
Convert Standardized Mean Difference to Common Language Effect Sizes
Source:R/convert_between_common_language.R
d_to_cles.Rd
Convert Standardized Mean Difference to Common Language Effect Sizes
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.
See also
Other convert between effect sizes:
d_to_r()
,
eta2_to_f2()
,
odds_to_probs()
,
oddsratio_to_riskratio()