Hedges' g

Compute the standardised mean difference between two groups as Hedges' g, and see Cohen's d, the small-sample correction J and a plain-language effect-size label alongside it.

How the calculation works

The pooled standard deviation comes first: s_pooled = √[((n₁ − 1)s₁² + (n₂ − 1)s₂²) / (n₁ + n₂ − 2)]. Cohen's d = (M₁ − M₂) / s_pooled. Because d overstates the effect in small samples, Larry Hedges (1981, Journal of Educational Statistics) introduced the correction J = 1 − 3 / (4(n₁ + n₂) − 9), giving g = J × d.

Inputs are the two means M₁ and M₂, the sample standard deviations s₁ and s₂ (n − 1 denominator) and the group sizes n₁ and n₂ (at least 2 each). The sign of g gives the direction: positive means group 1 has the higher mean.

The label follows Cohen's (1988) conventions: |g| < 0.2 negligible, 0.2–0.5 small, 0.5–0.8 medium, 0.8 and above large. These are rules of thumb, not laws of nature.

Worked example

Group 1: mean 105, SD 10, n = 20; group 2: mean 100, SD 10, n = 20. Pooled SD = 10, d = 5 / 10 = 0.5. J = 1 − 3 / (4·40 − 9) = 1 − 3/151 = 0.9801, so g = 0.5 × 0.9801 ≈ 0.490. The calculator labels this “small” because it falls just under 0.5. With n = 10 per group, J = 0.9577 and g ≈ 0.479.

Things to keep in mind

• With large samples g and d are almost identical; the correction matters when groups have fewer than about 20 observations.
• Do not confuse standard deviation with standard error. If a paper reports SE, multiply it by √n to get the SD.
• No confidence interval is shown. An approximate variance is Var(g) ≈ J²·[(n₁ + n₂)/(n₁n₂) + d²/(2(n₁ + n₂))].
• This formula is for independent groups. Pre/post measurements on the same people need a paired-design effect size.
• Cohen's cut-offs are generic; what counts as meaningful depends on your field.