How to use
- Under Calculate from, choose what you know — means and SDs, t, F, r or an odds ratio.
- Enter the values.
- Read the effect sizes and size labels.
Options explained
- Cohen's d and Hedges' g
- d = mean difference ÷ pooled SD; g corrects d for small samples and is common in meta-analysis.
- Conversions
- r = d / √(d² + 4) for equal groups; η² = F·df₁ / (F·df₁ + df₂); odds ratio to d uses ln(OR)·√3/π.
Worked example
Two groups of 30, with means 24 and 20 and both SDs equal to 5. The pooled SD is 5, so:
| Measure | Value | Label |
|---|---|---|
| Cohen’s d | 0.80 | Large |
| Hedges’ g | 0.79 | Large |
| r | 0.37 | Medium |
| η² | 0.138 | Medium |
pooled SD = √(((n₁−1)s₁² + (n₂−1)s₂²) ÷ (n₁+n₂−2))
g = d × (1 − 3 ÷ (4(n₁+n₂) − 9)) = 0.8 × (1 − 3/231)The same result can get a different label under d, r and η² because each has its own benchmark scale, so they are not interchangeable. The labels use Cohen’s (1988) cut-offs:
| Label | d | r | η² |
|---|---|---|---|
| Small | 0.2 | 0.1 | 0.01 |
| Medium | 0.5 | 0.3 | 0.06 |
| Large | 0.8 | 0.5 | 0.14 |
An F value converts to d only when it compares two groups (df₁ = 1).
Frequently asked questions
What is a large effect?
Cohen's rough benchmarks are d 0.2 small, 0.5 medium, 0.8 large; r 0.1/0.3/0.5; η² 0.01/0.06/0.14. Context matters.
How is d calculated for paired samples?
As dz = t / √n, the mean difference divided by the SD of the differences. It isn't directly comparable with an independent-samples d.
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No. Calculations run in your browser.
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