Effect Size Converter

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histogram Effect size converter

Convert between different effect sizes

By convention, Cohen's d of 0.2, 0.5, 0.8 are considered small, medium and large effect sizes respectively.

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

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

Cohen's d to area-under-curve (auc) 1

$$\text{auc} = {\phi { d \over \sqrt{2}}} $$

\(\phi\): normal cumulative distribution function
R code: pnorm(d/sqrt(2), 0, 1)
Cohen's d to Cohen's f 2

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

Correlation r Fisher's z 4

$$ z' = 0.5 * (log(1 + r) - log(1 - r)) $$

Cohen's d to log odds ratio 3

$$ \text{log odds ratio} = {d \pi \over \sqrt{3}} $$

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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