A Monte Carlo Evaluation of Tests for Comparing Dependent Correlations

Abstract

The authors conducted a Monte Carlo simulation of 8 statistical tests for comparing dependent zero-order correlations. In particular, they evaluated the Type I error rates and power of a number of test statistics for sample sizes (Ns) of 20, 50, 100, and 300 under 3 different population distributions (normal, uniform, and exponential). For the Type I error rate analyses, the authors evaluated 3 different magnitudes of the predictor-criterion correlations (p_y,x1 = p_y,x2=.1, .4, and .7). For the power analyses, they examined 3 different effect sizes or magnitudes of discrepancy between p_y,x2 and p_y,x2 (values of .1, .3, and .6). They conducted all of the simulations at 3 different levels of predictor intercorrelation (p_x1,x2 = .1, .3, and .6). The results indicated that both Type I error rate and power depend 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). When the authors considered Type I error rate and power simultaneously, the findings suggested that O. J. Dunn and V. A. Clark's (1969) z and E. J. Williams's (1959) t have the best overall statistical properties. The findings extend and refine previous simulation research and as such, should have greater utility for applied researchers.

Key Words:

• dependent correlations
• Monte Carlo simulation
• statistical power
• Type I error rate
• zero-order