Correcting bias in the meta-analysis of correlations

• Published in: Psychological methods
• Main Authors: Stanley, T D, Doucouliagos, Hristos, Maier, Maximilian, Bartoš, František
• Format: Journal Article
• Language: English
• Published: United States 03.06.2024
• ISSN: 1939-1463
• DOI: 10.1037/met0000662

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, -hacking, or other biases). Transformation to Fisher's often greatly reduces these biases but still does not mitigate them entirely. Although all are small-sample biases ( < 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 that renders any remaining bias scientifically trivial. (PsycInfo Database Record (c) 2024 APA, all rights reserved).