Understanding effect sizes: Cohen's d, eta-squared, and R-squared

Updated March 2026

A p-value tells you whether an effect exists. An effect size tells you how large the effect is. APA 7th edition requires effect sizes for all statistical tests, and an increasing number of journals will reject manuscripts that report only p-values.

This guide covers the most common effect size measures, when to use each, and how to interpret them.

Why effect sizes matter

Consider two studies that both find p < .05:

• Study A: t(200) = 2.10, p = .037, d = 0.30
• Study B: t(20) = 3.15, p = .005, d = 1.41

Both are statistically significant. But Study A found a small effect in a large sample, while Study B found a very large effect in a small sample. Without the effect size, you'd treat these as equivalent — they're not.

Effect sizes are essential for:

• Practical significance — Is the effect large enough to matter in the real world?
• Power analysis — Planning sample sizes for future studies (try our free sample size calculator)
• Meta-analysis — Combining results across studies requires standardized effect sizes
• Publication — APA 7th edition mandates effect size reporting

Cohen's d: comparing two groups

Cohen's d measures the standardized difference between two group means. It expresses the difference in standard deviation units.

Interpretation benchmarks (Cohen, 1988)

Magnitude	Cohen's d	What it means
Small	0.20	The groups overlap substantially; the difference is subtle
Medium	0.50	The difference is noticeable and often practically meaningful
Large	0.80	The groups are clearly different; minimal overlap in distributions

When to use Cohen's d

• Unpaired t-test (between two independent groups)
• Paired t-test (comparing two related measurements)
• Post-hoc pairwise comparisons after ANOVA

Eta-squared and partial eta-squared: ANOVA effect sizes

Eta-squared (η²)

The proportion of total variance in the outcome explained by the grouping variable. Used with one-way ANOVA.

Partial eta-squared (η²_p)

The proportion of variance explained by one factor after removing variance explained by other factors. Used with factorial ANOVA and repeated measures ANOVA.

Interpretation benchmarks

Magnitude	η2 / η2p	What it means
Small	.01	The factor explains about 1% of variance
Medium	.06	The factor explains about 6% of variance
Large	.14	The factor explains about 14% or more of variance

R-squared: regression effect sizes

R² (the coefficient of determination) measures the proportion of variance in the outcome that is explained by the predictor(s) in a regression model.

• R² = .04 → The model explains 4% of variance (small)
• R² = .13 → The model explains 13% of variance (medium)
• R² = .26 → The model explains 26% of variance (large)

For multiple regression, report adjusted R², which penalizes for the number of predictors. This prevents overfitting from inflating the apparent effect size.

Other effect sizes you may encounter

Effect size	Used with	Small / Medium / Large
Cramér's V	Chi-square test	.10 / .30 / .50
Rank-biserial r	Mann-Whitney U, Wilcoxon	.10 / .30 / .50
Odds ratio (OR)	Logistic regression	1.5 / 2.5 / 4.3 (Rosenthal, 1996)
Pearson r	Correlation	.10 / .30 / .50
Hazard ratio (HR)	Cox regression	Context-dependent; no universal benchmarks

Context matters more than benchmarks

Cohen himself called his benchmarks "small, medium, and large" with the caveat that they were starting points, not rules. In practice:

• In pharmacology, a d of 0.20 might be clinically meaningful if the drug has few side effects
• In education, a d of 0.40 could affect millions of students
• In basic neuroscience, d > 1.0 is common because experimental control is tight

Always interpret effect sizes in the context of your field, your intervention, and the practical consequences of the effect.

Reporting checklist

1. Choose the effect size appropriate to your test (Cohen's d for t-tests, η² for ANOVA, R² for regression, etc.)
2. Report the effect size alongside the test statistic and p-value — in the same sentence
3. Include a confidence interval for the effect size when possible
4. Note the magnitude label (small/medium/large) but interpret in context
5. Use the same effect size measure consistently throughout a paper for the same type of comparison