Effect size & clinical significance

Two studies both report 'p < .05.' One moved clients a hair; the other transformed them. The p-value can't tell them apart — but effect size can. That gap is exactly why examiners test this topic.

A p-value tells you whether an effect is likely real (unlikely due to chance), but not how big it is — and it is inflated by large samples, so a trivial difference can look 'significant.' Effect size answers the question p ignores: how large / how strong is the effect? That is why p isn't enough on its own.

The most tested metric is Cohen's d, used for the difference between two means (expressed in standard-deviation units). Memorize the benchmarks: d = .2 = small, .5 = medium, .8 = large. So a d of .8 means the groups differ by about eight-tenths of a standard deviation — a large effect.

Other common effect-size metrics: r (and r²) for correlation / variance explained — Cohen's rough r benchmarks are .1 small, .3 medium, .5 large, and r² gives the proportion of variance explained. Eta-squared (η²) and omega-squared report variance explained in ANOVA. Odds ratios / relative risk index effects for categorical outcomes.

Finally, clinical significance is a further step beyond effect size: does the change matter in the client's real life — e.g., moving from a clinical to a normative range, or a change the client actually notices? A result can be statistically significant, have a modest effect size, and still not be clinically meaningful. Best practice: report effect sizes alongside p-values so readers judge magnitude, not just chance.

Clinical Pearl: p tells you whether an effect is real; effect size tells you how big. Lock in Cohen's d: .2 small / .5 medium / .8 large — and remember clinical significance asks whether the change actually matters to the client's life.