m———_—— .7—« v PREDICTENG THE SELEEHGR 8F A. FEELB 0F CGNEENWATION AT MECHEGM SMYE UREVERSITY FROM THE PERSONAL ENFGRMATIGN INVENTORY A. Thesis for the Degree of Ph. D. MECHEQAN STATE UNEVERSITY DONALD JOHN CUTTING 1966 This is to certify that the thesis entitled Predicting the Selection of a Field of Concen- tration at Michigan State University from the Personal Information Inventory ‘ .- presented by Donald John Cutting has been accepted towards fulfillment of the requirements for Ph.D. dammein Counseling, Personnel Services and Educational Psychology Wf-Xeh V Raph E. ron T Major professor ~' A ” -H‘v Date October 13, I966 5%?“ 7 W Whit; W2” MU ABSTRACT PREDICTING THE SELECTION OF A FIELD OF CONCENTRATION AT MICHIGAN STATE UNIVERSITY FROM THE PERSONAL INFORMATION INVENTORY by Donald John Cutting The over-all purpose of this study was to identify through the predictive use of certain elements of self con- cept, the academic field of concentration that a college student would select. The study was designed to differentiate between criterion groups on the basis of fifteen variables of self concept of ability and occupational interest. The fol- lowing hypothesis was formulated and tested. It is possible to differentiate among groups of students classified by curriculum two years after ini- tial entrance to college, on the basis of an identi- fiable pattern of self concept of ability and occupational interest as freshmen. The pOpulation selected for this study consisted of the freshmen entering Michigan State University in the Fall of 1963. Of the 5,7hl students classified as first-time freshmen, a restricted sample of 2,258 students was chosen for the study. This selection was based on five factors which suited the pur- pose of the study. A validation subsample of twenty-five per cent was obtained by the selection of every fourth student from the selected sample to be analyzed. The sample had been previously classified by curriculum grouping numbering twenty- seven groups in all. A The instrument used was the Personal Information Inventory which contained the fifteen variables to be used as measures of Donald John Cutting self concept. This inventory was administered to all enter- ing freshmen during the Summer Counseling Clinics of 1963. The members of the sample were assigned to groups according to their major two years later in the Fall of 1965. Multiple discriminant analysis was chosen as the statis- tical method best suited to the problem of combining test scores and other data so as to maximize the difference be- tween the groups and minimize the difference within each group. Through the separation of individuals who are known to belong to mutually exclusive groups, it is possible to determine the combinations of variables which will maximally discriminate among the different groups. It is also possible to observe the magnitude of the group differences and to classify future individuals into one of these groups on the basis of similar data. All computations for the multiple discriminant analysis were performed by the CDC 3600 computer at Michigan State University. The analysis yielded ten significant discriminant func- tions. Thus, the null hypothesis, ”There is no difference in self concept of ability and occupational choice, as entering frehmen, among groups of students classified by curriculum two years after initial entrance to college", was rejected. These ten functions were interpreted by an examination of the factor patterns. These functions accounted for over 98 per cent of the total variance or dispersion among groups as defined by the variables. A closer look was given to the first three functions which accounted for approximately 70 per cent of the dispersion among groups. The first function accounted for Donald John Cutting approximately to per cent of the dispersion and was artistic- social service (feminine) versus numerical-physical science (masculine) in nature. The second function, accounting for approximately 17 per cent of the dispersion among groups, was a verbal-business detail versus biological science-mechanical- technical function. The third function accounted for approx- imately 13 per cent of the dispersion among groups and was interpreted to be a general (non-numerical) scholastic ability versus business detail-executive-managerial function. These functions were interpreted by plotting the group centroids for the three functions in three-dimensional space. Weighted co- efficients were conventionalized and applied to the raw scores of the validation subsample. The validation was carried out in two separate procedures. The first validation produced a discriminant score for each individual by each of the ten significant discriminant func- tions. The second validation afforded classification into 27 different groups in rank order with a discriminant function value for each. This second validation was a discriminant classification operation with all ten discriminant functions together performing the differentiation. PREDICTING THE SELECTION OF A FIELD OF CONCENTRATION AT MICHIGAN STATE UNIVERSITY FROM THE PERSONAL INFORMATION INVENTORY By Donald John Cutting A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Counseling, Personnel Services, and Educational Psychology 1966 PREFACE ”Trust in the LORD with all thine heart: and lean not unto thine own understanding. In all thy ways acknowledge Him, and He shall direct thy paths.” -- A Proverb of Solomon ii ACKNOWLEDGMENTS The assistance and understanding that has been given by each member of the doctoral cmmmittee of the writer is acknow- ledged with sincere and deep appreciation. Special gratitude is extented to Dr. Ralph E. Kron for his guidance in the form- ulation of the study and his continued counsel throughout its development. Dr. James W. Costar, for assuming the chairman- ship of the doctoral committee when an unforeseen change occurred, Dr. Bill L. Kell, for enduring empathy and continued encouragement, and Dr. Ted W. Hard, for his critical review of the finished thesis, all deserve rich praise. Mr. Bruce Rogers is to be commended for his unreserved assistance in the computer phase of the study. ”And the LORD God said, It is not good that the man should be alone; I will make him an help meet for him." Words are too inadequate to express all that the writer's wife, Norma, has been to him during these days. The Biblical text stands alone. Two sons, Tim and Dan, also deserve recog- nition for their consideration of the writer during this time of preparation. 111 Chapter II. III. TABLE OF CONTENTS TITLE PAGE PREFACE ACKNOWLEDGMENTS TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES LIST OF APPENDICES THE PROBLEM Need Purpose Delimitations Hypothesis Theory OVerview THE REVIEW OF THE LITERATURE Definition of Terms Self-Concept Theory Choice Theory and Career Development Curriculum Choice Multiple Discriminant Analysis Summary THE DESIGN AND METHODOLOGY OF THE STUDY The Population Sample Classification of the Sample Instrumentation Collection of the Data The Statistical Model and Computation Pro- cedures Description of Multiple Discriminant Analysis Assumptions of the Statistical Model Summary iv ' Page ii iii iv vi vii viii \OO‘ 0‘ UIWNNHH l-’ Chapter IV. V. THE ANALYSIS OF THE DATA Results of the Multiple Discriminant Analysis The Test of the Hypothesis Interpretation of the Significant Discri- minant Functions Interpretation of Factor Patterns of Discriminant Functions Interpretation of Group Centroids The Validation The First Validation The Second Validation Summary SUMMARY AND CONCLUSIONS Summary Conclusions Implications for Future Research BIBLIOGRAPHY APPENDICES Page O‘O‘U‘L U1 \TlU'l-P’JT’JT-t' #1" Wk») U Nl-HO \O NS’OCDUIN l--J O‘O‘ b») O‘C‘ \OU'l Table 1. 2. 9. 10. 11. LIST OF TABLES Definitions of Self Terms Number of Students in Each Group, Classified by Curriculum II. Abilities VI. Occupational Experiences and Plans Coefficients of Total Intercorrelation Among The Variables Used in the Study Latent Roots, Chi Square Values, Degrees of Freedom, and Statistical Significance Levels for Each of the Fifteen Discriminant Functions Latent Roots in Rank Order by Corresponding Percentage of Variance F‘Ratios Used to Determine Significant Dif- ference of Variables Factor Pattern for Discriminant Functions Classification of Validation Subsample Group Clusters Measuring "Hits" in Validation vi Page 23 25 26 3h 38 39 in 143 so 55 Figure 1. 2. LIST OF FIGURES Group Centroides in Two-Dimensional Space Three-Dimensional Plotting of Group Means on the First Three Discriminant Functions, Ac- counting for Approximately 70% of Dispersion Variability vii Page ’47 52 Appendix A B LIST OF APPENDICES Page Academic Structure of Michigan State University 69 Group-Means for All Twenty-Seven Groups and for the Total Group on the Measures Employed in the Study . 70 Standard Deviations of the Measures Employed in the Study for all Twenty- Seven Groups and for the Total Group 72 Conventionalized Discriminant Coefficients Corresponding to the Ten Significant Dis- criminant Functions 7h Centroid Coefficients 76 viii CHAPTER I THE PROBLEM N339 In the mainstream of counseling there flows a continual current of concern relative to the selection of a college major. There is a common concern on the part of administra- tors and students. Student anxiety relates not simply to the initial selection, but also to subsequent major change. As one counsels with these young people it becomes increasingly evident how heavily this decision or choice weighs upon their minds. College administrators, likewise, are faced with meeting student needs in providing for adequate faculty, in- structional facilities, and staff. It is imperative that personal, vocational, and academic counseling be available for all students; in coordination with all other administrative procedures. Thus, the earlier the student makes his choice of undergraduate major, and the more clearly defined the choice may be, the better it becomes for all concerned. Prediction and classification are signally important in the counseling of the freshman student. Purpose The over-all purpose of this study is to identify through the predictive use of certain elements of self con- cept, the academic fields of concentration that a college student will select. This will deal with the problem of classification, primarily; that is, to answer the question, ”To which group does a person most belong?" This study is not intended to identify the vocational choice of incoming students, or in any way to relate choice of major to such vocational choice. It does not intend to predict the degree of success the individual may expect to enjoy in his chosen field of concentration. Delimitations This study is limited to testing a method of predicting the area of concentration for the incoming freshmen student. Some significance must be placed upon the fact that the in- dividual's preferences are subject to change. Experience has shown how choice of major may be affected by a change which takes place within the student after entering the freshman year of study. Environmental, social, and academic influences are some of the causative factors. It must be recognized that young people are constantly in a state of change which intensifies with their growth in independence from the family and interdependence with society in general. The application of this change to any prediction that is made may have a profound effect in the end. Hypothesis Self-concept theory clearly points up the aspect of in- ' dividual difference and in turn suggests the reason for dif- ferences in academic choice and field of concentration. ‘The notion has grown that there exists sufficient criteria to discriminate in relation to college, curriculum, or major, depending upon an adequate number for reliability. The choice of curriculum grouping is made on the grounds of this adequacy of membership. The subsequent hypothesis re- sults: HR: It is possible to differentiate among groups of students classified by curriculum two years after initial entrance to college, on the basis of an identifiable pattern of self concept of ability and occupational choice as entering freshmen. For the purpose of statistical testing, the hypothesis is stated in null for as follows: HO: There is no difference in self concept of ability and occupational choice, as entering freshmen, among groups of students classi- fied by curriculum two years after initial entrance to college. The null hypothesis assumes that all of the groups of students may be considered members of the same parent pop- ulation and no differences exist among groups, as entering freshman, in self concept of abilities and occupational choice. Upon analysis of the data, if the null hypothesis should be rejected, the difference among groups will be examined. It is expected that these differences will supply a discri- minant function in the form of a linear equation which, when applied to the validation sample, will identify the group that the individual student most closely resembles. Theory Adolescence is, clearly, a period of exploration. It is a period in which boys and girls explore the A society in which they live, the subculture into which they are about to move, the roles they may be called upon to play, and the opportunities to play roles which are congenial to their personalities, interests, and aptitudes. It would be a mistake, however, to view adolescence solely as a process of finding out "what goes“ in the adult world and then adopting these modes of behavior. The adolescent brings a great deal to this world him- self: he brings his SELF. ‘What he sees, what he tries, how well he likes it, and how well he succeeds at it, depend upon his self as well as upon the culture. Donald Super's extensive investigation of the field of vocational choice and vocational counseling has produced significant understanding of development of self concept. It becomes increasingly clear that self concept, even in its emergent stage, influences the young person in many ways. One of these, it is thought, is that choice of an area of concentration upon entry into the university life. Partic- ularly, when faced with a decision which for the most part is his own to make, the student realizes the importance of such choice. It is felt that he calls upon all the resources of his past experience and that his self concept often emerges sovereign to thus influence his choice. For those who are unable to make the choice and who continue in some type of curricular exploration for the first year or two, it is hoped that some measure of direction could be supplied by an anal- ysis of his self concept. Where there has been considerable use of achievement and aptitude test scores in the past for this purpose, this study will apply only measurements of self concept of ability and occupational choice. lsuper, Donald E. THE PSYCHOLOGY OF CAREERS. Harper and Rowe, New York, 1957, p. 61. Overview In the foregoing pages of this chapter there has been set forth the problem as it relates to the need, the pur- pose, the hypothetical setting and the theoretical base. Following, in chapter two, is a review of the litera- ture dealing with the related studies and the expediency of the use of discriminant analysis. 9 In chapter three there is presented the methodology of the study. Included is a description of the population and validation sample, together with the instrumentation, the processing of data, and the analytic procedures. Chapter four includes the analysis of the data and a discussion of the significant findings. Summary, conclusions, and implications for further re- search are reported in chapter five. CHAPTER II THE REVIEW OF THE LITERATURE Definition of Terms The literature is replete with publications which re- late to self concept. Books, journal articles, papers, and research are rather profuse. One can find support for almost any position he wishes to take. Although Super may appear to have some special influence in this study, it is not intended that his theoretical position is hereby accepted for the basis of this study. It is felt, however, that Super does present a theoretical position with which this study can closely identify. Self concept as Super suggests is a con- stellationl. The self-concept system is made up of the various self concepts, the pictures which the individual has of him- self in different roles and in different types of sit- uations. Thus it should be noted that it is incorrect to write of the self concept as though each person had just 222: each person has a number of self concepts, but one self-concept system at any point in time. What he is suggesting is that the self concept has, first, a simplicity and, second, a complexity. In its simple form, a self concept is the individual's picture of himself. There seems to be something of a more basic nature, then, in the perception of self. This self percept enables one to 1Super, Donald E.; Starishevsky, Reuben; Natlin, Norman; Jerdaan, Jean Pierre. CAREER DEVELOPMENT: SELF-CONCEPT TBEggY. New York: College Entrance Examination Board, 1963. p. O 6 see himself in some role, situation, position, or relation- ship. Thus, as self percepts relate to other self percepts, one acquires a self concept. The self concepts, in turn, abstract and generalize into complex self concepts, organ- ized around some status or role. Super speaks of complex concepts as "...organizations of simple concepts (themselves percepts with accrued meanings), they constitute frameworks into which new percepts are fitted as judgments of relevance are made by the perceiver; .....Self concepts therefore tend to be self-perpetuating and are relatively enduring".2 This leads directly into Super's self-concept system which, being general and inclusive, contrasts with the more specific and limited aspect of the self concept. Development takes place as certain self percepts evolve into occupational terms. With this comes the vocational self concept which is often synonymous with vocational preference. Super, however, would decide against this rather absolute identification. He suggests that there is room for accepting or rejecting this position as the individual considers the vocational relevance of the situation. Since there have been several treatments of the "ego", "self", and "self concept", it is felt that this study should be limited to those definitions which relate to its theore- tical base. Table I lists these definitions. A mere definition does not suffice, either. Combs and 2Super. Ibid., p. 12. TABLE 16 DEFINITIONS OF SELF TERMS SELF PERCEPT Primary self percept: unmodified or raw impression of an aspect of the self. Secondary self percept: simple self concept which has come to function as a percept. SELF CONCEPT Simple self concept: organized, related percepts with accrued meaning. Complex self concept: abstraction from and generalization of simple self concepts, generally organized in a role framework. SELF-CONCEPT SYSTEM The constellation, more or less well organized, of all of the self concepts. VOCATIONAL SELF CONCEPT The constellation of self attributes considered by the in- dividual to be vocationally relevant, whether or not they have been transplanted into a vocational preference. 6Super, op. cit. p. 19-20. Snygg3 say that self concepts are inferred from behavior as contrasted to reported (self report) self concepts. English and English define concept as follows: any object of awareness together with its signi- ficance or meaning; anything that one can think about that can be distinguished from other things. 4 It is inconceivable that a self concept, by its inherent nature, can exist without the individual having awareness. Wylie5 argues for the value of the reported self concept. Her argument is from logic that says that without awareness the individual cannot report, and without reporting how can another know if the individual has a self concept. Inferred self suggests an outsider's concept. Self-Concept Theory Within recent years there has been a resurgence of interest among psychologists in the concept of the self. William James in his famous chapter on the self in Principles of Psychology (1890, Chapter X) set the stage for contemporary theorizing, and much of what is written today about the self and the ego derives di- rectly or indirectly from James. James' consideration of the self involved the "Empirical Me” and revolved around self-constituents, self-feelings, and actions of self-seeking and self—preservation. From this 3Combs, A. w. and Snyg , D. INDIVIDUAL BEHAVIOR. New York: Harper and Bros., 19 9. pp. hho-NNZ. “English, H. B. and English, Ave C. A COMPREHENSIVE DICTIONARY 0F PSYCHOLOGICAL AND PSYCHOANALYTICAL TERMS. New York: Longmans, Green & Co., 1958. 5Wylie, Ruth C. THE SELF CONCEPT. Lincoln: University of Nebraska Press, 1961. p. 18. 7Ha11, Calvin 3.; Lindsay, Gardner. THEORIES or PERSON- ALITY. New York: John'Wiley & Sons, Inc., 1960. p. h67. 10 grand summation, others began to delineate. Leckya, al- though not developing a comprehensive theory of personality, contributed the idea of unification to personality develop- ment. In the foreword of Lecky's book, Gardner Murphy says ”Lecky had in his own way developed...the conception that the individual must define for himself the nature of that totality which he is. He must throughout life assimilate new experiences in such fashion as both to be and to appear a living unit.”9 There appears to be a close tie in this aspect with Super's idea of the self-perpetuating and endur- ing nature of self-concept. Following upon Lecky's mid-thirty treatise, Allport ”rediscovers" the ego in psychology. Ear- 1ier, he had avoided self-concept issues10 but finally had to face the crucial question ”Is the concept of self necessary?”11 ' To avoid confusion he takes shelter in his ”proprium” which includes bodily sense, self-image, propriate striving, and knowing. Super positions himself very positively relative to self- concept theory. He views the self concept as a dynamic phe- nomenon, which is always exerting influence upon the individ- ual according to the stage of life in which he finds him- self.12 The self concept finds its beginning as it develops 8Leaky, P. SELF CONSISTENCY. New York: Island Press, 19h5- 91bid., p. l. 10Allport, G. w. PERSONALITY: A PSYCHOLOGICAL INTERPRE- TATION. New York: Holt, 1937. 11Allport, G. W. ”The E o in Contemporary Psychology,“ 50 Psychological Review, (19 3), h51-h78. IZSuper, Donald E. THE PSYCHOLOGY 0F CAREERS. New York: Harper and Bros., 1957. pp. 80-161. 11 out of the roots of earlier identifications. Probably during adolescence and the attendant exploration, if not earlier, the individual enters into initial ideas of self concept re- lative to a career. These may not always be realistic or compatible with each other, but through trial and error, the individual sorts out the satisfying elements. Out of that self, then, which each person brings to this world, emerges the self concept as it comes into vital contact with the world of experience around him. Through explorations of many types the self concept grows and widens. A transition takes place as the individual moves from the home into a world of work. Home offered much identification and limited self concept; the school allowed a broadening out of the self concept and associated part-time work enabled further development. With the move from this environment came a time for reality testing both of a cultural and occupational nature. In this framework arises the conflict of aspiration level and achievement. Later it will be established that herein lies the problem with which this study is involved. The implementation of self concept involves an adjustment process in every area of life. With this adjustment comes recognition of reality and the acceptance of those components of the self concept which are compatible with each other. Aspects of the self concept which bring satisfaction are re- tained, while those which do not bring gratification are in due course rejected and replaced by traits and behaviors which stand the test of reality. One or more of the con- flicting traits or behavior patterns is modified in a way 12 compatible with the rest of the self. This is the process of personality integration13. It would appear that the theory of self concept is a theory of personality integra- tion, to the extent that it would involve self-awareness and self-actualization. From this vantage point one sees the application of such theory to the area of curriculum choice. Torrancelh descri- bed the use of self-concept data in the educational counse- ling of college students, and concludes as follows: Securing self-evaluations from entering college freshmen is a quick, inexpensive procedure, and could well become a part gf a college program of evaluating entering freshmen.l Its correlates of adjustment and the insight it gives of the individual's own per- ception of himself add much to the meaning of the re- sults of freshmen test batteries. The device for re- cording self-estimates places the notion of the self- concept in sufficiently concrete terms to be meaning- ful to faculty advisers. The techniques for using it can be made sufficiently simple to be useful to fac- ulty advisers and yet potent enough to achieve the depth necessary for modifying self-concepts. Choice Theory and Career Development Wrenn16 indicated that there is not one self concept, but many. In one sense every new role or relationship into which an individual enters may produce a new self concept. 13Ibid., p. 231. 11"Torrance, E. Paul. ”Some Practical Uses of a Know- ledge of Self-Concepts in Counseling and Guidance," 1h Ed- ucational and Psychological Measurement, (l9Sh), 127. 15Michigan State University Summer Counseling Clinics beginning in 1962 have already begun such an evaluation. This study finds its basis in such an evaluation. 16Wrenn, Gilbert C. "The Self Concept in Counseling," 5 Journal of Counseling Psychology, (1958), 10h-109. 13 Thus it is possible to conceive of a special, vocational self concept which is composed of those distinctives like atti- tudes, ideas, feelings, and desires which a person holds about himself and his relationship to a world of work. The self concept has been tied in with various aspects of voca- tional choice in any number of theories of occupational development. With the use of the Strong Vocational Interest Blank, Carterl7 suggests that inventoried interests of adol- escents are organized as are those of adults in various occu- pations even before they have had experience in those occu- pations. Bordin18 also theorized that it would be possible to view all studies of vocational interest inventories as investigations of self concepts in relation to vocational interests; and, when the study is longitudinal or deals with several cross-sections, to relate self concept to vocational development. In more recent days Blocher and Schutz19 have indicated the similarity between self concept and occupa- tional concept. Super20 takes an almost absolute position in suggesting that occupational choice is actually an at- tempt to develop and implement a certain self concept. He 17Carter, H. D. "The Development of Vocational Atti- tudes,” A Journal of Counseling Psychology (19h0), 185-191. 18Bordin, E. S. “A Theory of Interests as Dynamic Phe- flgmgza,“ 3 Educational and Psychological Measurement, (19h3), 19Blocher, D. H. and Schutz, R. A. "Relationships Among Self-Descriptions, Occupational Stereotypes and Vocational gigfgignces," 8 Journal of Counseling Psychology (1961), 20Super, Donald E. ”Vocational Adjustment: Implement- ing a Self Concept," 30 Occupations (1951), 88-92. 1h virtually equates self concept development with vocational development. Definitionally, he speaks of "a reality-tested choice."21 Stephenson's22 presentation of occupational choice as a crystallized self concept establishes implementation of choice or entry as more realistic than simple preference in the Ginzberg theory23. In an earlier day Tylerzh suggested a relationship between aptitudes and interests to build a theory of vocational development around the concept of iden- tity. In more recent times she has reached toward a broader or possibly more basic position in expressing, "the core of individuality consists of a person's choices and the way he organizes them."25 Her feeling was that practice in choice situations could increase a person's self-awareness and self- direction. The future holds great opportunity for investi- gating the whole process by means of which the individual sets the pattern for his own further development by the ZISuper, Donald E. "A Theorg of Vocational DeveIOpment," 8 American Psychologist (1953), 1 5-190. 22Stephenson, Richard R. “Occupational Choice as a Crystallized Self Concept," 8 Journal of Counseling Psycho- logy (1961), 211-216. 23Ginzberg, E.; Ginsburg, S. W.; Axelras, S.; and Herma, J. L. OCCUPATIONAL CHOICE. New York: Columbia University Press, 1951. 2 uTyler, L. E. "The Development of 'Vocational Inter- ests': The Organization of Likes and Dislikes in Ten-Year 01d Children," 86 Journal of Genetic Psychology, (1955), 33-uu. 2STyler, L. E. "Research Explorations in the Realm of gggice," 8 Journal of Counseling Psychology (1961), 195- 15 choices he himself makes. In the understanding of choice theory one is led to recognize that the idea of choice is not just single in nature but a succession of choices which sets up the notion of career development. There is not an affluence of literature in this area as there is in occupa- tional and vocational choice. Many of the outstanding con- tributions in the theory of occupational choice could so easily have reached out to this aspect of choice theory. Curriculum Choice The sophistication of the self-concept development, in theory, has almost entirely by-passed, in practice, its im- plementation to college freshmen for their choice of academic major and field of concentration.~ This intermediate stage is becoming more critical as the academic preparation of young people becomes more specialized. This critical stage is best expressed in terms of choice of academic major. Borow, et. a1.,26 speaks for an emphasis on self-theory in, coun- seling students within a framework of occupational psycho- logy which would avoid, to considerable extent, the psycho- metric patterns as in the General Aptitude Test Battery of the U. S. Employment Service and Strong's Vocational Inter— est Blank. His colleagues would call for "student develop- ment in the educational setting"27 (Pepinshy) and an inte- 26Borow, H.; Pepinsky, H. B.; and Dresselfi P. L. ”Frontiers in Personnel Research in Education, in Henry, N. B. (ed.) Personnel Services in Education, 58th Yearbook, Part II (Chicago: National Society for the Study of Edu- cation, 1959). 271bid. 16 gration of educational experience and self-fulfillment28 (Dressel). The critical issue appears to be individual dif- ference in the self concept as it relates to choice of aca- demic major. Studies in this field of prediction are rare using differential indices. Some work has been done in pre- dicting success in specific institutions and with specific groups, but, much remains to be done with prediction for new groups 0 Multiple Discriminant Analysis The intention in this study is to utilize the multiple discriminant analysis method as a research tool. Previous research has indicated without question its utilitarian value. Tatsuokoa and Tiedeman29 have summarized in consid- erable detail the literature and research of discriminatory analysis. The historical, theoretical, and mathematical development has been handled rather efficiently in a sum- mary by HodgesBO. One finds considerable overlap in these two summaries but without distress or loss of impact. The literature of this field pertaining to education has been summarized periodically in the REVIEW OF EDUCATIONAL RE- SEARCH, as well as other publications. The American Council 28Ibid. 29Tatsuokoa, M. M. and Tiedeman, D. v. "Discriminant Anal sis," 2h Review of Educational Research, (December, 195h s hOZ-HZO. 30Hodges, Joseph L., Jr.' "Discriminatory Analysis: 1. Survey of Discriminatory Analysis, Report No. 1, Project No. 21-h9-00h, U.S.A.F. School of Aviation Medicine, Randolph Field, Texas, October, 1950. 17 on Education sub-committee study on prediction of success in professional schools reviews results obtained using various predicters31. Baker32 selected nine studies to review in- cluding Rulon, Baggaley, Jackson, Bryan, Tiedeman (Bryan, Rulon), Collister, Christensen, Tiedeman and Bryan, and Dunn. His work of comparing objectives and distinguishing aspects of the research undertaken by each is clearly presented and handled with considerable efficiency. Kron's report on the literature, as well as the results of his research, although primarily centered in the area of nursing, clearly indicates the advantage of the use of non- intellective variables for research by multiple discriminant analysis.33 In consideration of the literature as it relates to the use of multiple discriminant analysis, Collister sums it up: The multiple discriminant technique requires that all members of the groups in the analysis take the same tests. This technique then uses all of the avail- able information to make inter-group comparisons. The statements that can be made on the basis of discrimin- ant analysis do not concern goodness or badness along the criterion scale. Rather, they concern the belong- ingness of the individual to the criterion group.... It is suggested that when the major question to be answered concerns the likeness of an individual to a defined 3lstuit, D. B., et. al.s "Predicting Success in Profes- sional Schools,” American Council on Education, Washington, Dc Co, 191490 32Baker, Charles D. "Classification into College Major- Areas of Concentration by Means of Multiple Discriminant Function Weighting of College Entrance Test Scores." Unpub- lished doctoral dissertation, University of Kansas, 1957. 33Kron, Ralph E. "Multivariate Classification for Con- trasted Success Groups of Student Nurses." Unpublished doc- toral dissertation, University of Kansas, 1957. 18 group from a number of alternative groups, discriminant analysis is more appropriate. A Summary The foregoing review of literature has consisted of a critical examination of the theory which constitutes the basis for this study. Super3S has proposed that occupation- al choices are sets in the implementation of a self concept. The person choosing an occupation does so in the belief that the roles he will play in that occupatiOn will be consistent with his picture of the kind of person he is. Choices will be made to maintain compatibility between occupational roles and self concept. Although the literature does not suggest any study as ambitious as this having been undertaken, yet, there is evidence to suggest that the time is ripe with the avial- ability of computer assistance and the ready program of CDC 3600. It may also be noted that Kron demonstrated that when he made use of non-academic test variables there was an imm portant increase in the predictive efficiency of the battery.36 3“Collister, E. Gordon. ”A Comparison of Interest In- ventory Scoring Keys Based on Educational and Vocational Groups with Respect to Effectiveness of Classifying Entering College Freshmen Among Alternative Colleges by Multiple Dis- criminant Analysis." Unpublished doctoral dissertation, Syracuse University, 1952. 3SSuper, op. cit., 1951. Super, op. cit., 1957. Super, D. B.; Crites, J. 0.; Hummel, R. C.; Moser, Helen P.: Overstreet, Phoebe L.; and Warnath, C. F. VOCA- TIONAL DEVELOPMENT: A FRAMEWORK FOR RESEARCH. New York: Columbia University, 1957. 36Kron, op. cit., pp. 7h-75. 19 It is felt, therefore, that such research of non-intellective factors for the purpose of prediction is highly justified. Self-concept theory, as Super et a1 apply to vocational choice, is similarly handled in this study as it relates to curriculum choice. The assumption is made that occupational interest tends to affect academic choice. The instrument was developed on the order of the Strong Vocational Interest areas, and, therefore, presents some occupational stereo- types. CHAPTER III DESIGN AND METHODOLOGY OF THE STUDY THE POPULATION The population selected for this study consists of the freshmen entering Michigan State University in the Fall of 1963. Five thousand seven hundred and forty-one students _were classified as first-time freshman at Michigan State University during the fall registration periodl. Sample In order to best achieve the goals of the study, cerm tain restrictions were placed on the population. The fol- lowing suggest the delineations which took place for member- ship in the study sample: 10 All members must have been first-time Michigan State University entering freshman, in the Fall term of 1963. 2. All members must have attended a Summer Counseling Clinic prior to registering for the Fall term of 19 3. 3. All members must have satisfactorily completed the Personal Information Inventory. h. All members must have been enrolled for classes two years later, Fall term of 1965. 5. All members must have chosen a major area of con- centration. With these qualifications observed, the restricted popu- 1Data obtained from Michigan State University, Office of the Registrar. 2O 21 lation of the study numbered 2,258 students. This total in— cluded male and female and disregarded any demographic or other available data. It is interesting to note that the total number of students registered for the counseling clinics was h,h33 first-time freshmen, and 66h transfer students. The attrition can be attributed to the restric- tion for membership, the drawing off of a validation sample of 25% by the extraction of every fourth IBM card, and var- ious errors committed during the key punch Operations. Classification of the Sample In view of the rigid requirements for membership, the sample for analysis is very selected. By nature of the method by which the validation sample was obtained, a true random sample of the selected sample to be analyzed resul- ted. The method will be noted later. Entering freshman in the Fall of 1963 were required to have filled out a Personal Information Inventory if they at- tended a Summer Counseling Clinic. Those students whose in- ventories which were filled in completely and with sufficient clarity were checked two years later in the Fall of 1965 to ascertain, first, whether they were enrolled, and, second, their choice of academic major. This choice of academic major was the initial basis for classification into groups. However, it was felt that several of the groups, classified by major, lacked sufficient numbers for reliability. A mix- ture of unrelated groups could not be justified. Thus, it was felt that hmmogeneity of groups could be obtained by 22 enlarging the classification to curriculum groups. In this sense a curriculum is considered to be a cluster of special- izations (majors) within a defined discipline of study. The established base for size was set at 30 members. The final classification used in the analysis and the numbers in the various groups are reported in Table 2. The inclusion of three academic majors among the curriculum groups may be notedz. This may be defended on the grOunds that their individual size and significant area of special- ization set them apart from the curriculum of which they are a member. The randomization of the validation sample was achieved by arbitrarily selecting every fourth IBM card from leach of the classified groups3. 2AppendixA indicates the structure of academic study at Michigan State University. 3Students at Michigan State University are assigned student numbers. Each number consists of six digits. The student number of each student whose Personal Information Inventory was complete was punched in the first six columns of an International Business Machine card. The balance of the information frmm the inventories was also punched into the cards. This included the group classification and var- iables to be used in the analysis. 23 TABLE 2 NUMBER OF STUDENTS IN EACH GROUP, CLASSIFIED BY CURRICULUM GROUP # CLASSIFICATION FREQUENCY 1 Agriculture 92 2 *Packaging 57 3 Humanities 135 % Art 0 Literature 105 6 Romance Languages 51 3 History ' 66 Accounting & Financial Administration 76 9 Hotel, Restaurant & Institutional Management NH 10 Business Law, Insurance & ‘ Office Administration 136 11 Marketing & Transportation Administration NO 12 Communication Arts 126 13 Elementary Education 257 1h *Special Education AZ 15 Health, Physical Education & Recreation 55 16 *Electrical Engineering 55 17 Engineering 77 18 Home Economics 1N3 19 Biological Sciences 95 20 Physical Sciences 65 21 Mathematics and Statistics 89 22 Nursing 20 2 Social Science 1 0 2 Political Science 69 2 Psychology 8h 26 Social Work 62 27 Veterinary Medicine N1 TOTAL 2258 flMcjcr areas included in curriculum groupings. 2h INSTRUMENTATION In order to achieve the purposes of the study, it is necessary to relate only to the Personal Information Inven- tory. This inventory lists such data as General Information, Abilities, Activities, and Preferences, Educational Exper- ience and Plans, Occupational Experiences and Plans. The data to be used in the study relates to those self concepts which reflect abilities and occupational choice. Fifteen variables were used; six reflecting self concept of ability and nine indicating self concept in occupational roles. The measurement of self concept of ability in each of the six variates ranks from zero (superior) to four (low). The student was required to arrange the nine occupational roles in rank order according to the way he perceived himself in relation to them. Table 3 gives indication of the means of measuring self concept of abilities. Table N indicates the means of rank ordering of occupational roles. In the original form of 1963, the first three choices of occupational roles were required and also an indication of those which were completely rejected, by use of the ”X" column. In the 1965 form, a rank ordering of all nine was required. Thus, in order to equate the two forms in a parallel manner, insofar as possible, the 1963 ranking was restructured on the IBM cards so that 1 was punched l, 2 was punched 2, 3 was punched 3, X was punched 8, and any not chosen were punched 5. This may be justified by considering 8 as the mean of the last three possibilities and 5 as the mean of the intermediate three where there was some uncertainty. 25 TABLE 3 II. ABILITIES” Compared with other entering students here, I think my gen- eral capacity for college work is 0. Superior 1. Above Average 2. Average 3. Below Aver- (Upper 10%) (Upper quarter) (Middle 55%7 (Lower quar- age A. Low ter) (Lower I0%) Compared to other entering students here, I think my aptitude for solving numerical reasoning problems is 0. Superior 1. Above Average 2. Average 3. Below Aver- (Upper 10%) (Upper Quarter) (Middle 5&37 (Lower quar- age A. Low tar) (Lower 10%) Compared to entering students here, I think my aptitude for understanding and reasoning words is 0. Superior Vl.‘ L 4 _ 1. Above Average 2. Average 3. Below Aver- age h. Low Comparing my own abilities in these two areas, I do 0. Better in verbal than numerical 1. Equally well in either 3. Better in numerical than in verbal. . Compared to other entering students here, I think my reading skill is 0. Superior 1. Above Average 2. Average 3. Below Aver— age h. Low The grade average I think I will be able to obtain at M.S.U. is O. A 10 B to B" 20 C" to B" 30 C Ll. C'- or under hReproduced from the Personal Information Inventory, Fall 1963, Michigan State University, East Lansing. 26 TABLE 1, VI. OCCUPATIONAL EXPERIENCES AND PLANSS In the following list select the one group of occupations in which, on the basis of interests and abilities, you believe you best fit. Check it under the first choice. Select the one group of your second choice and mark it under second choice. Mark a third choice too. Then mark under X any group of the six remaining in which you feel you would £22 fit. - i - 1st 2nd 3rd A X Occupation requiring special artistic abilities, such as musician, actor, artist, designer, interior decorator, etc o Occupations involving work in physical scienCBs, such as engineer, chemist, ‘mathematician, physicist, et. Occupations involving work in biolo- gical sciences, such as zoologist, botanist, nurse, physician, etc. Occu ations involving mechanical and or technical skills, such as farmer, aviator, printer, industrial arts, etc. Occupations involving social service activities, such as social worker, teacher, personnel man, youth leader, etc. Occupations involving business detail, such as cashier, accountant, banker, r statistician, stenographer, clerk, etc. Occupations involving business contact with people, such as sales, promotion- al work, politics, etc. I 5Reproduced from the Personal Information Inventory, Fall,1963, Michigan State University, East Lansing. This measurement was loosely derived from the occupational groupings suggested through use of the Strong Vocational Interest Blank, 1960. 27 TABLE h (Continued) lst 2nd 3rd Occupations involving verbal or lin- quistic work, such as lawyer, author, newspaper man, advertising, librarian, etc o Occupations involving responsibilities such as director, office manager, foreman, production manager, etc. 28 COLLECTION OF DATA During the Counseling Clinics for freshman in the summer of 1963, it was requested of the attending students that they fill out the Personal Information Inventory. The data from this instrument were initially gathered by the Michigan State University Counseling Center. Having met the first three restrictions, previously mentioned, those remaining students were checked through the Office of the Registrar to ascertain their acceptability relative to the last two restrictions. THE STATISTICAL MODEL AND COMPUTATION PROCEDURES Frances E. Dunn6 of Brown University established two possibilities for predicting choice of college majors. In this article she discusses the validity of the two proce- dures. Multiple discriminant analysis was suggested as superior to multiple regression analysis for determining to which group a student seems to "belong”. Since there is no idea of predicting success, which the regression method undertakes, it was felt that multiple discriminant analysis best suited our needs. Multiple discriminant analysis is a statistical method of combining test scores or other data so as to maximize the differences between the groups and gig;- ‘migg the difference within each group. Through the separa- tion of individuals who are known to belong to mutually exclusive groups, it is possible to determine the combine- 6Dunn, Frances E. "Two Methods for Predicting the Se- lection of a College Major," 6 Journal of Counseling Psycho- logy, (June, 1959)9 15‘270 29 tions of variables which will maximally discriminate among the different groups. It is also possible to observe the magnitude of the group differences and to classify future individuals into one of these groups on the basis of similar data. In this study, individuals had been classified ac- cording to curriculum choice two years later at Michigan State University. A set of fifteen measurements for each member of twenty- seven defined and mutually exclusive groups was collected.7 The study required a statistical approach which would give maximum discrimination among the twentymseven groups on the basis of the information available. The intensity and di- rection of the difference also was vital. Because of the nature of the interrelationship between the variables, it was viewed as necessary to use a technique which would identify basic, independent factors which accounted for group differences. Description of Multiple Discriminant Analysis Computations required for obtaining discriminant func- tions, when a large number of groups and variables are being studied, are such that modern card-punching and/or electron- 8 ic equipment is needed . This analysis produces discrimine ants of such linear nature as to weight the variates and 7See Table I 8Computer Institute for Social Science Research, Mich- igan State University, Technical Report 33, "DISCRIM: MUL- TIPLE DISCRIMINANT ANALYSIS,“ Programmed by Dr. P. Lohnes, University of Buffalo; Modified for CD0 3600 by A. V. Wil- liams, CISSR. Language: 3600 FORTRAN. October 26, 1965. 3O produce the greatest amount of separation among the fields possible with the data used. When the weights are then applied to test scores of a new student, the resultant dis- criminant scores would suggest to which group the individual most likely belongs. This study will not include the detail of the computational procedure involved to develop such sta- tistical elements as intercorrelation matrix, means, standard deviations, variances and co=variances, A matrix, W matrix, etc., since this was handled by the CDC3600 programming. This basic information is available in several different presentations. 9 clearly dessribes the multiple discriminant Ikenberry analysis computational procedures required to solve the de- terminantal equation. He follows closely the procedures ’A -}\wlv= 0. provided by Bryan10 in his doctoral dissertation and an Air Force research report by Bryan, Rulon, and Tiedeman.ll A comprehensive treatment of the development and perfection of multiple discriminant analysis technique has been pub- 9Ikenberry, Stanley 0. "A Multivariate Analysis of the Relationship of Academic Aptitude, Social Background, and Attitudes and Values of Collegiate Persistence." Unpub- iizhed doctoral dissertation, Michigan State University, 9 0. 10Bryan, Joseph G. "A Method for the Exact Determine ation of the Characteristic Equation and Latent Victors of a Matrix with Applications to the Discriminant Function for More than Two Groups." Unpublished doctoral dissertation, Harvard University, 1950. 11Tiedeman, David V.; Bryan, Joseph G.; and Rulon, Phil- lip J. "The Utility of the Airman Classification Battery for Assignment of Airmen to Eight Air Force Specialties." Cam- bridge, Mass.: Educational Research Corporation, June, 1951. 31 lished by Tatsuokoa and Tiedeman.l2 Assumptions of the Statistical Model The assumption is made for normality of distribtuion of test scores of the population to produce equal variance and co-variance matrices. No method to test the assumption was found in the literature, or in the review of previous studies using multiple discriminant analysis. Ikenberry13 refers to a correspondence with David V. Tiedeman discussing the avail- ability of a method of testing the assumption as well as the advisability of testing the assumption. Negative response precluded further activity. It was therefore determined to assume multivariate normal distribution and equality of variance-covariance matrices based upon the lack of tests. SUMMARY This study involved a population of firstatime entering freshmen of the Fall, 1963, at Michigan State University. It was required that membership in the sample include at- tendance at a freshman counseling clinic prior to fall re- ‘gistration as well as being registered for courses two years later in the Fall, 1965, with a declared major field of con- centration. This sample was classified according to curriculum. This established twentyeseven mutually exclusive groups. Pc, 12Tatsuokoa, Maurice and Tiedeman, D. V. "Discrimi- nant Analysis," 2h Review of Educational Research,(Decem- ber, 1951;)... tea-A20 13Ikenberry, Op. cit., p. 72. 32 Selection of every fourth student allowed for the provision of a validation sample. This subesample also retained its mutually exclusive group nature at the same time being rep- resentative of the sample under analysis. The instrument used in this study was the Personal In- formation Inventory. The measurements were of the nature of self concept of ability, and interest. Six of the former and nine of the latter gave a total of fifteen variables. The analysis of the data was performed through the im- plementation of multiple discriminant analysis. Computa- tional procedures were accomplished through use of the Mich- igan State University computer CDC 3600. CHAPTER IV THE ANALYSIS OF THE DATA The multiple discriminant analysis program known as Discrim and modified for use with CDC 3600 includes in the printed output a total correlation matrix indicating the interrelationships among the variables. As a matter of re- cord, group means on each of the variables used in the study are presented in Appendix B. The total intercorrelation matrix of the fifteen variables used in the study may be found in Table 5 to assist in understanding the basic rela- tionships of the variables. Generally, there appears to be some close relationship between the self-concept variables inthe area of ability. Some extension of this may also be noted upon consideration of the physical sciences interest variable. It may also be noticed that those variables, seven through fifteen, which reflect occupational interests are significantly lower in regard to interrelationship. One might assume that it may be possible to collapse the ability variables into one, using the General Ability variable as a measurement of self concept of ability along with the occu- pational interest variates to discriminate substantially the same as the fifteen variables did. However, later consider- ation of the test of hypothesis will not allow for this col- lapsing to be justifiable. 33 3h .Bovoohm Ho mochwoe coca moans nosnfianopno oocmoahacwwm* owo.ul moo.l Hao.t J¢Mmdu no.1 oHo.I wmo.| Howmmmmmmiio>Hpsowmmlldww mmo.- moo. limwmu cam. mos. moo.- mos. caunsomcaq s Haswoe wmw mso.- mmo.n omo. was. «so. moa.- HHo.- aosacoo anocaasm .ww eoo.- oma.- NHH.- moo.- omH.- omo.- moo.- Hassoo onocwnsm .NH mooo.- HNH.- moo. mod. mno.- omm.- moo.- cowasom Hanson .HH o:o.n o:o.- eoo.u mHH.a ooo.- mao. Hso.- nHHasm cooe\sooz .oH Hoo.n oeo. NHo.- mmo. sao. moo.- mmo. woocoaom Hsommmaoam .o :0a.u pea. mmo.u 001.: omo.n and. 00H. nooCOHom Hooanhnm .m meo.» mmo. has. Hmo. moH.u emo.- casuaahe .e mmm. mmo.- Hem. mom. ommw, em: as smashes sense .o mom. oom., ooa. Ame. Haasmimefiesom Ami mma. mmm.- eoo.- 7w a N no conswsmawo .: was. mom. (immaconsom Hohhoe .n woa. moaconoom Hmoahossz .N Sssaass Hanoaoe .H e a . m l s . m N H mesmeHmse. *HQDBm NEE ZH QfimD mmHm¢HM4> HMS $2024 ZOHB wmw Nao.- Hmo.- Hoo.q omH.- Hma.- cospcoo uncannsm «mm mHo. moo.- Nza.- pao.- Hanson nnocansm .NH omH.- omH.- New.: coaswom assocm .HH emo. omo. nHHHsm sooa\oooz .oH mHo. anacoaom Hsoswofloam .o moodofiom Hooamhnm .w chansons .e pm: pm Dumme>< Omaha .0 Hassm mmmmsom .m m a N no conawommmm new mcficonmom Hanm> .Mi mchonmom Hmoanoesz .N hanafina Hosoooe .H ma :H 1 ma ma .- as ,. oH o m . qumsHmw> Amen—canoes m NAB; 36 Based upon the appropriate F test, a correlation coef- ficient of .081 is significantly different from zero at the 1% level of confidence. A coefficient of .062 is significant at the 5% level of confidence.1 Accordingly, the percentage of significance among the six self concept of ability vari- ables is 86.7%. In comparison, the percentage of signifi- cance among the nine self concept of interest variables is h7.2%, and the percentage of significance between all fif- teen variates amounts to h6.3%. RESULTS OF THE MULTIPLE DISCRIMINANT ANALYSIS The Test of the Hypothesis As indicated in Chapter Three, the within and among matrices were computed in the Discrim Program by CDC 3600.2 These matrices along with the balance of the output are available for ready reference through the Michigan State University Counseling Center.3 The solution of the deter- minantal equation, lA ->\W’V = 0, was also a part of the computation output by CDC 3600. This solution was required for the test of the hypothesis of the study. Stated in null form, the hypothesis stated the following: 1Arkin, Herbert and Colton, Raymond R. TABLES FOR STA- TISTICIANS, COLLEGE OUTLINE SERIES. New York: Barnes & Noble, Inc., 1950. p. lhO. 2Computer Institute for Social Science Research, op. cit. 3The complete set of data is filed with Dr. Ralph Kron, Michigan State University Counseling Center. This volume of data includes all raw data punched on IBM cards as well as the total output both of the discriminant analysis and the validation samples. 37 There is no difference in self concept of ability and Occupational interest, as entering freshmen, among groups of students classified by curriculum two years later. Rao has established a test of statistical significance of the latent roots, or discriminant functions, to test mul- tivariate discrimination among several groups.“ This test of statistical significance of the latent roots makes use of the following equation, using chi square. x2=lN-%(p-k)lloge (1 -)\) N= the total sample of 2258 individuals p= the total number of 15 variables k= the total number of 27 groups = the latent root or discriminant function A chi square value for each root was derived by this ' formula and referred to a distribution table of chi square values. Table 6 indicates the significance level obtained for each function or latent root. The table also lists the chi square value, the degrees of freedom, and rank ordering of the latent roots or discriminant functions. Nine discriminant functions Show significance beyond the .001 level of confidence. The tenth function is signi- ficant at the .05 level such that .OS)P).02. The last five remaining roots do not show statistical significance by rea- son of their lower magnitude. These five functions were not included in the interpretation since they could represent chance variation. Considering the sum of the latent roots as an estimate ’4Rao, c. Radhakrishna. ADVANCED STATISTICAL METHODS IN BIOMETRIC RESEARCH. New York: John Wiley 8. Sons, Inc., 1952. PP- 372-72 38 TABLE 6 LATENT ROOTS, CHI SQUARE VALUES, DEGREES OF FREEDOM AND STATISTICAL SIGNIFICANCE LEVELS FOR EACH OF THE FIFTEEN DISCRIMINANT FUNCTIONS Digfigémiggnt A. X2 D. F. Sigfiiiisance v1 .756 1252.72 no .001 v2 .317 603.99 38 .001 v3 .2u1 N92.1u 36 .001 VA .185 380.29 3A .001 V5 .150 313.18 32 .001 v6 .087 178.96 30 .001 v7 .ouu 89.u8 28 .001 v8 .035 67.11 26 .001 v9 .027 58.162 2a .001 v10 .017 35.792 22 .05 v11 .018 29.081 20 .1 v12 .007 15.659 18 .75 V13 .007 15.659 16 .5 V1“ .008 8.988 18 .9 v15 .003 6.711 12 .9 39 of the total variance or dispersion among groups5 the per- centage accounted for by each root can be computed. Table 7 lists the percentage of variance accounted for by each latent root. Accordingly, the first discriminant function accounts TABLE 7 LATENT ROOTS IN RANK ORDER BY CORRESPONDING PERCENTAGE OF VARIANCE Latent Discriminant Level of Root Percentage Function Significance Value of'Trace Cumulative V1 .C01 .756 39.8630 39.8630 V2 .001 .317 16.7h13 56.60h3 Va .001 .l 5 9.7562 79.0873 V5 .001 .150 7.9100 86.9973 v6 .001 .087 8.5939 91.5912 V7 .001 .Ouh 2.3235 93.91u7 V3 .001 .035 1.8h9h 95.76u1 V9 .001 .027 1.8003 9g.16hg V1 .50 .007 0.3837 99.6098 V1 .90 .00h 0.2170 99.8268 V1 .90 .003 0.1730 99.9998‘ for approximately 39.9 per cent of the dispersion among groups; the second discriminant function would account for 16.7 per cent of the total dispersion; 12.8 per cent of the total dispersion by the third discriminant function. The last five functions fall below the accepted level of signi- ficance and account for less that 2 per cent of the total dispersion among groups.. 51bid., p. 372. hO Accordingly, the null hypothesis was rejected since it is possible to differentiate among groups of Students. Sub- sequently the interpretation of the discriminating functions which are significant to the differentiation will be presented. The solution of the determinantal equation produced a Wilks Lambda equal to 0.200858h for the test of the hypothesis of Over-all group differences. For test of hypothesis, F = 9.7285856 which greatly exceeds the F value for signifi- cance of 1.19. Again the null is rejected. Saupe6 states that each significant function is ortho- gonal to all the other functions of the analysis. The fol- lowing Table 8 of F ratios of among/within means squares establishing significant difference for each variable sup- ports the assumption of Saupe's statement. The appropriate F test sets a significant value of 1.53 at the .05 level of confidence using 26 and 2231 degrees of freedom. Cooley and Lohnes7 establish the relative contributions of the original variates to the discriminant functions. With the research hypothesis established, interpretations of func- tions is approached. An interpretation is made of only the first ten discriminant functions. 6Saupe, Joe L. "Factoral-Design Multiple-Discriminant Analysis: A Description and an Illustration," 2 American Educational Research Journal, #3 (May, 1965), 176. 7Cooley, William N. and Lohnes, Paul R. MULTIVARIATE PROCEDURES FOR THE BEHAVIORAL SCIENCES. New York: John Wiley and Sons, 1962. p. 211. NI TABLE 8 F RATIOS USED TO DETERMINE SIGNIFICANT DIFFERENCE OF VARIABLES M Variable Among Means Within Means F Ratio Square Square 1 3.563 0.322 11.05 2 10.h73 0.u78 21.91 3, .329 0.%10 10.55 F value %. .727 0. M7 25.86 3.021 0.h23 7.13 1.53 6 .906 0.860 > 8.50 7 N3. .56% 2. 22 17.98 at 8 97. 36 2. 61 36.59 9 60. 678 3.019 20.10 .95 10 26.038 2.100 12. NO 11 9u.632 3.850 2h. 58 confidence 12 32. 66 2.9u9 11.08 13 1h. 5h 2.873 5. 06 level ‘ 1 no 599 3.027 13-h1 1 18. 0N6 2.832 6.37 Number of degrees of freedom are 26 and 2231 - INTERPRETATION OF THE SIGNIFICANT DISCRIMINANT FUNCTIONS Interpretation of the discriminant functions may be undertaken by an examination of the conventionalized coef- ficients weighted by the standard deviation of the corres- ponding variable. Tiedeman and Bryan comment on the inter- pretation of discriminant functions as follows: It can be shown that the individual values of the dis- criminant function are independent of the units of measurement, and origin of coordinates of the initial variates, since the coefficients automatically adjust themselves (linearly) to the scales employed. On the other hand, the interpretation of separate coefficient does depend on the units of the initial variates.8 8Tiedeman, David V. and Bryan, Joseph 0. "Predictions of College Field of Concentration," 2h Harvard Educational Review, Spring, 195h). 132. 82 Their conclusion is that interpretation of functions may be made di;ectly from the conventionalized coefficients. Since the variables used in this study did not have similar or comparable units of measurement, a weighting procedure to obtain conventionalized coefficients was necessary. The dis- criminant coefficients were divided by the value of the lar- gest coefficient which gave a value of 1 for that coeffi- cient and subsequent lesser values for the other coefficients. Weighted, or multiplied, by its standard deviation, each in- strument produced a conventionalized coefficient for each discriminant function. The conventionalized discriminant coefficients for all ten discriminant functions are to be found in Appendix D of this study. Appendix C presents the standard deviations of the variables. Ikenberryg, using three discriminant functions, gave a clear demonstration of this method of interpreting discriminant functions. Interpretation of Factor Patterns of Discriminant Functions Since this study has produced ten significant discrimi- nant functiOns, it was felt that interpretations of those functions could be more adequately handled by a considera- tion of the factor patterns of each discriminant function. Since the first three functions account for approximately 70 per cent of the total dispersion among groups, one might expect the factor patterns of these three functions to be more productive of interpretive information than the others. Table 9 is composed of the coefficients making up the factor 9Ikenberry, op. cit., p. 79-86. 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I‘A h8 support the previous interpretation of the second function by factor patterns. The third discriminant function, plotted as an elevation arising out of the intersection of the other two-dimensional plotting allows for some interpretation in the third dimen- sion. Conceiving the group centroids as clustering in space, there appears to be several balloon-like clusters. The largest of these includes the groups of elementary education, special education, home economics, art, and so- cial work. Nursing, veterinary medicine, and biological sciences constitute another. Mathematics, engineering, and electrical engineering make up a third. Accounting, mar- keting, and BLIO form another. Literature and romance lan- guages make still another. The group centroid values are presented in Appendix E. THE VALIDATION The over-all purpose of this study was to attempt to identify appropriate academic fields of concentration that a college student might select. Having obtained discriminant functions from an analysis of the parent sample and weighting them appropriately, these functions were used to classify each individual of the validation subsample as a member of one of the criterion curriculum groups. This classification was compared with actual group membership of each member of the subsample. Two separate validations were performed. A9 The First Validation -.by comparing sums of productslo In the first validation, a set of discriminant scores was computed for each individual by using the weighted con- ventionalized coefficients and the raw scores of the var- iables used for measurement. This computation resulted in a discriminant score from each Of the ten significant func- tions for each individual in the subsample. In a comparable manner, a set of scores was derived for each group using the means of each group and the weighted coefficients. Mean discriminant scores for each of the twenty-seven groups of the individual score with the group mean score one can at- tempt classification of the individual in that group. The group mean to which the individual score comes closest is the group in which he has membership. The validation is essentially a problem of correct assignment to a group. The probability of chance "hitting" of the correct group is l in 27, or 3.70 per cent. The total number of hits in all 27 groups amounted to 331. The total subsample amounts to 567 which results in the percentage of "correct" hits as being 58.h per cent. A complete picture of the "correct" hits by group and function is seen in Table 10. However, one cannot assume that there was not duplica- tion of "hits” by different functions. Therefore, consider- ing the 5670 possibilities for ”hits" a percentage of 5.8 resulted. To circumvent this confusion which arises when 10Computer Institute for Social Science Research, Mich- igan State University, East Lansing, Michigan. Technical Report 25, PRECOMPILING PROGRAM FOR MATRIX MANIPULATION, by Alan M. Lesgold. August, 1965. 50 TABLE 10 CLASSIFICATION OF VALIDATION SUBSAMPLE Group Discriminant Functions Name No. N 1 2 3 u 5 6 7 8 9 10 Total Agr 1 2h 0 h l O 0 2 1 3 l 2 1h Pkg 2 1h 0 1 2 0 0 0 0 0 0 0 3 Hum 3 11 0 0 0 0 0 0 0 0 0 0 0 Art u 20 0 0 0 0 7 1 0 0 1 0 9 Lit 5 26 0 2 0 l 0 0 0 0 0 1 u Rom Len 6 13 l O O O 0 1 0 0 1 0 3 Hist 7 17 0 0 2 1 0 1 1 O 1 0 6 Acctg 8 l9 0 7 1 O O u 1 0 0 h 17 HRIM 9 11 1 0 0 0 1 0 0 0 0 0 2 BLIO 10 3h 1 l 6 0 O u 0 0 2 O IN Mktg 11 11 0 0 0. 0 1 O 0 0 0 0 1 Com Art 12 31 2 h 0 1 O l h 0 0 0 12 El Ed 13 66 M2 0 1 9 20 0 17 2 0 3 9h Sp Ed 18 11 3 0 0 0 0 0 0 1 1 7 12 HPR 15 1h 1 0 0 l 2 3 0 0 0 l 8 E1 Engr 16 19 0 0 0 0 2 1 0 2 1 1 7 Engr l 1 5 1 1 0 0 3 0 6 h 0 20 Home Eo 1 3 0 6 3 u 0 0 7 2 21 0 N3 B10 Sc 19 23 1 0 l 0 l 2 0 0 2 1 8 Phy Sc 20 17 2 0 h 1 1 0 0 0 0 0 8 Math 21 22 2 l 0 0 0 0 0 o 1 O h Nurs 22 10 0 2 0 0 0 10 0 0 0 0 12 Soc Sc 23 ho 1 l O 0 0 0 l O O 2 5 P01 Sc 2h 17 O 0 1 O 0 0 2 0 0 0 3 PsyCh 25 21 0 0 0 1 1 0 0 1 0 0 3 Soc Wk 26 16 0 3 1 2 1 O 0 0 0 '0 7 Vet Med 27 10 0 6 0 3 l 0 1 0 0 1 12 Total 567 62 39 28 2h 38 33 3 36 23 VI ,4 .‘1 331 51 one attempts for direct "hits", it was felt that a projec- tion of groups into three dimensional space, by thirds of the range of values of group means, offered much promise and clarity. Figure II indicates the cell in which each of the 27 group means are located in three-dimensional space. The first function gives separation from left to right, in thirds. The highest third ems plotted to the right. The second function discriminates from front to back, in thirds. The highest third of the second function is plotted to the front. The third function differentiates on the vertical plane, in thirds. The highest third is at the top. The twenty-seven values (group means) for each discriminant function were arranged in rank order and the range was di- vided into thirds in order to establish the cell block form. The group means were then plotted according to the third of the distribution in which the means would fall. This was done sequentially by discriminant function. Each group was then coded according to the position of the cell in which it was plotted, e.g., Accounting 4 M B T (middle third, back third, and top third). In a similar manner, each individual in the validation subsample was coded. By simple visual comparison of codes, it was established whether a “hit" had occurred. The plotting of the groups indicated that there were rather significant clusters where groups appeared to iden- tify with other groups. With this concept before us, it was felt that prediction of the individual student to a cluster might be comewhat practical. Accordingly, five \ \ a . \ a \ .. 17‘ 3333.3» acacia:— HO *2. nasal-«Mona: you 33.5034 .233th «sang-ahead: sauna van: 3n. no 88: 9.25 «o 33on “333331.26. an "Bean 53 clusters were formed and one isolated cell was maintained. 0f the 567 individuals in the subsample, 183 were found to be "hits". This amounts to a correct prediction of 32.2 per cent, without any duplication involved. Table 11 presents the details of each cluster. Most significant was the ver- bal-linguistic, arts and letters cluster with 52 per cent "hits”. I The lack of "hits" in the psychology group may be accounted for in the light of the closeness of the psycho- logy cluster to the clusters of physical science, biologi- cal science, arts and letters-social science (Figure II). Chance probability for hits; considering six possible clusters, would be 1 in 6 or 16.6 per cent. By comparison, the 32 per cent prediction was double the chance probability. The chance probability for hits, considering 27 possible cells was 1 in 27 or 3.70 per cent. The first group of 2h individuals which composed the Agriculture group in the subsample for validation was plot- ted by X's in the cells in which the first three functions placed them (see Figure II). Some thought was given con- cerning those which were in close proximity to the cluster. It was felt that any unidentified cell immediately adjacent to'a cell with identifiable curriculum might well reflect the aura of the cluster involved. Should that cell be ad- jacent to two such clusters, the notion was held that there might be interdisciplinary study suggested. The counselor with such a tool at his disposal could readily present such ideas to an entering student for his consideration.. The two Sh plottings in the very center cell of Figure II, being adja- cent to four clusters, could suggest the possibility of an (interdisciplinary curriculum leading to science teaching, agricultural economics or business, business teaching, or agricultural education to mention just a few. When one considers the large number of entering fresh- men who select ”no preference" as a major, this means of prediction becomes quite significant. It suggests that as few as 1/3 of those "no preference" students could be di- rected into consideration of an area of study with some justification. A somewhat larger percentage might be reached when such an instrument is used by the counselor and the student to gain insight. This notion of insight becomes the more meaningful when one considers the fact that in the academic year 196h-l965 a memo issued by Uni- versity College on changes of major11 indicates 29h7 students changed major moving either into or out of the ”no prefer- ence" area. The Second Validation - a discriminant classification op- eration12 The second validation differs from the first in a pro- 11Memo from University College, Michigan State Univer- sity, East Lansing, Michigan. Major Changes - Fall 196A- Fall 1965, North and South Campus. The memo lists 5535 changes of major, among and within ten colleges. 12Program DISCRAS, under preparation for inclusion in the Program Library of the Michigan State University Compu- ter Institute for Social Science Research: Programmed by Alan Lesgold and Stuart Thomas. Michigan State University, East Lansing, Michigan, August, 1966. 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I owmoom. m omwm 0.- opaon.- mHmHHo. wHOHHo. \mewmo. . p mnmhmm. mmmmwm.- mmmzpo. moomms. mmmoom. - w ooomuo. mHmowo. moomaH.- Hooooa. - mmomzm. m meooo. ooom0H.u mmmmHm.- onpomm. :mwmow. : mpzom:.- ooomwo. ooomwo. mpzozH. - mpzpwz. . m omwzHH.- OHJJom.- oomooo. ooooww. ommmmH. . m oommzH.- oqmme.- ooozHH. oooomo. - ooommm. - H OH> o> w> ~> .o> oHnaHnm> Acosnauco 3 Q XHQzflmm¢ APPENDIX E 76 GROUP CENTROIDS A 1 1:. 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