How to use it
- Choose raw data or summary statistics.
- Enter group 1 and group 2. In summary mode type the mean, standard deviation and size, separated by commas.
- Read d, g, the size label and the interval.
Formulas
- Pooled SD: s_p = √(((n₁ − 1)s₁² + (n₂ − 1)s₂²) ÷ (n₁ + n₂ − 2))
- Cohen’s d = (mean₁ − mean₂) ÷ s_p
- Hedges’ g = d × (1 − 3 ÷ (4(n₁ + n₂) − 9))
- Glass’s Δ = (mean₁ − mean₂) ÷ s₂
- 95% interval: d ± 1.96 × √((n₁ + n₂)/(n₁n₂) + d²/(2(n₁ + n₂))), a normal approximation
Raw data use the sample standard deviation (dividing by n − 1).
Worked example
Group 1: 2, 4, 6 (mean 4, SD 2). Group 2: 1, 3, 5 (mean 3, SD 2).
s_p = √((2 × 4 + 2 × 4) ÷ 4) = 2, so d = (4 − 3) ÷ 2 = 0.5, a medium effect. Hedges’ correction is 1 − 3 ÷ (4 × 6 − 9) = 1 − 3/15 = 0.8, so g = 0.4. Glass’s Δ = 1 ÷ 2 = 0.5.
Tips and common mistakes
- The sign shows direction: d is negative when group 1 has the smaller mean.
- An effect size says how big a difference is, not whether it is statistically significant; report it next to the p-value of a t-test.
- Use the standard deviation, not the standard error, in summary mode. If a paper gives SE, multiply it by √n first.