Effect size — how big, not just whether
Significance tells you something is there. Effect size tells you whether it matters.
An effect size expresses the size of a difference or relationship in units that can be compared across studies. Cohen's d for two means: about 0.2 is small, 0.5 medium, 0.8 large. Eta squared (η²) for ANOVA: the proportion of variance explained. Cramér's V for categorical associations. Odds ratio and relative risk for binary outcomes.
Why it matters
With a large enough sample, a difference far too small to matter clinically will still be statistically significant. With a small sample, a large and important difference may not reach significance. The p-value alone cannot distinguish these, and journals increasingly refuse papers that report it alone.
An example
Two studies both report p = 0.03 for a pain reduction.
Study A: n = 800, mean difference 0.3 points on a 10-point scale, d = 0.14. Statistically significant, clinically irrelevant — nobody notices a third of a point.
Study B: n = 42, mean difference 1.4 points, d = 0.76. Same p-value, an effect a patient would feel.
Common mistakes
- Reporting effect size only when it is large.
- Quoting Cohen's benchmarks as though they were universal — they are rules of thumb, and what counts as large differs by field.
- Confusing the effect size with the mean difference. Report both.
Read next
- What a p-value is, and what it is not — The single most misreported number in postgraduate research.
- Confidence intervals, and why they say more than a p-value — A range of values your data are consistent with.
Chavery Research Companion applies this to your own study: it asks the questions in plain language, checks the assumptions against your data, recommends the test, and writes the sentence that reports it. Start free — planning and the master chart cost nothing.