Correcting Bias in the Meta-Analysis of Correlations

We demonstrate that all conventional meta-analyses of correlation coefficients are biased, explain why, and offer solutions. Because the standard errors of the correlation coefficients depend on the size of the coefficient, inverse-variance weighted averages will be biased even under ideal meta-analytical conditions (i.e., absence of publication bias, p-hacking, or other biases). Transformation to Fisher's z often greatly reduces these biases but still does not mitigate them entirely. Although all are small-sample biases (n < 200), they will often have practical consequences in psychology where the typical sample size of correlational studies is 86. We offer two solutions: the well-known Fisher's z-transformation and new small-sample adjustment of Fisher's z that renders any remaining bias scientifically trivial.