Cohen's d expresses a mean difference in standard-deviation units, so the size of an effect can be compared across studies and scales.
Why it matters
p-values depend on sample size. Effect size tells how big the difference is, whatever the sample size.
Key ideas
- d = (mean1 − mean2) ÷ pooled SD
- Rough guide: 0.2 small, 0.5 medium, 0.8 large
- Sign shows direction
- Report d with its CI
- Context matters more than labels
- Paired design: dz = mean(d) ÷ SD(d)
Real-life research example
Two teaching methods differ by 6 marks and the pooled SD is 12, so d = 0.5, a medium effect.
When to use
- Always alongside a t-test
When NOT to use
- Don't treat 0.2/0.5/0.8 as strict cut-offs
- Don't compare d from different designs without care
Mini example
Mean A = 70, Mean B = 64, pooled SD = 12 → d = 6 ÷ 12 = 0.5
Quick takeaway
d says how many SDs apart the groups are.
Try it yourself
In the t-test calculator, make the two groups far apart, then close together. How does d change compared with p?
Model answer
Both move, but d describes the size of the gap in SDs and does not depend on n the way p does. Adding more data lowers p without changing d much.