Cohen’s d Calculator (Two Samples)
Measure the standardized effect size between two groups with Cohen’s d from raw data — the mean difference in pooled standard deviation units, with a size label.
How it works
sₚ = √{[(n₁−1)s₁² + (n₂−1)s₂²] ÷ (n₁+n₂−2)} · d = (x̄₁ − x̄₂) ÷ sₚ · g = d·[1 − 3/(4(n₁+n₂)−9)]
Cohen’s d expresses the gap between two group means in units of their pooled standard deviation, so it is comparable across studies and unaffected by sample size in the way a p-value is. A d of 1 means the means are one standard deviation apart. Because plain d is slightly biased upward for small samples, the calculator also reports Hedges’ g, the small-sample-corrected version.
Worked example
Group 1 averages about 81.2 and group 2 about 71.5, with a pooled SD near 4.4. Cohen’s d = (81.2 − 71.5) ÷ 4.4 ≈ 2.2 — a very large effect, far beyond the 0.8 "large" threshold.
Sources: Effect size — Wikipedia
Frequently asked questions
How do I interpret the size of d?
Cohen’s rough benchmarks are 0.2 (small), 0.5 (medium) and 0.8 (large), with values below 0.2 negligible. These are conventions, not laws — what counts as meaningful depends on the field.
What is the difference between Cohen’s d and Hedges’ g?
They estimate the same thing, but plain d overestimates the effect for small samples. Hedges’ g multiplies d by a correction factor that shrinks it slightly; with large samples the two are practically identical.
Can effect size be large while the result is not significant?
Yes. With small samples you can see a large d but a p-value above 0.05, because significance also depends on sample size. Reporting both a p-value and an effect size gives the fuller picture.
Related calculators
For education — confirm the test assumptions (independence, sample size, roughly normal data) before drawing conclusions from a p-value.