Convert Standardized Mean Difference to Common Language Effect Sizes
d_to_cles(d)rb_to_cles(rb)
A numeric value of Cohen's d / rank-biserial correlation or
the output from cohens_d() / rank_biserial().
A list of Cohen's U3, Overlap, Pr(superiority), a
numeric vector of Pr(superiority), or a data frame, depending
on the input.
This function use the following formulae for Cohen's d: $$Pr(superiority) = \Phi(d/\sqrt{2})$$
$$Cohen's U_3 = \Phi(d)$$
$$Overlap = 2 \times \Phi(-|d|/2)$$
And the following for the rank-biserial correlation: $$Pr(superiority) = (r_{rb} + 1)/2$$
Cohen, J. (1977). Statistical power analysis for the behavioral sciences. New York: Routledge.
Reiser, B., & Faraggi, D. (1999). Confidence intervals for the overlapping coefficient: the normal equal variance case. Journal of the Royal Statistical Society, 48(3), 413-418.
Ruscio, J. (2008). A probability-based measure of effect size: robustness to base rates and other factors. Psychological methods, 13(1), 19<U+2013>30.
Other convert between effect sizes:
d_to_r(),
eta2_to_f2(),
odds_to_probs(),
oddsratio_to_riskratio()