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().

## Value

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

## 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: $$Pr(superiority) = (r_{rb} + 1)/2$$
$$WMW_{Odds} = Pr(superiority) / (1 - Pr(superiority))$$

## 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.

• 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.