The odds favor antitypes - A comparison of tests for the identification of configural types and antitypes

This article presents results from a simulation study on the relative performance of the z-test, Pearson's X2 component test, Anscombe's z-approximation, and Lehmacher's approximative hypergeometric test when employed in Configural Frequency Analysis (CFA). Specifically, the focus was on the relative probability of detecting types versus antitypes. Frequency distributions were simulated in 2 x 2-, in 2 x 2 x 2-, and in 3 x 3 tables for sample sizes up to N = 1500. Results suggest that Lehmacher's test has the most balanced antitype-to-type ratio, followed by the z-test and the X2-test. Each of these tests typically detects more types than antitypes when samples are small, and more antitypes than types when samples are large. Anscombe's z-approximation almost always detects more antitypes than types. Lehmacher's test always has more power than the z-test and the X2-test. Anscombe's z lies between the z- and the X2-tests for types, and between Lehmacher's test and the z-test for antitypes.