In Bias in Mental Testing (1980, pp. 546-548), Arthur Jensen showed that a congruence coefficient test from a factor analysis of the within- (WF) and between-family (BF) correlations among blacks and whites could yield an identical g factor structure. A similarity in factorial structure for these four groups having been evidenced, he writes :
These correlations are statistically homogeneous; that is, they do not differ significantly from one another. Thus it appears that the g loadings of these seven tests show a very similar pattern regardless of whether they were extracted from the within-family correlations (which completely exclude cultural and socioeconomic effects in the factor analyzed variance) or from the between-families correlations, for either whites or blacks. … This outcome would seem unlikely if the largest source of variance in these tests, reflected by their g loadings, were strongly influenced by whatever cultural differences that might exist between families and between whites and blacks.
Jensen (1980, Table 4) has been replicated by Nagoshi and Johnson (1987, pp. 310-314). I will replicate those earlier tests using NLSY97 and NLSY79. As Jensen (1998, pp. 99-100) noted, the congruence coefficient (CC) can be interpreted as being an index of factor similarity.
