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.
It is not useful to repeat how the test is done. My Excel sheet (here) is in itself self-explanatory. Basically, we need to correlate the ASVAB subtests from sibling score means ((sib#1+sib#2)/2) and then from sibling score differences (sib#1-sib#2) for each racial group. Having these six sets of subtest intercorrelations in hand, we can to submit them to a PC or PAF analysis. The congruence coefficient is calculated from the g-loadings for each groups. We could also indicate that, whether we use PC or PAF analysis, the result appears to be the same. Generally speaking, the variance explained by the g factor is higher with regard to the between-family correlations. In the NLSY79, the variance explained by g (PC1 or PAF1) is 64% for black BF, 47% for black WF, 68% for hispanic BF, 45% for hispanic WF, 67% for white BF, 46% for white WF. By way of comparison, in the NLSY97, the variance explained by g (PC1 or PAF1) is 62% for black BF, 44% for black WF, 59% for hispanic BF, 38% for hispanic WF, 57% for white BF, 43% for white WF.
Below is the table showing the CCs from the NLSY97 :
And here is the corresponding table for the NLSY79 :
The numbers speak for themselves. An identical structure is evidenced when the congruence is at least 0.90 or 0.95, as strict minimum. Regarding PC1, the CCs computed from principal component analyses are higher than 0.99. See the NLSY97 syntax and NLSY79 syntax for preparing the above analysis.