Viewing Spearman's hypothesis from the perspective of multigroup PCA - A comment on Schonemann's criticism

Jensen's test of Spearman's hypothesis is meant to demonstrate the importance of general intelligence in Black-White (B -W) differences in psychometric intelligence test scores. Schonemann purports to demonstrate, through an analysis of real and simulated data, and the presentation of a theorem, that Spearman correlations are artifacts. We discuss the theorem and conclude that the theorem cannot be advanced in support of the contention that Spearman correlations are positive and substantial by mathematical necessity. The theorem encompasses a multigroup principal component analysis (PCA), which is a viable model to investigate Jensen's proposition that Blacks and Whites differ mainly with respect to g, We view Schonemann's simulation study in the light of the multigroup PCA model, and interpret it as a study of the specificity of Spearman correlations, given model violations. As such, we find it to be open to several criticisms. Schonemann does raise an important issue, namely whether Spearman correlation can be trusted to prove the importance of g in B-W differences in psychometric IQ scores. Based on recent studies, we consider the Spearman correlation to be a suboptimal test of Spearman's hypothesis, and contend that an explicit model-based approach should be used. (C) 2001 Elsevier Science Inc. All rights reserved.