Hedges' g calculator

What this computes

Hedges' g is the standardized mean difference between two groups, corrected for the small-sample upward bias that inflates Cohen's d. When samples are small, d systematically overstates the true effect; g applies a multiplicative correction factor J that pulls the estimate back toward the true value. In a meta-analysis, g is the effect size you actually pool. It is what tools and the Cochrane Handbook mean by "SMD."

The formula

Starting from Cohen's d and the two group sizes n₁, n₂ (degrees of freedom df = n₁ + n₂ − 2):

J      = 1 − 3 / (4·df − 1)
g      = J · d
Var(g) = (n₁ + n₂) / (n₁·n₂) + g² / (2·(n₁ + n₂))
95% CI = g ± 1.95996 · √Var(g)

If you only have raw statistics, d is recovered first from the pooled within-groups SD: s_pooled = √[((n₁−1)·SD₁² + (n₂−1)·SD₂²) / (n₁+n₂−2)], then d = (M₁ − M₂) / s_pooled. The J used here is the standard approximation; it agrees with the exact gamma-function form to within about 1% at df = 2, better than 0.1% by df ≈ 7, and better than 0.01% once df exceeds ~20.

When it's valid (and when it isn't)

This applies to two independent groups on a continuous outcome measured once (post-only or a single change score per arm). It is the right effect size whenever you would otherwise report Cohen's d but want the pooled, bias-corrected value. Below about 20 total participants the calculator flags the small-sample regime: J is shrinking d noticeably there, and the normal-approximation interval understates uncertainty, so a t-based CI is the safer report at that size.

It does not apply to paired/within-subject designs (the variance term assumes independence), to dichotomous or count outcomes, or to crossover trials without first converting to a paired-difference effect size. If your two arms share subjects, or the outcome isn't continuous, this number will be wrong regardless of what it prints.

Reference

Hedges, L.V. & Olkin, I. (1985). Statistical Methods for Meta-Analysis. Academic Press. The correction factor and large-sample variance are given in the same form in the Cochrane Handbook §6.5.1.