Peter H. Schonemann
Some new results on the Spearman hypothesis artifact
Bulletin of the Psychonomic Society, 1989, 27, 462-464
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 how one interprets Jensens'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 matirces, if one assumes multinormality, positivity of both subgroup covariance matrices, and an equal split into a HI and a LO group, regardless whether Spearman's factor model holds or not.
Essentially an early version of the main results presented and discussed in more detail in Famous Artefacts. I decided to put my results on record in this non-reviewed outlet since it had become apparent by this time that it would be a long uphill struggle to have these results published in a "peer reviewed" journal. In the event, it took 12 years.
It should be noted, in this connection, that the implications of Spearman's Hypothesis, had it not been a artifact, would have been momentous, as Jensen himself had made clear:
"...black people, statistically, will have a greater handicap in those eductional, occupational, and military assignments that are most likely correlated with measures of intelligence" (A. Jensen, Bias in Mental Testing, 1980, p. 206).
Such racist implications did not disturb the peace of mind of several editors of main stream journals, including The American Psychologist, Psychological Review, and Harvard Educational Review. For a detailed chronicle of their responses, see Schonemann (unpublished).