Convert Standardized Differences to Common Language Effect Sizes
d_to_p_superiority(d)rb_to_p_superiority(rb)
rb_to_vda(rb)
d_to_u2(d)
d_to_u1(d)
d_to_u3(d)
d_to_overlap(d)
rb_to_wmw_odds(rb)
A list of Cohen's U3, Overlap, Pr(superiority), a
numeric vector of Pr(superiority), or a data frame, depending
on the input.
A numeric vector of Cohen's d / rank-biserial correlation or
the output from cohens_d() / rank_biserial().
This function use the following formulae for Cohen's d:
$$Pr(superiority) = \Phi(d/\sqrt{2})$$
$$\textrm{Cohen's } U_3 = \Phi(d)$$
$$\textrm{Cohen's } U_2 = \Phi(|d|/2)$$
$$\textrm{Cohen's } U_1 = (2\times U_2 - 1)/U_2$$
$$Overlap = 2 \times \Phi(-|d|/2)$$
And the following for the rank-biserial correlation:
$$Pr(superiority) = (r_{rb} + 1)/2$$
\(WMW_{Odds} = Pr(superiority) / (1 - Pr(superiority))\)
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), 19–30.
cohens_u3() for descriptions of the effect sizes (also,
cohens_d(), rank_biserial()).
Other convert between effect sizes:
d_to_r(),
eta2_to_f2(),
odds_to_probs(),
oddsratio_to_riskratio()