Averaging correlations: An examination of alternative procedures
In meta-analysis, results of individual studies are analyzed to determine whether there is a single effect-size parameter, and if so to provide a point-estimate of that parameter. The present research examined estimation of the correlation parameter, rho, using various numbers of independent Pearson product-moment correlation coefficients (rs). In three studies, methods for obtaining a point-estimate of rho and constructing confidence intervals around that estimate were examined. In Study I several transformations of r and Fisher's z transformation (z ') were used to estimate rho and accuracy was evaluated via bias, variability, and variance-around-rho. Compared to the mean untransformed r, the alternative estimates were not found to improve accuracy. In Study 2 several analytical estimates of the standard error of the mean r and mean z' were examined. Only Fisher's (1958) estimate of the standard error of the mean z ' was consistently accurate, as determined by confidence interval (CI) width and Type I error rate when CIs were used for significance testing. In Study 3, the estimates of rho examined in Study 1 were used to construct CIs, however, none of the alternative estimates was found to improve CI width, relative to the mean z '