Effect Size Calculator
Measure a standardized effect size with Cohen's d.
How Cohen's d works
Cohen's d is a standardized measure of effect size: the difference between two means (or a mean and a target) divided by a standard deviation. Because it is unit-free, effect sizes from different studies can be compared.
For independent groups, d uses the pooled standard deviation. For a paired design it uses the standard deviation of the differences (sometimes called d_z). For one sample it compares the mean to a target value.
Labels like 'small' (0.2), 'medium' (0.5) and 'large' (0.8) are Cohen's conventions. They are heuristics, not universal scientific rules — what counts as a meaningful effect depends entirely on your field and context.
The formulas
d = (x̄₁ − x̄₂) / s_pooled · s_pooled = √(((n₁−1)s₁² + (n₂−1)s₂²) / (n₁+n₂−2))
For one-sample, d = (x̄ − μ₀)/s. For paired data, d = d̄/s_d. The sign indicates the direction of the effect; the magnitude matters for interpretation.
Worked example
Groups 1,2,3 vs 4,5,6
The pooled standard deviation is 1 and the mean difference is −3, so d = −3. The magnitude 3 is far beyond the 'large' convention (0.8), indicating a very large effect.
Frequently asked questions
Are the 'small, medium, large' labels universal?
No. They are Cohen's widely used conventions and depend on context. A 'small' effect in one field may be important in another — always interpret effect size within your domain.
What does the sign of d mean?
It indicates direction: a positive d means the first group (or sample) has the higher mean. For interpretation, the absolute value is what matters.
Why report effect size alongside a p-value?
A p-value tells you whether an effect is likely real; an effect size tells you how large it is. A statistically significant result can still have a trivially small effect.
Related tools
Related guides
- Understanding P-Values and Statistical SignificanceWhat a p-value actually means, what it does not mean, the role of the significance level, and why the field is moving away from the 0.05 bright line.
- T-Test vs Z-Test vs ANOVAWhen to use a z-test, a t-test or an ANOVA, the assumptions behind each, and how the tests relate — including why F equals t² for two groups.
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