Philip R. Merrifield

10: Factor Analysis in Educational Research:

Most educational researchers will admit to some kind of knowledge of factor analysis. The terminology is widely used, and the technique appears to be almost too easy to apply. It has been said that power corrupts; the technique of factor analysis is very powerful and robust for many sets of data, and, accordingly, the responsibility of the factor analyst to his colleagues is large. There are, however, reasonable guidelines for using factoranalytic techniques which permit the clarification of much data obtained in educational research and which at the same time restrain the practitioner from wasteful exercises at the computer.

Ethnicity and Sex Distinctions in Patterns of Aptitude Factor Scores in a Sample of Urban High School Seniors

Three aptitude factor scores for each of 2,985 college-bound, urban high school seniors were used to compare patterns and levels of performance by sex and ethnic group membership. The results indicated that within ethnic groups, men and women exhibit patterns of scores characteristic of their sex. Significant differences in levels of performance between ethnic groups were found on the three factors, and differences on two factors were found for males and females.

Redundancy in the Stanford Achievement Test

The Stanford Achievement Test, Advanced, provides nine subtests which are often used by schools as normed measures of school achievement. As part of a larger study, the relation between each of these subtests and measures of special aptitudes and temperament traits was studied with a sample of 226 eighth graders. Principal factors were sought. The first eigenvalue was 6.64; the second was 0.64; the remaining eigenvalues were less than one. Convergence was obtained in eight iterations. A plot of the first factor against the second showed that all points were included in an angle of 45 degrees with several of the verbal measures clustering on one factor and all the mathematics measures clustering on the other. Results suggested the need for new discriminant validity studies of the test.

Reviews: Harman, Harry. Modern Factor Analysis. 2nd Ed. Chicago: University of Chicago Press, 1967. 474 + xx pp.

The first edition of this reference work, published in 1960, was widely and deservedly received as a major contribution to the field. The second edition may be disappointing to those seeking a text appropriate to students who do not intend to become specialists in multivariate analysis. Modern Factor Analysis must be accepted as a standard reference work, definitive and reasonably comprehensive for the middle sixties. The organization of the book is basically the same as that of the first edition. The earlier chapters provide a somewhat scanty orientation to the problems of factor analysis, a rather thorough discussion of the basic statistical model and its usual variations, and cogent summaries of the matrix algebra and vector geometry needed to assimilate the remainder of the book. As do most mathematicians, Harman assumes that once a concept has been presented and articulated with other concepts, it may be referred to by its name or symbol without repeating its definition. This approach is efficient for mathematically oriented students who will find the occasional well-placed recapitulations useful in their integration of this inherently complex method of data analysis.

12.50.:

Relationships between achievement measures and those of aptitude, sex, and personality traits were explored in a sample of 226 eighth grade students in a suburban school. Eighteen aptitude measures and a 14-scale personality inventory were administered and factor analyzed; salient tests and scales were selected as predictors of standardized measures of academic achievement. Results of a sequential, step-wise multiple regression analysis indicated that an evaluation of systems test (Figure Analogies) and a production of systems test (Word Grouping) together predicted 48 to 52% of variances in standardized tests of language, mathematics, and social studies. That sex was not a significant predictor of achievement reflected a possible breakdown in the previously identified strong sex-linked patterns between traits and achievement.

Relationships of Indices of Eighth Grade Academic Achievement to Sex and to Measures of Differentiated Aptitudes and Personality Traits

underway are seen to be focusing primarily on the instruments of change, for example, family grouping, rather than on what has happened to children and teachers working in informal ways. On looking over this collection, one is reminded of a mural which has been painted by a group of brilliant artists. Each artists style is somewhat different, and the viewer may find a particular part of the mural more appealing and pleasing than others. He may choose to focus his attention solely on that one section, perhaps because it is most familiar or because it is the easiest to study. He may be moved to admire the particular element to the extent of isolating it from the mural so that he can study it by itself, and it is to be hoped that he will realize that any small section can never represent the whole. This is a living mural which has taken twenty or more years to arrive at the present stage. It is by no means complete, but the viewer will find it a worthwhile experience to view its progress through th eyes of the authors in this collection.

Book Reviews: Cronbach, Lee J., Gleser, Goldine C., Nanda, Harinder, and Rajaratnam, Nageswari. The Dependability of Behavioral Measurements: Theory of Generalizability for Scores and Profiles. New York: John Wiley and Sons, Inc., 1972. 410 + xix pp.

that feminist isssues are addressed directly at relevant points in The Psychology of Sex Differences, but these issues are not central to the books conception. Maccoby and Jacklin state in their preface that they are both feminists; and certainly feminists and non-feminists alike have an interest in determining the facts about sex similarities and differences. In The Psychology of Sex Differences Maccoby and Jacklin have provided a sound resource for anyone interested in this search. This book is by far the best summary of sex difference research available today. It is wellwritten as well as well-organized for day-to-day reference purposes. It is a reference book well worth its price.