Testing Dependent Correlations With Nonoverlapping Variables: A Monte Carlo Simulation

Abstract

The authors conducted a Monte Carlo simulation of 4 test statistics for comparing dependent correlations with no variables in common. Empirical Type I error rates and power estimates were determined for K. Pearson and L. N. G. Filon's (1898) z, O. J. Dunn and V. A. Clark's (1969) z, J. H. Steiger's (1980) original modification of Dunn and Clark's z, and Steiger's modification of Dunn and Clark's z using a backtransformed average z procedure for sample sizes of 10, 20, 50, and 100 under 3 different population distributions. For the Type I error rate analyses, the authors evaluated 3 different magnitudes of the predictor-criterion correlations (ρ₁₂ = ρ₃₄ = .10, .30, and .70). Likewise, for the power analyses, 3 different magnitudes of discrepancy or effect sizes between correlations with no variables in common (ρ₁₂ and ρ₃₄) were examined (values of .10, .40, and .60). All of the analyses were conducted at 3 different levels of predictor intercorrelation. 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 intercorrelations and (b) the effect size (for power) or the magnitude of the predictor-criterion correlations (for Type I error rate). For the conditions examined in the present study, Pearson and Filon's z had inflated Type I error rates when the predictor-criterion correlations were low to moderate. Dunn and Clark's z and the 2 Steiger procedures had similar, but conservative, Type I error rates when the predictor-criterion correlations were low. Moreover, the power estimates were similar among the 3 procedures.

Keywords:

• dependent correlations
• Monte Carlo simulation
• nonoverlapping variables
• statistical power
• Type I error