Tests for Comparing Dependent Correlations Revisited: A Monte Carlo Study

Abstract

A Monte Carlo evaluation of 4 test statistics for comparing dependent zero-order correlations was conducted. In particular, the power and Type I error rates of Hotelling's t; Williams' t; Olkin's z; and Meng, Rosenthal, and Rubin's Z were evaluated for sample sizes of 20, 50, 100, and 300 under 3 different population distributions (normal, uniform, and exponential). For the power analyses, 3 different magnitudes of discrepancy or effect sizes between ρy, x1 , and ρy, x2 were examined (values of .1, .3, and .6). Likewise, for the Type I error rate analyses, 3 different magnitudes of the predictor-criterion correlations were evaluated (ρy, x1 = ρy, x2 = .1, .4, and .7). All of the analyses were conducted at 3 different levels of predictor intercorrelation (ρx1, x2 = .1, .3, and .6). The results indicated that the choice as to which test statistic is optimal, in terms of power and Type I error rate, depends not only on sample size and population distribution but also on (a) the predictor intercorrelation and (b) the effect size (for power) or the magnitude of the predictor-criterion correlations (for Type I error rate). The results extend and refine previous studies that have only manipulated sample size and population distribution and as such should have greater utility for applied researchers.