Some properties of r equivalent: a simple effect size indicator.
One version of r equivalent, calculated from Fisher's exact test p values and recommended for small samples, is considered "a more realistic . . . [and] a more accurate estimate of the population correlation than . . . the sample correlation, r sample" (R. Rosenthal & D. B. Rubin, 2003, p. 494). Small sample properties of r sample and of two effect size estimators (r equivalent* and r hybrid) that use r equivalent were examined: r sample is preferable to r equivalent* (defined as r equivalent used without restrictions) in terms of bias and mean squared error (MSE); r hybrid (defined as r equivalent only when r sample = 1.0) is generally preferable to r equivalent*, and preferable to r sample in terms of MSEs, except when population correlations are very large. Conditions favoring r sample over r equivalent* and r hybrid in meta-analyses are noted.
Hsu
Louis M
LM
School of Psychology, Fairleigh Dickinson University, Teaneck, NJ 07666, USA. lhsu@fdu.edu
D000704:Analysis of Variance; D002986:Clinical Trials as Topic / Q000706:statistics & numerical data*; D006801:Humans; D008960:Models, Psychological; D011589:Psychology, Experimental / Q000706:statistics & numerical data*; D015203:Reproducibility of Results