Choosing the Best Correction Formula for the Pearson r2 Effect Size

In the present Monte Carlo simulation study, the authors compared bias and precision of 7 sampling error corrections to the Pearson r2 under 6 x 3 x 6 conditions (i.e., population 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 R2 corrections applied to the Pearson r2. The authors' results indicate that the Pratt and the Olkin-Pratt Extended corrections more consistently provided unbiased estimates across the sample sizes, 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.