Effect sizes of the differences between means without assuming the variance equality and between a mean and a constant

Abstract: Hedges' d, an existing unbiased effect size of the difference between means, assumes the variance equality. However, the assumption of the variance equality is fragile, and is often violated in practical applications. Here, we define e, a new effect size of the difference between means, which does not assume the variance equality. In addition, another novel statistic c is defined as an effect size of the difference between a mean and a known constant. Hedges' g, our c, and e correspond to Student's unpaired two-sample t test, Student's one-sample t test, and Welch's t test, respectively. An R package is also provided to compute these effect sizes with their variance and confidence interval.