Effect Size Calculator
Cohen’s d and Hedges’ g for the difference between two group means, from each group’s mean, standard deviation and size, with the pooled standard deviation.
Result
Cohen’s d: 1.126908
Assumes two independent groups with similar spread. For paired or repeated measures, a different d applies.
- Hedges’ g, small-sample corrected
- 1.079292
- Pooled standard deviation
- 0.887384
- Difference in means, group 1 − group 2
- 1
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How to use the Effect Size Calculator
- For each group, enter its mean, its standard deviation and how many observations it has.
- Read Cohen's d, the difference in means measured in pooled standard deviations, and Hedges' g beside it.
- Swap the groups to change the sign; the size stays the same.
The formulas
pooled SD = √[((n1 − 1) × s1² + (n2 − 1) × s2²) ÷ (n1 + n2 − 2)]d = (M1 − M2) ÷ pooled SDg = d × (1 − 3 ÷ (4 × (n1 + n2) − 9))The sign of d follows group 1 minus group 2, so a negative d means group 1 has the lower mean.
Assumptions
The groups are independent, such as two classes or a treatment and a control group, and their spreads are similar enough to pool. For the same people measured twice, a paired design, the standard deviation of the differences is used instead, and this page does not cover it. If both standard deviations are zero, there is no spread to measure against and d does not exist; the page says so.
What the diagram shows
Two normal curves with the same spread, one for each group, their centres d pooled standard deviations apart. The more they overlap, the smaller the effect.
With your numbers
- Pooled SD = √[((n1 − 1) × s1² + (n2 − 1) × s2²) ÷ (n1 + n2 − 2)] = 0.887384
- d = (M1 − M2) ÷ pooled SD = 1 ÷ 0.887384 = 1.126908
- g = d × (1 − 3 ÷ (4 × (n1 + n2) − 9)) = 1.079292
Quick reference
Assumes two independent groups with similar spread. For paired or repeated measures, a different d applies.
| Example | Cohen’s d |
|---|---|
| 8.7 (0.82) against 7.7 (0.95), 10 each | 1.126908 |
| 105 against 100, SD 15, 50 each | 0.333333 |
| 20 (4, 12) against 23 (6, 30) | -0.543214 |
| 7.7 (0.95) against 8.7 (0.82), 10 each | -1.126908 |
| Equal means | 0 |
| 72 against 68, SD 8 and 10, 200 each | 0.441726 |
Common questions about the Effect Size Calculator
- What does Cohen's d measure?
- How far apart two group means are, in units of the spread within the groups. A d of 1 means the means are one pooled standard deviation apart. Because it has no units, it lets a difference in test scores be compared with a difference in reaction times, which is why meta-analyses use it.
- What is the pooled standard deviation?
- A single spread for both groups: the two variances averaged, each weighted by its degrees of freedom, n − 1, then square-rooted. With SDs of 0.82 and 0.95 and 10 in each group, it is about 0.887, so a 1-point difference in means is a d of about 1.13.
- When should I use Hedges' g instead?
- With small groups. d computed from samples runs slightly large, and g multiplies it by 1 − 3 ÷ (4(n1 + n2) − 9) to correct for that. At 10 per group, d of 1.127 becomes g of 1.079; with a few hundred in each group, the two agree to two decimal places.
- Is a d of 0.5 medium?
- Cohen suggested 0.2, 0.5 and 0.8 as rough guides when nothing better was known, and he and later authors, such as Lakens, warn against applying them mechanically. Whether a difference matters depends on the field and the outcome, so this page reports the number and leaves the judgement to you.