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 that renders any remaining bias scientifically trivial. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

中文翻译：

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纠正相关性荟萃分析中的偏差。


我们证明所有传统的相关系数荟萃分析都是有偏差的，解释原因并提供解决方案。由于相关系数的标准误差取决于系数的大小，因此即使在理想的荟萃分析条件下（即不存在发表偏差、p-hacking 或其他偏差），逆方差加权平均值也会存在偏差。转换为 Fisher z 值通常会大大减少这些偏差，但仍然不能完全消除它们。尽管都是小样本偏差 (n < 200)，但它们通常会在心理学中产生实际后果，相关性研究的典型样本量为 86。我们提供两种解决方案：著名的 Fisher z 变换和新的小样本费舍尔的调整使任何剩余的偏见在科学上变得微不足道。 （PsycInfo 数据库记录 (c) 2024 APA，保留所有权利）。