Statistics and research
Effect size calculator
Cohen’s d, Hedges’ g and Glass’s Δ from group means, or odds ratio, risk ratio and risk difference from a 2×2 table, each with confidence intervals.
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Results
- Pooled SD
- 5.0249378
- Correction factor J
- 0.99232409
- Glass’s Δ (SD of group 2)
- 0.666667
- Probability of superiority Φ(d / √2)
- 0.66355
| Measure | Estimate | SE | Lower | Upper |
|---|---|---|---|---|
| Cohen’s d | 0.597022 | 0.204407 | 0.196392 | 0.997652 |
| Hedges’ g | 0.59244 | 0.202838 | 0.194885 | 0.989995 |
Cohen’s benchmarks (0.2 small, 0.5 medium, 0.8 large) are rough conventions; compare with effects in your own field.
Method and limits
How to use it
For a continuous outcome, enter each group’s n, mean and SD. For a yes/no outcome, enter the 2×2 counts: group 1 (treated or exposed) events and non-events, then group 2 (control).
Formulas
- Cohen’s d = (x̄₁ − x̄₂) / sp, with the pooled SD sp; Var(d) = (n₁ + n₂)/(n₁n₂) + d²/(2(n₁ + n₂)).
- Hedges’ g = J d with the exact correction J = Γ(ν/2) / (√(ν/2) Γ((ν − 1)/2)), ν = n₁ + n₂ − 2 (≈ 1 − 3/(4ν − 1)); SE(g) = J SE(d).
- Glass’s Δ = (x̄₁ − x̄₂) / s₂ (SD of the control group).
- Odds ratio ad/bc with SE(ln OR) = √(1/a + 1/b + 1/c + 1/d) (Woolf); risk ratio with SE(ln RR) = √(1/a − 1/(a + b) + 1/c − 1/(c + d)) (Katz); risk difference with the Wald SE; number needed to treat = 1/|RD|.
- Intervals: estimate ± z SE, on the log scale for ratios. A zero cell adds 0.5 to every cell for the ratios.
Assumptions and limits
- Independent groups; d and g assume similar SDs in the two groups (otherwise report Glass’s Δ).
- Normal-approximation intervals; for very small samples prefer exact methods.
- Cohen’s labels (0.2 small, 0.5 medium, 0.8 large) are only a rough guide.
Worked example
Borenstein et al. (2009), chapter 4: means 103 and 100, SDs 5.5 and 4.5, n = 50 each. Pooled SD 5.025, d = 0.597 (variance 0.0418), J = 0.9923, g = 0.592. Chapter 5: 5 of 100 events versus 10 of 100 — risk ratio 0.50 (95% CI 0.18 to 1.41), odds ratio 0.47 (0.16 to 1.44).
References
- Borenstein, Hedges, Higgins and Rothstein (2009), Introduction to Meta-Analysis, Wiley, chapters 4–5
- Hedges (1981), Journal of Educational Statistics 6(2)
- Woolf (1955), On estimating the relation between blood group and disease, Annals of Human Genetics 19
- Katz, Baptista, Azen and Pike (1978), Obtaining confidence intervals for the risk ratio in cohort studies, Biometrics 34(3)
- McGraw and Wong (1992), A common language effect size statistic, Psychological Bulletin 111(2)
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