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.