Effect Size Calculator
Use this effect size calculator to see how large the difference between two groups is relative to their spread. Cohen’s d answers that. Example: means of 105 and 100 with standard deviations of 15 and 12 give d = 0.36, a small to medium effect.
Example: Group 1: mean 105 · Group 1: standard deviation 15 · Group 1: size 36 · Group 2: mean 100 · Group 2: standard deviation 12 · Group 2: size 30 → Cohen’s d: d = 0.364 (small effect). Source: Wikipedia – Effect size: Cohen’s d, Hedges’ g. Updated: .
How it is calculated
Effect size tells you how large a difference really is, regardless of sample size. Cohen's d measures the difference between two means in units of the common standard deviation. A p-value only says whether a difference could be due to chance; d says whether it also matters.
The formulas
- Pooled standard deviation: s = √(((n₁ − 1) · s₁² + (n₂ − 1) · s₂²) / (n₁ + n₂ − 2)).
- Cohen's d: d = (M₁ − M₂) / s.
- Hedges' g: g = d · (1 − 3 / (4 · (n₁ + n₂) − 9)), more accurate for small groups.
Interpretation
According to Cohen, d ≈ 0.2 is small, 0.5 medium and 0.8 large; from about 1.2 it is called very large. These are rules of thumb, not a substitute for expert judgement: at d = 0.2 the distributions still overlap by about 92%.
Example
Group 1: M = 105, s = 15, n = 36; group 2: M = 100, s = 12, n = 30. Pooled s = 13.72, so d = 5 / 13.72 = 0.36. That corresponds to a probability of superiority of about 60%: a random value from group 1 is above one from group 2 in 60% of pairs.
Notes
Enter the sample standard deviation (dividing by n − 1). The confidence interval is an approximation after Hedges and Olkin. For dependent measurements (before and after) a different formula applies.
Frequently asked questions
What is Cohen’s d?
A standardised measure of the difference between two means: the difference divided by the common (pooled) standard deviation. It lets you compare differences independently of the measurement scale.
When is an effect small, medium or large?
According to Cohen: about d = 0.2 small, 0.5 medium, 0.8 large. These are rules of thumb; what matters depends on the field.
What is the difference between Cohen’s d and Hedges’ g?
Hedges’ g corrects the slight overestimate of d in small samples. For large groups the two are practically the same.
What does the probability of superiority mean?
It tells how often a randomly drawn value from group 1 is higher than one from group 2. At d = 0 it is 50%, at d = 1 about 76%.
Do I need effect size in addition to the p-value?
Yes. With very large samples even a tiny difference becomes significant; only the effect size shows whether it matters in practice.
Sources and legal basis
- Wikipedia – Effect size: Cohen’s d, Hedges’ g
- Wikipedia – Probability of superiority (common-language effect size)
As of: · Editorial policy
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