Some new results on the Spearman hypothesis artifact

Abstract

This note constitutes a summary of the main results of two papers devoted to Jensen’s (1980) “Spearman hypothesis”: (1) Elementary geometry shows that positive (“Spearman”) correlations between the mean black/white difference vector and the leading eigenvector of correlation matrices are artifacts, regardless of how one interprets Jensen’s ambiguous definitions of “Spearman’s hypothesis” (Level I versus Level II interpretation). (2) Empirically, the stronger Level II interpretation (which predicts positive correlations with both within eigenvectors) also arises with data that have nothing to do with g, such as SES variables indicating the number of toys and games. (3) Mathematically, the Level II interpretation implies not just approximate but perfect collinearity between the mean difference and the eigenvectors of all three covariance matrices, if one assumes multinormality, positivity of both subgroup covariance matrices, and an equal split into an HI and an LO group, regardless of whether Spearman’s factor model holds or not.