# diff_to_cles: Convert Standardized Differences to Common Language Effect... In effectsize: Indices of Effect Size

 diff_to_cles R Documentation

## 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) = pnorm(d / sqrt(2))

U3 = pnorm(d)

U2 = pnorm(abs(d)/2)

U1 = (2 * U2 - 1) / U2

Overlap = 2 * pnorm(-abs(d) / 2)

And the following for the rank-biserial correlation:

Pr(superiority) = (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.

`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()`