We demonstrate that all meta-analyses of partial correlations are biased, and yet hundreds of meta-analyses of partial correlation coefficients (PCCs) are conducted each year widely across economics, business, education, psychology, and medical research. To address these biases, we offer a new weighted average, UWLS+3 . UWLS+3 is the unrestricted weighted least squares weighted average that makes an adjustment to the degrees of freedom that are used to calculate partial correlations and, by doing so, renders trivial any remaining meta-analysis bias. Our simulations also reveal that these meta-analysis biases are small-sample biases (n < 200), and a simple correction factor of (n - 2)/(n - 1) greatly reduces these small-sample biases along with Fisher's z. In many applications where primary studies typically have hundreds or more observations, partial correlations can be meta-analyzed in standard ways with only negligible bias. However, in other fields in the social and the medical sciences that are dominated by small samples, these meta-analysis biases are easily avoidable by our proposed methods.

Centre for Economic Policy Research London UK

Department of Economics Deakin University Burwood Victoria Australia

Institute of Economic Studies Faculty of Social Sciences Charles University Prague Czech Republic

Meta Research Innovation Center at Stanford Stanford University Palo Alto USA

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