Effect size converter

Cohen's d
Pearson's correlation r
R-squared
Cohen's f
Odds ratio (OR)
Log odds ratio
Area-under-curve (AUC) *common language effect size statistic
Fisher's z (z')

Conversion formulae

All conversions assume equal-sample-size groups.

Cohen's d to Pearson's r ¹

$r = \frac{d}{\sqrt{d^{2} + 4}}$

Cohen's d to area-under-curve (auc) ¹

$auc = ϕ \frac{d}{\sqrt{2}}$

$ϕ$ : normal cumulative distribution function

R code: pnorm(d/sqrt(2), 0, 1)

Cohen's d to Cohen's f ²

$f = \frac{d}{2}$

Correlation r Fisher's z ⁴

$z^{'} = 0.5 * (l o g (1 + r) - l o g (1 - r))$

Cohen's d to log odds ratio ³

$log odds ratio = \frac{d π}{\sqrt{3}}$

References

1. Ruscio, J. (2008). A probability-based measure of effect size: Robustness to base rates and other factors. Psychological Methods, 13(1), 19-30. doi:10.1037/1082-989x.13.1.19

2. Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.), Hillsdale, NJ: Erlbaum.

3. Sánchez-Meca, J., Marín-Martínez, F., & Chacón-Moscoso, S. (2003). Effect-size indices for dichotomized outcomes in meta-analysis. Psychological Methods, 8(4), 448-467.

4. Wikipedia: Fisher's z-transformation of r

5. Borenstein, M., Hedges, L. V., Higgins, J. P. T., & Rothstein, H. R. (2009). Introduction to meta-analysis. Chichester, West Sussex, UK: Wiley.

6. Rosenthal, R. (1994). Parametric measures of effect size. In H. Cooper & L. V. Hedges (Eds.), The Handbook of Research Synthesis. New York, NY: Sage.

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Convert between different effect sizes

Conversion formulae

Cohen's d to Pearson's r 1

Cohen's d to area-under-curve (auc) 1

ϕ: normal cumulative distribution function