Point‐biserial correlation: Interval estimation, hypothesis testing, meta‐analysis, and sample size determination

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.