MONTE-CARLO COMPARISONS OF 3 TESTS FOR HOMOGENEITY OF INDEPENDENT CORRELATIONS

A comparison of the power and Type I error rates of three tests of hom ogeneity for independent product-moment correlation coefficients (chi2 , Q, and LRS) were evaluated using Monte Carlo methods. Conditions sim ulated include data having varying sample sizes, reliabilities, and ra nge restriction, with central and noncentral conditions, and having no rmal and nonnormal distributions. The LRS test almost always had a Typ e I error rate higher than the nominal alpha. Correspondingly, it was always more powerful than the other two tests given the same condition . The chi2 and Q tests performed comparably regarding their Type I and Type II error rates. However, for all three tests power decreases sub stantially with the introduction of range restriction or measurement e rror when fewer than 18 correlations are being tested. Average Type II error rate for ''perfect'' data was less than .01 for both alpha = .0 5 and .01. The presence of range restriction and unreliability increas ed the average Type II error rate to approximately .56 for alpha = .05 and to .76 for alpha = .01 with no effect on Type I error rate. The Q test is recommended based on its performance in this paper and findin gs presented by Alexander, Scozzaro, and Borodkin (1989). A general co mputer program was used to generate these results which can be employe d to estimate power for specific situations.