How to use the cohen's d effect size calculator
- Choose summary numbers or raw values. With raw values, paste each group's numbers and the tool finds the mean, standard deviation and size for you.
- For summary numbers, enter the mean, standard deviation and sample size for group 1, then the same three numbers for group 2. The example numbers show the layout.
- Open the options if you want a different confidence level from the 95% shown.
- Read Cohen's d, Hedges' g, Glass's delta and the interval, with the pooled standard deviation and the steps.
Formula
pooled SD = sqrt(((n1 - 1) s1^2 + (n2 - 1) s2^2) / (n1 + n2 - 2))
d = (mean 1 - mean 2) / pooled SD
Hedges' g = d x J, where J = Gamma(df / 2) / (sqrt(df / 2) x Gamma((df - 1) / 2)), df = n1 + n2 - 2
SE of d = sqrt((n1 + n2) / (n1 n2) + d^2 / (2 (n1 + n2))), interval = d plus or minus z x SE
Glass's delta = (mean 1 - mean 2) / SD of group 2
Cohen's d expresses the difference in means in units of the pooled standard deviation. Hedges' g shrinks it a little to remove the upward bias in small samples.
Two classes of 32 and 29 students
Group 1 has a mean of 78.4, a standard deviation of 10.2 and 32 students, and group 2 has 72.1, 11.5 and 29. The pooled standard deviation is 10.836, so d = 6.3 / 10.836 = 0.5814. The correction factor is 0.98722, which gives g = 0.5739.
The standard error of d is 0.2617, so the 95% interval runs from 0.068 to 1.094. Glass's delta, using group 2's standard deviation, is 6.3 / 11.5 = 0.5478. The interval is wide because the groups are small, and it shows how uncertain the size of the effect is.
What the number means
A d of 0.5 means the group means are half a standard deviation apart, and about 69% of the lower group falls below the mean of the higher group if both are normal. Cohen suggested 0.2, 0.5 and 0.8 as rough reference points for small, medium and large effects in the behavioral sciences, but whether an effect matters depends on the field, the measure and the cost of acting on it.
An effect size is not a test of significance. For a p value from the same summary numbers, use the P Value Calculator, and to plan a study that can detect a chosen d, see the Sample Size Calculator.
Choosing between d, g and delta
Use d when both groups have similar spread. Use g for small samples, where d is slightly too large. Use Glass's delta when one group is a control with its own spread and the treatment may change the variation. On this page the standard deviation used for Glass's delta is the one from group 2, so enter the control as group 2. For a t test on the same groups, see the P Value Calculator, which also reports d.
More statistics tools
For related statistical tests and measures, try the AUC ROC Calculator, Confusion Matrix Calculator and Test Item Analysis Calculator.
Assumptions and limits
- The two groups are independent samples with roughly similar standard deviations.
- The interval uses a normal approximation to the standard error of d.
- Means and standard deviations are for the same measure in both groups.
- Example numbers are shown until you replace them.
Frequently asked questions
How do you calculate Cohen's d?
Subtract the two means and divide by the pooled standard deviation. For means of 78.4 and 72.1 with a pooled standard deviation of 10.836, d is 0.581.
What is the difference between Cohen's d and Hedges' g?
Hedges' g multiplies d by a correction factor slightly below 1 that removes the small sample bias. With large samples the two are almost the same.
Is a Cohen's d of 0.5 good?
It is a medium difference by Cohen's rough guide, but whether it matters depends on the field and the stakes. Look at the interval and what the units mean in your setting.
Why is the confidence interval so wide?
The standard error of d is large when samples are small, and it also grows with d. More participants make the interval narrower.