Free Effect Size Calculator for Clinical Research and Meta-Analysis

An effect size is a single number that quantifies the size of a difference between two groups, on a scale that lets you compare or pool results across studies that may have used different sample sizes or measurement units.

How does Hedges' g relate to Cohen's d?

For continuous outcomes this calculator can compute either. Cohen's d is the difference in means divided by the pooled standard deviation: d = (M₁ − M₂) / SD_pooled. Hedges' g is the small-sample bias-corrected version: g = d × J, where J = 1 − 3/(4·df−1) and df = n₁+n₂−2. Hedges' g is the standardized mean difference convention used in Cochrane-style meta-analyses, and it is slightly smaller in magnitude than uncorrected Cohen's d for smaller studies; the two converge as sample size grows. Both use the same pooled SD, so switch between them with the buttons above to compare.

Odds ratio

Computed on the log scale using Woolf's method - SE{ln(OR)} = √(1/a + 1/b + 1/c + 1/d) - then exponentiated back for display. Common in case-control studies and logistic regression.

Risk ratio

Also computed on the log scale, then exponentiated for display. More directly interpretable than an odds ratio for cohort or RCT data where the outcome is not rare.

Risk difference

Computed directly on the linear scale as the difference in event proportions between arms - an absolute (not relative) measure of effect, useful for clinical decision-making.

A 0.5 continuity correction (the Haldane-Anscombe correction) is applied automatically to all four cells of the 2×2 table if any cell is zero, since the log odds ratio or log risk ratio is otherwise undefined.

Required inputs

For OR, RR, or RD: events and total participants in each of the two arms. For Cohen's d, Hedges' g or mean difference: the mean, standard deviation, and N in each of the two arms.

Worked hypothetical example

With 30 events out of 100 in the treatment arm and 20 events out of 100 in the control arm, enter those four numbers in Dichotomous mode above to see the OR, RR, or RD for that comparison. For a continuous outcome, enter a treatment mean/SD/N and a control mean/SD/N in Continuous mode to see Cohen's d, Hedges' g or the mean difference - the exact figures depend on your inputs, so use the calculator itself to reproduce a specific result rather than a fixed number quoted here.

Interpretation cautions

An effect size from a single study is not a pooled estimate - it describes that one study's result, with uncertainty reflected in its standard error and confidence interval. A single study's effect size should not be treated as a definitive answer, especially with a small sample or a wide confidence interval.

Using effect size for sample-size planning

An anticipated effect size (a difference in proportions or means) is exactly the input a sample-size calculation needs. See the sample size calculator to estimate participants per group for a planned two-proportion or two-mean comparison.

Using effect sizes in meta-analysis

This tool computes one study's effect size at a time. To pool multiple studies and quantify heterogeneity across them, use the I² calculator alongside this one, or run a full analysis with forest plots in EvidenceFlow.

References

Higgins JPT, Thomas J, Chandler J, et al. (editors). Cochrane Handbook for Systematic Reviews of Interventions (current version). training.cochrane.org/handbook. Hedges LV, Olkin I. Statistical Methods for Meta-Analysis. Academic Press; 1985.