Approximating Pearson Product-Moment Correlations from Kendall's Tau and Spearman's Rho

Abstract

This article used Monte Carlo methods to investigate the accuracy of formulas presented by Kendall for estimating Pearson's r from X and by Pearson for estimating Pearson's r from rs. Results indicated that the formula for approximating r from r is somewhat more accurate than the formula for approximating r from rs. However, both formulas were found to be quite accurate. The largest asymptotic difference between a converted and actual r was -.005. In addition, the standard errors of the transformed X and rs coefficients were compared to the standard error of r, and the empirically derived percentage increase in standard error was compared to theoretically derived estimates. Implications of these findings for meta-analyses of correlations are discussed.