Multivariate Behavioral Research, 27 (2), 249-252 Copyright 0 1992, Lawrence Erlbaum Associates, Inc. Reaction to Other Commentaries Edward E. Roskam & Jules Ellis University of Nijmegen The main issue should be whether or not Guttman7s arguments concerning the relevance or irrelevance of factor analysis for the study of group differences are valid. Schijnemann adds a further argument to Guttman's, and ends his commentary by simply declaring Jensen7sconclusion another expression of the black inferiority myth. Gustafsson presents his view against Guttman's, and adds an example to demonstrate the usefulness of factor analysis. Loehlin analyses Guttman's arguments and finds them fascinating, but argues that they are only partly relevant to the issue. Loehlin's position appears t~o be similar to our own. Jensen, in his commentary, reiterates his own arguments, claiming (correctly as we blelieve), that Guttman has misunderstood or mi:sinterpreted his claims, but he fails to analyze the relevance of Guttman's arguments for the issue of studying group differences. We should sharpen our own conclusion concerning the "first I,aw" and the "missing theorem": All items from a universe of content have rlon-negative covariances in every (sub)population if and only if onelatent trait8 is involved. In addition, the iterm-trait regressions are all linear (i.e., the items are congeneric) if and only if the correlations among every (sub)set of items satisfy the tetrad condition in every (sub)population, and if and only if normalized group differences are proportional to the g-loadings of the items (for all groups). Moreover, if Spearman's (1927) two-factor theory is true, that is, each item (or test, resp.) depends on g and on a test-specific factor, and if there are group differences not limited to one factor (either g or a specific factor), it is not likely that the correlation matrix of any (sub)population will satisfy the tetrad condition, and so ]the missing theorem does not apply. The best that can be expected is that a major principal factor is present which closely re:sembles g. Loehlin proposes to rephrase Jensen7s (1985) task as one of determining whether in fact the identical factor structure holds in the combined population as in the subpopulation. We have argued that this need not be the case even if the two factor theory (g and specific factors) is true. The factor loadings should be invariant across groups, but the factor (co-)variances will in general be different. The assumption that g and specific factors are always uncorrelated can be violated by group differences. One might think of the population where MULTIVARIATE BEHAVIORAL RESEARCH Downloaded by [Memorial University of Newfoundland] at 12:02 29 January 2015