant. j I j I j I , 5 . 2 LIMITATIONS I | The present investigation was subject to a number of i (limiting influences. j 1. The piloting limited the effectiveness of the instrument to measure the construct reliably in the subsequent data sample: the piloting of the instrument involved in the in 71 vestigation was not completed on groups that were equiva lent to the responses of the subsequent data sample; the groups on which the piloting was conducted were different tin both racial and socioeconomic status from the data Sam i ' Iple; this limitation occurred because of the problems of I jidentifying a suitable target population for the investiga tion. j 2. The sample of respondents was self selected which limits j i the generalizability of the findings: the investigator en- j I {countered considerable difficulty locating a school dis- | I trict that would allow its students to respond to the in- J vestigation1s inventory, since only two of the 27 districts; i contacted consented, no randomization was possible. j 1 l * 3. The results are limited by a smaller than recommended* i |sample upon which to conduct a factor analysis: according I to researchers that use factor analysis such as Nunnally t (1980), a factor analysis should have at least 10 responses for each item placed into the factoring process, therefore, jthe present investigation would have required at least 210 responses; this criteria was not satisfied in the first part of the analysis; there does not seem to exist a rule i |of thumb for multi-group simultaneous analyses. 4, The stability of the factor structure is questionable because of the small amount of identified common variance upon which the factor structure was tested in the black po pulation and the overfit of the middle white data to the hypothesized model. 5.3 RECOMMENDATIONS The following are a list of recommendations that have been i i imade based on the present investigation. j i 1 . 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Children's estimates of their schoolwork ability ! as a function of sex, race and SES level. Journal of ! Personality T 1969, 3_L, 203-224* [ I i Wylie, R. The Self Concept. Lincoln, Nebraska: University of Nebraska Press, 1979. i jYancy, W. & McCarthy, J. Social position and self- ' evaluation: the relative importance of race. American Journal of Sociologyr 1972, Z8., 338-359. 80 Appendix A ACADEMIC SELF CONCEPT INVENTORY Alwys Some- Never or or almst time almst alwys never 1. Would you tell a teacher that he or she is wrong? 0 0 0 2 . Do you try to behave yourself in school? 0 0 0 3. Do you plan to go to college or a university? 0 0 0 4 . Is school interesting to you? 0 0 0 5 . Are teachers fair? 0 0 0 6. Do you get in trouble at school? 0 0 0 7. Do you get grades that most anyone would like. 0 0 0 8. Do you want to be one of the better students in class? 0 0 0 9. Schools are a nice place. 0 0 0 10 .Do you dislike children that fight. 0 0 0 11 .When you make plans at school do you feel they will work? 0 0 0 12.Do your classmates follow your ideas? 0 0 0 13.Do you work hard even on assignments that are very hard? 0 0 0 14.Do you get into fights at school? 0 0 0 15.Do you try to get good grades? 0 0 0 16.Is school a nice place to be. 0 0 0 17.At school, do you get blamed for things that are not your fault? 0 0 0 18.Do you feel you can read any book a teacher gives you? 0 0 0 19.Do you suggest to your teacher things to do in class? 0 0 0 20,Do you think the work you do in school will help you be a success after school? 0 0 0 21.Do teachers try to make schoolwork fun for you? 0 0 0 22.1s it your fault when things go wrong? 0 0 0 23.Does your teacher tell you off? 0 0 0 24.Do you like to be the leader at school? 0 0 0 25.Do you think school rules are fair to you? 0 0 0 26.Does it bother you when you get in trouble? 0 0 0 27.Do teachers talk nicely to you? 0 0 0 28.Do you get angry at school? 0 0 0 29.Do teachers nag a lot? 0 0 0 i 82 30.Do teachers want to listen to you? 0 0 0 31.Do teachers think you are a | troublemaker? 0 0 0 I [32.Do you have trouble asking a question over again in class? 0 0 0 33.Do teachers care about their students? 0 0 0 34.Do you want to please your teacher with your work? 0 0 0 35.Do you get nervous when the teacher asks you a question? 0 0 0 ! :36.Do your classmates think you ; have good ideas? 0 0 0 ;37.Do principals want students i to do well. 0 0 0 ;38.Do you want to be one of the | best students in your class? 0 0 0 1 i39.Dc you worry about your j schoolwork? 0 0 0 !40.Do they make you do things at : school that you don't want to do? 0 0 0 1 |41.Is it important to do well in ; school to get a good job? 0 0 0 1 42.Do you feel that hard work ! in school is important? 0 0 0 i ;43.Do you worry when you have to i take a test? 0 0 0 I |44.Do you do things without mistakes? 0 0 0 83 Appendix B ITEMS USED IN HYPOTHETICAL FOUR FACTOR MODEL Expectation/Aspiration -Do you plan to go to college or a university? -Do you want to please you teacher with your work? -Is it important to do well in school to get a good job? -Do you want to be one of the best students in class? -Do you feel that hard work in school is important? Locus of Control -When you make plans at school do you feel they will work? -Do you feel you can read any book the teacher gives you? -Do you suggest to your teacher things to do in class? -Do you like to be the leader at school? -Do teachers want to listen to you? 84 -Do your classmates think you have good ideas System Blame -Do teachers try to make schoolwork fun for you? -Do you think school rules are fair to you? -Do teachers nag a lot? -Do teachers care about their students? -Do principals want students to do well? -Does your teacher tell you off? t ! !Anger/Aggression -Do you get in trouble at school? -Do you get into fights at school? j-At school are you blamed for things ! that are not your fault? | !-Do you get angry at school?

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Creator Wilson, Michael James (author)

Core Title Factorial invariance and the construct validity of a school related self-concept measure

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Degree Doctor of Philosophy

Degree Program Education

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag education, educational psychology,OAI-PMH Harvest

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Permanent Link (DOI) https://doi.org/10.25549/usctheses-c26-520555

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