Choosing the Best Correction Formula for the Pearson r²Effect Size

Abstract

In the present Monte Carlo simulation study, the authors compared bias and precision of 7 sampling error corrections to the Pearson r ² under 6 × 3 × 6 conditions (i.e., population ρ values of 0.0, 0.1, 0.3, 0.5, 0.7, and 0.9, respectively; population shapes normal, skewness = kurtosis = 1, and skewness = –1.5 with kurtosis = 3.5; ns = 10, 20, 40, 60, 100, and 200, respectively). Limited previous studies focused primarily on the efficacy only of multiple R ² corrections applied to the Pearson r ². The authors’ results indicate that the Pratt and the Olkin-Pratt Extended corrections more consistently provided unbiased estimates across the sample sizes, ρ values, and shape conditions that they investigated, although the Ezekiel correction arguably is also reasonable. The precisions of the estimates were homogeneous across the 108 simulation conditions.

Keywords:

• bivariate relationship
• correlation
• effect sizes
• Monte Carlo studies
• Pearson r
• simulation
• unbiased estimates