Group differences and first principal-component loadings in the Hawaii family study of cognition: a test of the generality of ‘Spearman's hypothesis’

The generality of Spearman's hypothesis that varying differences between whites and blacks on various tests of mental ability are correlated with their g-loadings was tested by analyzing group data from the Hawaii Family Study of Cognition. Data from the three largest ethnic groups tested in the Hawaii Study (Americans of Japanese, Chinese or European ancestry; total N = 5333) were subjected to a principal-component analysis and the first principal component was used as a measure of g. Ethnic group and generation (parent-offspring) differences on 15 tests of specific cognitive abilities were then correlated with their first principal-component loadings. In general, correlations between ethnic group differences and g-loadings are smaller than those recently reported for white-black differences by Jensen (1983); however, those between generation differences and g-loadings are larger. Ethnic group differences on first principal-component scores in the Hawaii Study are less than parent-offspring differences; thus, the correlation between group differences on tests of mental ability and their g-loadings may be a function of the magnitude of the group difference for general mental ability. Because a group difference on g requires group differences on tests which load on g, an observed group difference in general mental ability may necessarily result in a correlation between group differences on individual tests and their g-loadings.