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

Effect sizes of the difference, or standardized mean differences, are widely used for meta-analysis or power-analysis. However, common effect sizes of the difference such as Cohen's d or Hedges' d assume variance equality that is fragile and is often violated in practical applications. Based on Welch's t tests, we defined a new effect size of the difference between means, which did not assume variance equality, thereby providing a more accurate value for data with unequal variance. In addition, we presented the unbiased estimator of an effect size of the difference between a mean and a known constant. An R package is also provided to compute these effect sizes with their variance and confidence interval.