Effect Size Calculator (Cohen's d)
Cohen's d, Hedges' g, Glass's Δ, paired d_z, and conversions from t or F, with overlap and common-language effect size.
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Effect Size Explained: Cohen's d, r and Eta Squared
What Cohen's d, Hedges' g, r, eta squared and Cramér's V measure, how to calculate d by hand, and why a small p-value is not enough.
Statistical Power Explained
What 80% power means, how effect size, sample size and alpha change it, and the sample size per group needed for small, medium and large effects.
Why effect size matters
A p-value only answers whether an effect is distinguishable from zero; it confounds effect magnitude with sample size. Cohen's d puts the mean difference in pooled SD units so results compare across studies: the load-example teaching comparison gives d = 0.6338 (medium).
Choosing d, g, or Glass's Δ
Independent groups: d = (m₁ − m₂) / s_p, g = d × J(df)
Paired: d_z = (mean of differences) / SD(differences)
Glass's Δ = (m_treatment − m_control) / SD_control
Use Hedges' g (via exact J) when samples are small. Use Glass's Δ when only the control group SD should standardize the effect (e.g., unchanged diagnostic group).
Paired d_z vs d_av
d_z divides by the SD of difference scores; d_av divides by the average within-subject SD of the two measurements. Reporting the wrong one is a common meta-analysis mistake: this calculator shows both for raw paired columns.
Related tools
Plan sample size with the sample size calculator, check significance with the t-test or two-sample t-test calculators, and see whether your n can detect an effect with the statistical power calculator.
Worked example (Load example)
Steps
Pooled variance: ((29)(100) + (29)(144)) / 58 = 122 → s_p = 11.0454.
Cohen's d = (85 − 78) / 11.0454 = 0.6338 (medium).
Hedges' g = 0.6338 × J(58) = 0.6255 with the exact gamma correction.
Frequently Asked Questions
What is the difference between Cohen's d and Hedges' g?
Both standardize a mean difference by a pooled SD. Hedges' g multiplies d by an exact small-sample correction J(df) so g is less biased when n is small; with 30+30 subjects they differ by about 0.008.
How do I get d from a published t statistic?
For independent groups: d = t × √(1/n₁ + 1/n₂). For paired data: d_z = t / √n. Choose the mode that matches the design that produced t.
Are 0.2, 0.5, and 0.8 universal?
No, they are Cohen's rough conventions. Compare to effects typical in your field and to the cost of being wrong, not only to these cutoffs.
What is the overlap percentage?
For two normal groups separated by d, overlap = 2Φ(−|d|/2). At d = 0.6338 about 75% of the two distributions still overlap.
When should I use Glass's delta?
When the control group's variability is the meaningful yardstick: common in clinical trials with a stable reference group.
What is d_z for paired data?
It is the mean change divided by the SD of the changes. It usually differs from an independent-groups d computed on the same raw scores.
Can I convert d to a correlation r?
Yes for designs linkable to point-biserial r: r = d / √(d² + 4) with equal n, or r = d / √(d² + 4/n*) with unequal n*.
Where do η² and Cohen's f fit?
From ANOVA: η² = (F·df₁)/(F·df₁ + df₂) and f = √(η²/(1−η²)). They describe variance explained, not mean differences on the original scale.
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