Cohen's d Calculator (Effect Size Between Two Groups)

What this tool does

A p-value says whether a difference is likely to be real; the effect size says how big it is, in units that do not depend on the scale: the gap between the two means divided by their pooled standard deviation. Cohen's rough labels are 0.2 small, 0.5 medium and 0.8 large, though what counts as large depends on the field. Hedges' g shrinks d slightly for small samples. The common-language figure answers a plainer question: pick one person at random from each group, and how often does the first score higher? A d of 0.5 gives about 64 %. The interval is a large-sample approximation.

Formula

d = (M₁ − M₂) ÷ s_pooled, s_pooled = √(((n₁−1)s₁² + (n₂−1)s₂²) ÷ (n₁+n₂−2)) · g = d × (1 − 3 ÷ (4(n₁+n₂−2) − 1)) · SE = √((n₁+n₂) ÷ n₁n₂ + d² ÷ 2(n₁+n₂))

Variables

Worked example

Limitations

• The calculation runs at full precision and only the display is rounded. If you copy an intermediate value and retype it, small differences can appear.
• Standard deviation and variance are calculated for a sample (dividing by n − 1). For a full population, divide by n instead.