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.
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Analogy
Statistical significance says there is a signal. Effect size says how loud it is.
Example
Method A mean 80, SD 10Method B mean 74, SD 12Pooled SD = square root of 122 = 11.05d = 6 / 11.05 = 0.54A 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.