Convert Standardized Mean Difference to Common Language Effect Sizes

Usage

d_to_cles(d)

rb_to_cles(rb)

Arguments

d, rb: A numeric value 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: $$Pr(superiority) = \Phi(d/\sqrt{2})$$
$$Cohen's U_3 = \Phi(d)$$
$$Overlap = 2 \times \Phi(-|d|/2)$$
And the following for the rank-biserial correlation: $$Pr(superiority) = (r_{rb} + 1)/2$$

Note

These calculations assume that the populations have equal variance and are normally distributed.

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.