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 research methods
- Hypothesis Testing
- Estimation
When to use this tool
Use this after (or alongside) a significance test to quantify how large a difference is, which a p-value alone does not convey.
Assumptions
- The standard deviation used to standardize the difference is appropriate to your design.
- Independent groups unless you choose a within-subjects design.
Limitations
- Conventions for 'small', 'medium' and 'large' effects are rules of thumb, not absolute thresholds, and depend on your field.
- Effect size does not tell you whether the effect is practically important.
How to interpret the result
Cohen's d expresses the mean difference in standard-deviation units. A d of 0.5 means the two group means differ by half a standard deviation.
How to report the result
Report the standardized effect size with the confidence interval and, ideally, the raw means and standard deviations so readers can verify it.
Next steps in your analysis
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.
- Effect Size and Statistical Power: Designing Studies That Can Detect EffectsWhy statistical significance is not enough — how to measure effect size with Cohen's d and design studies with adequate statistical power before you collect data.
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