Effect Size Calculator
Quantify the practical significance of your findings. Calculate Cohen's d, Hedges' g, eta squared (η²), omega squared (ω²), and Cramér's V — for any test type.
About Effect Sizes
Effect size measures the magnitude of a statistical effect — how large the difference or association is in practical terms, independent of sample size. A p-value tells you whether an effect is statistically unlikely under H₀; effect size tells you whether the effect is clinically meaningful. CONSORT 2010 and APA mandate reporting effect sizes and 95% CIs for all primary outcomes.
Cohen's d (independent): d = (M₁ − M₂) / SD_pooled, where SD_pooled = √[((n₁−1)SD₁² + (n₂−1)SD₂²) / (n₁+n₂−2)]
Hedges' g: g = d × J(df), where J(df) = 1 − 3/(4df−1) is the small-sample bias correction. Preferred over d when n < 20 per group.
η² (ANOVA): η² = (F × df₁) / (F × df₁ + df₂). Omega squared ω² = (df₁ × (F−1)) / (F × df₁ + df₂ + 1) is less biased.
Cramér's V: V = √[χ² / (n × (min(r,c)−1))]. For 2×2 tables, V is equivalent to φ (phi coefficient).
Frequently Asked Questions
What is effect size and why does it matter?
Effect size quantifies the magnitude of an effect independent of sample size. A small p-value tells you the result is statistically unlikely, but says nothing about how large or clinically important the effect is. With large samples, even tiny, clinically irrelevant differences can reach statistical significance.
What are Cohen's d benchmarks?
Conventional thresholds (Cohen, 1988): d = 0.20 = small; 0.50 = medium; 0.80 = large. In clinical medicine, even a "small" d can be meaningful if the outcome is mortality. Always interpret effect size in the context of the specific clinical question and outcome.
What is the difference between Cohen's d and Hedges' g?
Both measure standardised mean difference. Hedges' g applies a small-sample correction J(df) = 1 − 3/(4df−1) to reduce the positive bias that Cohen's d shows in small samples. When n per group is large, d ≈ g. For small samples, report Hedges' g as it is less biased.
What is eta squared (η²)?
Eta squared is the proportion of total variance explained by the group factor in ANOVA. Benchmarks: η² = 0.01 = small; 0.06 = medium; 0.14 = large. Omega squared (ω²) adjusts for small-sample bias and is preferred in published reports.
How do I report effect size in a paper?
Include alongside test statistic and p-value. Examples: "t(86) = 3.24, p = 0.002, Cohen's d = 0.69"; "F(2,42) = 8.34, p < 0.001, η² = 0.28, ω² = 0.25"; "χ²(1, N=200) = 12.40, p < 0.001, Cramér's V = 0.25." CONSORT requires effect size and 95% CI for all primary outcomes.