Effect Size Calculator
Calculate Cohen's d and the correlation r from group means and standard deviations or from a t statistic. Interpret effect size with the 0.2 / 0.5 / 0.8 benchmarks.
What is Effect Size?
Effect size measures the magnitude of a difference or relationship, independent of sample size. While a p-value tells you whether an effect exists (statistical significance), effect size tells you how large it is (practical significance).
Cohen's d is the standardized difference between two means: the difference divided by the pooled standard deviation. It is expressed in standard deviation units, so d = 0.5 means the group means differ by half a standard deviation.
Common benchmarks by Jacob Cohen: d ≈ 0.2 is small, 0.5 medium, and 0.8 large. These are rough conventions, and the practical importance of an effect always depends on context.
Cohen's d Formula
The pooled standard deviation and Cohen's d are computed as:
d = (m1 − m2) / s_pooled
How to Use This Calculator
Follow these steps:
- Choose the tab that matches your data: group means and SDs, or a t statistic.
- Enter the required values. The tool computes Cohen's d, the correlation r and the pooled SD automatically.
- Read the effect size interpretation bar to see whether the effect is negligible, small, medium or large.
Worked Example
An intervention study reports mean scores 22 and 18, pooled SD of 5:
Frequently Asked Questions
Have another question? Let us know.
Why report effect size in addition to p-values?
A p-value only tells you whether a result is statistically significant, which depends heavily on sample size. Effect size quantifies the magnitude of the effect, making results comparable across studies and supporting meta-analysis.
How do I interpret Cohen's d?
Conventionally, |d| ≈ 0.2 is a small effect, 0.5 a medium effect, and 0.8 a large effect. These benchmarks are rough guides; interpret them in the context of your research area.
How is effect size related to the correlation r?
For a two-group comparison, r = d / √(d² + 4) (with equal group sizes). r ranges from 0 to 1 and can be interpreted as the correlation between the grouping variable and the outcome.
Does sample size affect effect size?
No. Effect size is a property of the population and is independent of sample size (though sample estimates get more precise with larger samples). That is why it complements significance testing.
