Journal of Mental Science (1958) 104: 713-721. doi: 10.1192/bjp.104.436.713
© 1958 The Royal College of Psychiatrists
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Discrepancies Between Factor Analysis and Multivariate Discrimination among Groups as Applied to Personality Theory

Lowell H. Storms, B.A., M.S., Ph.D.

Institute of Psychiatry, Maudsley Hospital, University of London

ABSTRACT

To illustrate some of the problems arising from attempts to relate results of factor analyses to differences among groups, discriminant functions, principal component analyses, and canonical variate analyses were performed using the data from two sets of tests which were administered to six neurotic groups and a normal group (the tests had been included in a larger test battery). One set consisted of ten tests selected primarily on the basis of high factor loadings on neuroticism and introversion :extraversion factors computed with the same subjects and the larger battery of tests. The other set consisted of six tests selected primarily because they gave the largest F ratios for differences among neurotic groups. Four of the tests were common to the two sets.

It was found that the smaller set of tests yielded more significant discriminations than the larger in the discriminant function analysis. Principal component analyses of the within groups variances and covariances resulted in a similar first "dimension" in each set of tests, but the other dimensions were not alike. An important discrepancy found in this analysis was that for neither set of tests did the major dimensions of the within groups scatter (principal components) correspond with the major dimensions of the between groups dispersion (canonical variates).

The results seem to indicate that adherence to dimensions derived from factor analyses when analysing differences among groups can lead to a serious loss of information and may lead to in efficiency in practical applications or over-simplification in theoretical interpretations. It was shown that dimensions describing between groups differences need not be the same as those appearing within groups and that it is better for purposes of discriminating groups if they are not.

On the basis of the results of our analysis, Eysenck's interpretation of a canonical variate analysis which he performed and his pooling of hysterics and psychopaths to form criterion groups for the study of extraversion were called into question.