Humphreys's attenuated test of Spearman's hypothesis

Humphreys's test of Spearman's hypothesis (viz., that the size of the standardized black-white differences on various psychometric tests is positively related to the tests' loadings on g, the general intelligence factor) is methodologically weak. It is based on comparison of a fairly representative sample of the black population of U.S. school children with a highly selected sample of the white school population, representing the lowest 15 to 20% of whites in socio-economic status (SES). A fair test of the hypothesis requires that the black and white samples should not be selected on any g-correlated variable, such as SES. Selection attenuates and distorts the relationship between tests' g loadings and the magnitude of the standardized mean black-white differences on the tests. Other unorthodox conditions in Humphreys's study, such as performing factor analysis on the test-score means of various arbitrary demographic groups instead of on individual test scores inflates tests' g loadings and biases the test of Spearman's hypothesis by restriction of reliable variance in g loadings. Humphreys's study cannot be considered a proper replication of Jensen's examination of Spearman's hypothesis in 11 different studies comprising 74 different tests, which consistently bears out Spearman's hypothesis.