Famous artefacts: Spearman's hypothesis

In a number of publications, Jensen has recalled Spearman's (1927, p. 379) observation that the loadings of the first principal component (PC1) of various 'intelligence tests' tend to correlate positively with the corresponding Black/White mean differences ('Spearman's Hypothesis'). Jensen believes this sheds light on the true nature of g, Level II Ability, test bias, and Black/White differences. His claims have been warmly welcomed in some quarters (most recently by Herrnstein and Murray, 1994) as conclusive confirmation of the Black inferiority myth. Here it is shown by way of empirical, numerical, geometric, and algebraic demonstrations that the positive correlations predicted by Spearman's hypothesis are psychometric artefacts which also arise (a) with measures which have nothing to do with 'general ability', for example, the number of toys and books a child has; and, more generally, (b) with any set of moderately correlated random data, once the sample is split into high and low groups. Specifically, this interpretation predicts that if sample sizes differ substantially, then the correlation will be larger for the PC1 of the larger group. This prediction is borne out both in simulated and in 'real' data sets, including Jensen's.