Viewing Spearman's hypothesis from the perspective of multigroup PCA: A comment on Schoenemann's criticism.

A. R. Jensen's (1985) 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. P. H. Schoenemann (1989) purports to demonstrate, through an analysis of real and simulated data and the presentation of a theorem, that Spearman correlations are artifacts. The present article discusses the theorem and concludes 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. The authors view Schoenemann'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. Based on recent studies, it is concluded that the Spearman correlation is a suboptimal test of Spearman's hypothesis, and it is contended that an explicit model-based approach should be used.