What is Cohen's d?
Cohen's d is the standardized mean difference between two groups, calculated by dividing the difference between the two group means (\(M_1 - M_2\)) by their pooled within-group standard deviation (\(S_{\text{within}}\)). Because it expresses group differences in standard deviation units rather than raw scale points, studies using different instruments can be compared and synthesized directly in a meta-analysis.
When should I use Hedges' g instead of Cohen's d?
Cohen's d has a slight upward bias in small samples (particularly when total \(N < 20\)). Hedges' g multiplies d by a small-sample correction factor, \(J = 1 - \frac{3}{4(n_1 + n_2 - 2) - 1}\), producing an unbiased estimate of the standardized mean difference. In larger samples, d and g converge to nearly identical values, but reporting Hedges' g is standard practice in contemporary meta-analyses.