Imagine two studies. Both report "a statistically significant difference (p < 0.05)." In the first, a new teaching method raises test scores by half a standard deviation. In the second, it raises them by 0.02 of a standard deviation — a change nobody would ever notice. The p-value can't tell these apart. The effect size can. It's the single most important number that most beginners forget to report.
Why the p-value isn't enough
A p-value depends heavily on sample size. With a large enough sample, almost any difference — however trivial — becomes "statistically significant." That's not a bug; it's how the math works. So a small p-value tells you an effect probably exists, but says nothing about whether it's big enough to care about. Effect size fills that gap by measuring the magnitude of the effect on a standardized scale that doesn't inflate with sample size.
Statistical significance = "we're confident the effect isn't zero."
Practical significance = "the effect is big enough to matter."
You need both.
Cohen's d — for comparing two means
When you compare two group means (as in a t-test), the standard effect size is Cohen's d. It expresses the gap between the means in units of standard deviation:
d = (mean₁ − mean₂) / pooled standard deviation
A d of 1.0 means the two groups differ by one full standard deviation. Jacob Cohen's widely used benchmarks:
| |d| | Interpretation | Overlap between groups |
|---|---|---|
| 0.2 | Small | ~85% |
| 0.5 | Medium | ~67% |
| 0.8 | Large | ~53% |
These are rules of thumb, not sacred cutoffs — what counts as "large" depends on your field. A 0.2 effect can be hugely important in public health at population scale, while 0.8 might be unremarkable in a lab experiment.
Hedges' g — the small-sample correction
Cohen's d slightly overestimates the effect when samples are small. Hedges' g applies a correction factor that matters when you have fewer than about 20 per group, and becomes negligible above that. When in doubt with small samples, report g. Our effect size calculator gives you both automatically.
Correlation r — for relationships
For the relationship between two numeric variables, the correlation coefficient r is the effect size. It ranges from −1 to +1:
| |r| | Strength |
|---|---|
| 0.1 | Small / weak |
| 0.3 | Medium / moderate |
| 0.5+ | Large / strong |
Squaring it (r²) tells you the proportion of variance explained — an r of 0.5 means 25% of the variation in one variable is accounted for by the other.
Other common effect sizes
- Cohen's h — for the difference between two proportions (see the two-proportions z-test).
- Cramér's V — for association in a chi-square contingency table.
- Eta-squared (η²) — proportion of variance explained in ANOVA.
- Rank-biserial r — for the Mann-Whitney U test.
How to report it
Best practice is to report the effect size alongside the test statistic and p-value, ideally with a confidence interval. For example:
"The treatment group scored significantly higher than control, t(58) = 2.9, p = 0.005, with a medium effect size (d = 0.62)."
Calculate your effect size
Effect Size Calculator (Cohen's d & Hedges' g) →Two-sample, one-sample, or paired designs — with a visual overlap chart.Related reading: Interpreting p-values · Confidence intervals explained · Choosing a statistical test.