A Significance Test For Congruence Coefficients For Cattell's Factors Matched By Scanning

The personality theory of Cattell depends heavily on the methodology og factor analysis. One of the critical matters for the theory is the replication of factors both within and between variable domains, which depends on the development of significance levels for matching indices like the congruence coefficient. The tables of Schneewind & Cattell have been used to evaluate congruence coefficients, even though the tables are appropriately constructed and the null hypothesis which is tested is not appropriate. A Monte Carlo method is used to construct new tables that test the hypothesis that an independent set of random vectors has been matched. Less than half of the congruence coefficients reported by Cattell in two articles exceed the critical values thus created. There is some non-random structure in Cattell's results, but not enough to support the conclusion that factors have been replicated.