| Popis: |
We demonstrate that all conventional meta-analyses of correlation coefficients are biased, explain why, and offer solutions. Because the standard error of the correlation coefficient depends 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 several solutions: a newly developed estimator, UWLS+3 and two small-sample adjustments. UWLS+3 is the unrestricted weighted least squares weighted average (UWLS) that adjusts the degrees of freedom used to calculate correlations and thereby renders any remaining bias scientifically trivial. We also offer a simple small-sample correction, (n-2)/(n-1), for random-effects that works nearly as well as these other adjustments in most applications and a small-sample adjustment, (4n-2)/(4n-1), to Fisher’s z-transformation that is better still. |
