Monte Carlo Comparisons of Three Tests for Homogeneity of Independent Correlations

Abstract

A comparison of the power and Type I error rates of three tests of homogeneity for independent product-moment correlation coefficients (X;, Q, and LRS) were evaluated using Monte Carlo methods. Conditions simulated include data having varying sample sizes, reliabilities, and range restriction, with central and noncentral conditions, and having normal and nonnormal distributions. The LRS test almost always had a Type I error rate higher than the nominal alpha. Correspondingly, it was always more powerful than the other two tests given the same condition. The X2 and Q tests performed comparably regarding their Type I and Type II error rates. However, for all three tests power decreases substantially with the introduction of range restriction or measurement error when fewer than 18 correlations are being tested. Average Type II error rate for "perfect" data was less than .01 for both a = .05 and .01. The presence of range restriction and unreliability increased the average Type II error rate to approximately .56 for a = .05 and to .76 for a = .01 with no effect on Type I error rate. The Q test is recommended based on its performance in this paper and findings presented by Alexander, Scozzaro, and Borodkin (1989). A general computer program was used to generate these results which can be employed to estimate power for specific situations.