Effect-Size Converter
Papers report effects on different scales: Cohen's d here, r there, η² in the ANOVA table, odds ratios in the medical journals. Type any one of them to get all the others, and a picture of what that effect looks like.
Cohen's d—
r—
η² (= r²)—
Cohen's f—
Odds ratio ≈—
Distribution overlap—
U₃: treated above control mean—
P(random treated > random control)—
n/group for 80% power—
How to read the numbers
- Cohen's d is the group difference in standard-deviation units, and the easiest to compare across two-group studies.
- r / η². Effect as (squared) correlation: the share of outcome variance the effect explains. The d ↔ r conversion here assumes two equal-sized groups.
- Cohen's f is what ANOVA (and G*Power) asks for; for two groups f = d/2.
- Odds ratio. The usual effect size in logistic regression. The conversion (d = ln OR × √3⁄π) is an approximation, so treat it as a ballpark, not an identity.
U₃ and P(superiority) are the plain-language versions: what fraction of the treatment group beats the control average, and how often a random treated person beats a random control person.
| Benchmark (Cohen, 1988) | d | r | η² |
|---|---|---|---|
| Small | 0.20 | .10 | .01 |
| Medium | 0.50 | .24 | .06 |
| Large | 0.80 | .37 | .14 |
Benchmarks are a last resort. Cohen himself said so. A "small" d = 0.2 on mortality is enormous; a "large" d = 0.8 on a reaction-time task might be trivial. Compare an effect to others in its own literature; the numbers above are for when you have nothing else. The Effect Size & Power lesson covers this in full.