Jensen's procedure of calculating such correlations involves the following steps: (1) Exploratory factor analyses of psychometric data are carried out in representative samples of Blacks and Whites, separately, to extract factor loadings of the tests on g (Jensen suggests that this can be done in a number of ways, see Jensen & Weng, 1994); (2) Factorial invariance over groups is established by calculating measures of factorial congruence of the factor loadings in the White and the Black samples (congruence should be high); (3) Variation in factor loadings is required to be appreciable; (4) Differences in means are standardized by dividing by the pooled standard deviations; (5) The standardized differences in means are correlated with the g factor loadings.
The Level I interpretation is not relevant, given Jensen's procedure of testing Spearman's hypothesis.
Working within the context of PCA, one could investigate the soundness of Jensen's procedure by violating the premises of the theorem and gauging their effects on the Spearman correlation.
One can investigate Spearman correlations without relying on artificial selection by simply introducing violations of this model and carrying out Jensen's procedure.
Many commentators on Spearman's hypothesis appear to accept that Jensen's procedure is OK (for an overview, see Schonemann, 1997a, pp.