A critical reflection on computing the sampling variance of the partial correlation coefficient

The partial correlation coefficient quantifies the relationship between two variables while taking into account the effect of one or multiple control variables. Researchers often want to synthesize partial correlation coefficients in a meta-analysis since these can be readily computed based on the reported results of a linear regression analysis. The default inverse variance weights in standard meta-analysis models require researchers to compute not only the partial correlation coefficients of each study but also its corresponding sampling variance. The existing literature is diffuse on how to estimate this sampling variance, because two estimators exist that are both widely used. We critically reflect on both estimators, study their statistical properties, and provide recommendations for applied researchers. We also compute the sampling variances of studies using both estimators in a meta-analysis on the partial correlation between self-confidence and sports performance.

偏相关系数衡量了在考虑一个或多个控制变量影响的情况下，两个变量之间的关系。在元分析中，研究人员通常希望综合偏相关系数，因为这些系数可以基于线性回归分析的报告结果轻松计算。标准元分析模型中的默认逆方差权重要求研究人员不仅计算每个研究的偏相关系数，还要计算其相应的抽样方差。现有文献对如何估计这种抽样方差存在分歧，因为存在两种广泛使用的估计方法。我们对这两种估计方法进行了批判性反思，研究了它们的统计特性，并为应用研究人员提供了建议。我们还通过元分析计算了自我信心与运动表现之间偏相关系数的研究抽样方差，并使用这两种估计方法进行了计算。