What is Cohen’s d? Effect size, explained simply
Cohen’s d is a standardized effect size — the difference between two group means divided by the pooled standard deviation. Because it’s expressed in standard-deviation units rather than your original scale, it tells you how big a difference is in a way you can compare across studies, measures, and fields.
The benchmarks (and a warning)
| Cohen’s d | Conventional label | Roughly equals (r) |
|---|---|---|
| 0.2 | Small | ≈ 0.10 |
| 0.5 | Medium | ≈ 0.24 |
| 0.8 | Large | ≈ 0.37 |
These are Cohen’s rules of thumb — conventions, not laws. In a high-stakes clinical outcome a “small” d can be hugely important; in a noisy field a “large” d might be unremarkable. Always interpret an effect size against what matters in your context, ideally using prior studies as the yardstick.
Why effect size belongs in every results section
A p-value answers “is there a detectable effect?” The effect size answers “how big is it?” — and only the second question speaks to whether your finding matters. Because significance scales with sample size, a p-value alone can make a trivial difference look impressive. Reporting standards (APA and most journals) now expect an effect size and a confidence interval alongside the p-value.
d, r, odds ratios — they convert
For a two-group comparison, the common effect sizes are different views of the same thing and translate into one another: r = d / √(d² + 4) and ln(OR) = d × π/√3. This matters for meta-analysis, where you often need everything on one scale.
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Frequently asked questions
What is Cohen’s d?
A standardized effect size: the mean difference divided by the pooled SD, in standard-deviation units so it compares across studies.
What are the benchmarks?
≈ 0.2 small, 0.5 medium, 0.8 large — conventions, not rules; judge against your field.
Why report an effect size?
The p-value says whether; the effect size says how much. Journals expect it alongside a confidence interval.
How does d relate to r and OR?
r = d/√(d²+4); ln(OR) = d×π/√3. The converter does it for you.