Effect Size Calculator

Calculate Cohen's d and Hedge's g to quantify the practical significance of your results.

Effect size measures how big a difference is, independent of sample size — the practical complement to a p-value, which only tells you whether an effect exists. Cohen's d expresses a mean difference in standard-deviation units: 0.2 is small, 0.5 medium, 0.8 large. Unlike p-values, effect sizes do not drift toward “significant” just because the sample is large, which is why journals increasingly require them. Results are validated to full precision.

Effect Size Input

Why report an effect size

A p-value answers “is there an effect?” but not “how much?” With a large enough sample, a trivial difference becomes statistically significant. The effect size reports the magnitude in interpretable units, so readers can judge whether the finding matters, not just whether it cleared p < 0.05. See effect size explained.

Interpreting the numbers

See it: the effect size visualizer shows any d as two overlapping distributions, with plain-language translations.

Cohen's benchmarks — d = 0.2 (small), 0.5 (medium), 0.8 (large) — are rough conventions, not laws; a “small” effect can be hugely important in context. For correlations, |r| of 0.1 / 0.3 / 0.5 play the same roles. Always report the effect size with a confidence interval.

Worked example

Two groups with means 85 and 80 and a pooled SD of 10 give Cohen's d = (85−80)/10 = 0.5 — a medium effect. The same five-point gap with a pooled SD of 2 gives d = 2.5, a very large one. Enter your means and SDs above to compute d.

Common mistakes

Guide: Understanding Effect Size

Effect size measures the practical (or clinical) significance of a result — how large the difference between groups actually is, independent of sample size. A p-value only tells you whether a difference exists; effect size tells you how meaningful that difference is.

A study with a very large sample can find a statistically significant result (p < 0.05) for a tiny, practically useless difference. Effect size prevents this misinterpretation.

Cohen's d is the most widely used effect size measure for comparing two group means. It expresses the difference in means as a number of standard deviations:

d = (M₁ − M₂) / SDpooled

A Cohen's d of 0.5 means the groups differ by half a standard deviation. A d of 1.0 means they differ by one full standard deviation — a large and clearly noticeable effect.

Hedge's g is a corrected version of Cohen's d that accounts for the slight overestimation of effect size in small samples. It applies a correction factor that becomes negligible once n per group exceeds ~20.

As a rule of thumb: use Hedge's g when your sample sizes are small (<20 per group), and Cohen's d when they are larger. Both values are reported by this calculator.

  • Two-sample: Two different, independent groups — e.g. control vs treatment, men vs women
  • One-sample: One sample compared to a known population mean — e.g. testing whether your class's average differs from the national average
  • Paired: The same subjects measured twice — e.g. before/after intervention, matched pairs

The overlap visualisation shows two normal distributions with the same standard deviation, separated by the Cohen's d effect size you calculated. A larger d produces less overlap between the distributions — a clearer separation between groups.

At d = 0, the distributions are identical (100% overlap). At d = 2, only ~16% of values from one distribution overlap with the other. This is a powerful way to communicate effect sizes to non-statisticians.

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