Effect size
Effect size measures the practical importance of a result independently of sample size. A finding can be statistically significant yet trivially small. Cohen's d is the most widely used index for mean comparisons.
FrameworkHypothesis testing
See it move
Cohen's d divides the difference between two group means by the pooled standard deviation. Conventional benchmarks treat 0.2 as a small effect, 0.5 as medium and 0.8 as large, though what counts as meaningful still depends on context. A statistically significant result can still carry a trivially small effect size.
The formula
Variables
- Sample mean of group 1
- Sample mean of group 2
- Pooled standard deviation: √[((n₁ − 1)s₁² + (n₂ − 1)s₂²) ÷ (n₁ + n₂ − 2)]
Conventional benchmarks: |d| = 0.2 small, 0.5 medium, 0.8 large. What constitutes a practically important effect depends on context, not convention alone.
Check yourself
A randomised trial of a new study-skills workshop shows a statistically significant improvement in exam scores (p = 0.001) with Cohen's d = 0.08. What is the most accurate interpretation?