Meta‐analyses are often used to synthesize the findings of studies examining the correlational relationship between two continuous variables. When only dichotomous measurements are available for one of the two variables, the biserial correlation coefficient can be used to estimate the product–moment correlation between the two underlying continuous variables. Unlike the point‐biserial correlation coefficient, biserial correlation coefficients can therefore be integrated with product–moment correlation coefficients in the same meta‐analysis. The present article describes the estimation of the biserial correlation coefficient for meta‐analytic purposes and reports simulation results comparing different methods for estimating the coefficient's sampling variance. The findings indicate that commonly employed methods yield inconsistent estimates of the sampling variance across a broad range of research situations. In contrast, consistent estimates can be obtained using two methods that appear to be unknown in the meta‐analytic literature. A variance‐stabilizing transformation for the biserial correlation coefficient is described that allows for the construction of confidence intervals for individual coefficients with close to nominal coverage probabilities in most of the examined conditions. Copyright © 2016 John Wiley & Sons, Ltd.

中文翻译：

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二元相关性及其抽样方差的估计，用于荟萃分析。

荟萃分析通常用于综合研究两个连续变量之间的相关关系的研究结果。当只有二分法的测量值可用于两个变量之一时，二元相关系数可用于估计两个基本连续变量之间的乘积-矩相关性。与点-二元相关系数不同，因此可以在同一荟萃分析中将二元相关系数与乘积-矩相关系数整合在一起。本文介绍了用于二元分析目的的二元相关系数的估计，并报告了模拟结果，比较了用于估计系数采样方差的不同方法。研究结果表明，在广泛的研究情况下，常用的方法得出的抽样方差的估计值不一致。相反，可以使用在荟萃分析文献中似乎未知的两种方法来获得一致的估计。描述了双数相关系数的方差稳定化变换，该变换允许在大多数检查条件下构建具有接近标称覆盖率的单个系数的置信区间。版权所有©2016 John Wiley＆Sons，Ltd. 描述了双数相关系数的方差稳定化变换，该变换允许在大多数检查条件下构建具有接近标称覆盖率的单个系数的置信区间。版权所有©2016 John Wiley＆Sons，Ltd. 描述了双数相关系数的方差稳定化变换，该变换允许在大多数检查条件下构建具有接近标称覆盖率的单个系数的置信区间。版权所有©2016 John Wiley＆Sons，Ltd.