diff_to_cles() R function from [effectsize]

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)

d, rb: A numeric vector 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})Pr(superiority) = pnorm(d / sqrt(2))

\textrm{Cohen's } U_3 = \Phi(d)U3 = pnorm(d)

\textrm{Cohen's } U_2 = \Phi(|d|/2)U2 = pnorm(abs(d)/2)

\textrm{Cohen's } U_1 = (2\times U_2 - 1)/U_2U1 = (2 * U2 - 1) / U2

Overlap = 2 \times \Phi(-|d|/2)Overlap = 2 * pnorm(-abs(d) / 2)

And the following for the rank-biserial correlation:

Pr(superiority) = (r_{rb} + 1)/2Pr(superiority) = (rb + 1)/2

$WMW_{Odds} = Pr(superiority) / (1 - Pr(superiority))$

For d, these calculations assume that the populations have equal variance and are normally distributed.

Vargha and Delaney's A is an alias for the non-parametric probability of 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.