Effect Size Calculator (Cohen's d)
Cohen's d expresses the difference between two means in units of the pooled standard deviation. It answers not just whether a difference is statistically significant, but how large and practically meaningful that difference is.
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Formula
d = |μ₁ − μ₂| / σ_pooled
Subtract one group mean from the other (taking the absolute value so the result is always positive) and divide by the pooled standard deviation. The pooled standard deviation is typically the average of the two groups' standard deviations (or a weighted average if groups have different sizes). Cohen's d tells you how many standard deviations apart the two group means are.
How to use the Effect Size Calculator (Cohen's d)
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Enter your mean of group 1
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Enter your mean of group 2
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Enter your pooled standard deviation
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Read your results instantly
Results update in real time as you type.
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Interpreting Cohen's d
Jacob Cohen proposed conventional benchmarks: d = 0.2 is a small effect, d = 0.5 is a medium effect, and d = 0.8 is a large effect. These thresholds are rough guidelines developed for behavioral sciences and may differ in other fields.
For the default values (means 50 and 55, pooled SD 10), d = 0.5 — a medium effect. This means the two groups differ by half a standard deviation. About 69% of people in the higher-scoring group score above the average person in the lower-scoring group.
Statistical significance vs. practical significance
With a large enough sample, even a tiny difference can be statistically significant (p < 0.05). But a statistically significant result may have a Cohen's d of 0.05 — so small as to be practically meaningless. Effect size tells you whether a finding matters in the real world, not just whether it is unlikely due to chance.
Conversely, a study with a small sample might have a large Cohen's d (the effect is real and large) but fail to reach significance simply because of limited statistical power. Reporting both p-value and effect size gives the most complete picture.
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Pooled standard deviation explained
When the two groups have different sample sizes (n₁ and n₂) and standard deviations (s₁ and s₂), the pooled standard deviation is: σ_pooled = √[((n₁−1)s₁² + (n₂−1)s₂²) / (n₁+n₂−2)]. For equal group sizes, this simplifies to √[(s₁² + s₂²)/2].
If the groups have very different variances (violating the homogeneity of variance assumption), Glass's Δ — which uses only the control group's standard deviation — is a better measure of effect size.
Tips & Insights
Cohen's thresholds are field-specific
In medicine, even d = 0.2 can be clinically important if the outcome is mortality. In education, d = 0.4 is often considered meaningful. Always interpret effect size in the context of your field.
Use pooled SD, not group SD
If you only have one group's standard deviation, you can use it as an approximation, but the pooled standard deviation is more appropriate when comparing two groups.
Effect size guides power analysis
Before collecting data, use your expected effect size to calculate the sample size needed to achieve adequate statistical power (typically 80%). A larger expected effect requires a smaller sample.
Worked Examples
Drug vs. placebo trial
Cohen's d: 0.667 (medium-to-large effect). The drug group's outcome is two-thirds of a standard deviation lower — a clinically meaningful difference worth investigating further.
Teaching method comparison
Cohen's d: 0.40. A small-to-medium effect. The new teaching method shows a meaningful improvement that warrants broader implementation.
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Frequently Asked Questions
What is Cohen's d?
Cohen's d is a measure of effect size that expresses the difference between two group means in units of the pooled standard deviation. It quantifies the practical magnitude of a difference.
What is a large effect size?
By Cohen's conventions, d = 0.2 is small, d = 0.5 is medium, and d = 0.8 is large. However, what counts as large depends on the field — in some contexts, d = 0.2 is very important.
What is the difference between effect size and p-value?
The p-value tells you whether an effect is statistically significant (unlikely due to chance). Effect size tells you how large the effect is. A tiny effect can be significant with a large enough sample.
What is pooled standard deviation?
Pooled standard deviation is a weighted average of two groups' standard deviations, used when the groups are assumed to have equal population variances. It provides a single estimate of spread for the combined data.
Can Cohen's d be negative?
By convention, Cohen's d is reported as an absolute value (always positive). The direction of the effect (which group is higher) is described separately in the research context.
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