diff_to_cles: Convert Standardized Differences to Common Language Effect...

In effectsize: Indices of Effect Size

Convert Standardized Differences to Common Language Effect Sizes

Description

Convert Standardized Differences to Common Language Effect Sizes

Usage

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)

Arguments

d, rb

A numeric vector of Cohen's d / rank-biserial correlation or the output from cohens_d() / rank_biserial().

Details

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))

Value

A list of ⁠Cohen's U3⁠, Overlap, Pr(superiority), a numeric vector of Pr(superiority), or a data frame, depending on the input.

Note

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.

References

• 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.

See Also

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(), w_to_fei()

effectsize documentation built on June 8, 2025, 12:42 p.m.