The point-biserial correlation is a commonly used measure of effect size in two-group designs. New estimators of point-biserial correlation are derived from different forms of a standardized mean difference. Point-biserial correlations are defined for designs with either fixed or random group sample sizes and can accommodate unequal variances. Confidence intervals and standard errors for the point-biserial correlation estimators are derived from the sampling distributions for pooled-variance and separate-variance versions of a standardized mean difference. The proposed point-biserial confidence intervals can be used to conduct directional two-sided tests, equivalence tests, directional non-equivalence tests, and non-inferiority tests. A confidence interval for an average point-biserial correlation in meta-analysis applications performs substantially better than the currently used methods. Sample size formulas for estimating a point-biserial correlation with desired precision and testing a point-biserial correlation with desired power are proposed. R functions are provided that can be used to compute the proposed confidence intervals and sample size formulas.

中文翻译：

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点双列相关：区间估计、假设检验、荟萃分析和样本量确定。

点双列相关是两组设计中常用的效应量度量。点双列相关的新估计值来自不同形式的标准化平均差。点双列相关是为具有固定或随机组样本大小的设计定义的，并且可以适应不等方差。点双列相关估计量的置信区间和标准误差源自标准化平均差的合并方差和分离方差版本的抽样分布。建议的点双列置信区间可用于进行定向两侧检验、等价检验、定向非等价检验和非劣效检验。荟萃分析应用中平均点双列相关性的置信区间比目前使用的方法要好得多。提出了用于估计具有所需精度的点双列相关性和测试具有所需功率的点双列相关性的样本大小公式。提供了 R 函数，可用于计算建议的置信区间和样本大小公式。