# Effect size

Effect size measures how big a difference is, not just whether it is detectable. Cohen's d is the difference in means divided by the pooled standard deviation. Around 0.2 is small, 0.5 medium and 0.8 large.

Statistics (university) · Part 07: Comparing categories and many groups · Card 8 of 8 · Last updated 2026-10-19

## Analogy

Statistical significance says there is a signal. Effect size says how loud it is.

## Example

**Cohen's d**

Method A mean 80, SD 10
Method B mean 74, SD 12
Pooled SD = square root of 122 = 11.05
d = 6 / 11.05 = 0.54
A medium effect

## In practice

With a huge sample, a trivial gap can be significant. Effect size shows whether it matters.

## Practice

### Flashcards

- **What does Cohen's d measure?** The difference between means in pooled standard deviation units.

## Questions people ask

### Why report effect size as well as the p-value?

A p-value tells you whether a difference is unlikely to be chance, but not whether it is large enough to care about. With a big sample, tiny effects become significant. Effect size and an interval show the practical importance, which readers need to judge whether a result is worth acting on.

### How do I choose between a small, medium and large effect?

Cohen suggested 0.2, 0.5 and 0.8 as rough labels, but these are only guides. What counts as large depends on the field and the costs. A 0.2 improvement in a medical outcome for millions may matter greatly, while a 0.8 shift in a trivial measure may not matter at all.

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