A note on the effects of score transformations in Q and R factor analysis techniques.

Abstract

In a recent article in this journal addressed to the effects of score transformations in Q and R factor analysis techniques, Broverman (1961) claims to have presented ". . . new arguments and empirical evidence of important differences not previously recognized between the two techniques as they are commonly employed." These differences are said to include "differences in results, differences in the type of inference possible from the results, and consequently differences in the theoretical implications of the data"-in a word, "differences . . . of the greatest magnitude for research in psychology."The present note is intended to demonstrate that the differences Broverman obtained from his -Q and R factor analyses do not constitute the empirical warrant for such claims. It will be shown that when Broverman's own data are reanalysed and the appropriate comparisons are made, a clear and understandable relationship emerges between the results of Q and R factor analyses "as they are commonly employed." BROVERMAN'S REASONING Broverman correctly observes that Burt's (1937) proof of the exact transposability of person and test factors does not apply to Q and R factor analyses "as they are commonly employed." He goes far beyond this, however, when he asserts that factor solutions obtained from a Q analysis (correlating people) are not even

Roles of activation and inhibition in sex differences in cognitive abilities.

“…Elimination of the "g" factor through "ipsatization" of scores, that is, expressing individual scores as deviations from the individual's general level of performance, has consistently produced bipolar factors in which simple perceptual-motor and inhibitory restructuring tasks are contrasted (Broverman, 1964), and which are related in the expected directions to physical indices of androgen stimulation (Broverman et al, 1964). However, since the removal of "g" variance, either by ipsatization or by standard factor extraction procedures, tends to artifactually induce negative relationships in the residual variance (MacAndrew & Forgy, 1963;Ross, 1963), such oppositions between abilities have been necessarily interpreted cautiously as statis-tical rather than functional expressions of relationships between abilities. Unfortunately, no unambiguous statistical method of demonstrating inverse relationships between abilities in the presence of an overriding "g" factor exists.…”

The Effect of Double Standardized Scoring on the Semantic Differential

“…The analysis of the raw data yielded the usual factors of evaluation, potency, and activity, but when only intraindividual variability was analyzed, the results were different. MacAndrew and Forgy (1963) have criticized Broverman's findings on the basis that Broverman's method of factor extraction produced rotated factors, and when rotated factors extracted from the principle components R technique was used, the results were comparable. The present study, however, revealed distinct differences between the rotated factor structure of the raw scores and the double standardized scores even though a principal axis solution was used in both instances.…”

ABILITY TO AUTOMATIZE AND AUTOMATIZATION COGNITIVE STYLE: A VALIDATION STUDY Monograph Supplement 2-V23

“…Ipsatization of scores removes normative differences between individuals which would otherwise appear as the first "g" factor in a factor analysis of normative scores (Broverman, 1963;MacAndrew & Forgy, 1963;Ross, 1963). Factors extracted from the remaining within-individual variance, either by analysis of ipsative scores, or as residual factors in a centroid analysis of normative scores, are necessarily bipolar.…”