Calculate and convert between common effect size measures used in meta-analysis. Includes Cohen's d, Hedges' g, odds ratios, risk ratios, and correlation coefficients with 95% confidence intervals.
Enter means, standard deviations, and sample sizes for two independent groups.
Use SMD (Cohen's d or Hedges' g) for continuous outcomes measured on different scales. Use OR or RR for dichotomous outcomes. Use correlation (r) for association studies.
Point estimates alone are insufficient. The 95% CI tells readers how precise your estimate is and whether it crosses clinically meaningful thresholds.
Cohen's d slightly overestimates effect sizes in small samples. Hedges' g applies a correction factor (J) that approaches 1 as sample size increases.
Odds ratios and risk ratios should be log-transformed before meta-analytic pooling. The calculator provides both the natural log and the raw ratio.
An effect size is a standardized measure of the magnitude of an observed effect. In meta-analysis, effect sizes allow researchers to combine and compare results across studies that may use different measurement scales or report different statistics. Common effect sizes include standardized mean differences (for continuous outcomes), odds ratios and risk ratios (for binary outcomes), and correlation coefficients (for associations).
Hedges' g is generally preferred in meta-analysis because it corrects for the small upward bias in Cohen's d that occurs with small sample sizes. The correction factor J = 1 - 3/(4*df - 1) is close to 1 for large samples, so the two measures converge as sample size increases. For individual studies with n > 50 per group, the difference is negligible.
Cohen (1988) proposed benchmarks: d = 0.2 (small), 0.5 (medium), 0.8 (large). For odds ratios: OR ≈ 1.5 (small), 2.5 (medium), 4.3 (large). For correlations: r = 0.1 (small), 0.3 (medium), 0.5 (large). These are rough guides -- clinical significance depends on context.
Yes, this calculator supports conversion between Cohen's d and correlation r using the formula d = 2r/√(1-r²). Conversions between SMDs and odds ratios are also possible using the logistic approximation OR = exp(d × π/√3). Note that conversions assume certain distributional properties.
Yes, completely free with no sign-up required. All calculations run in your browser -- no data is sent to any server. You can use it for as many studies as you need.
Our statisticians can handle effect size extraction, heterogeneity assessment, subgroup analyses, sensitivity analyses, and publication bias testing for your entire review.