Effect Size Calculator
Turn group means and SDs, a t statistic or an ANOVA result into a standardized effect size — Cohen's d, Hedges' g, Glass's Δ, dz and dav for paired data, η², partial η² and Cohen's f — or convert between r, d and an odds ratio. Every output states the formula it used, with your numbers substituted, and how it compares with Cohen's benchmarks.
Group 1 (treatment)
Group 2 (comparison)
Fill in the fields above to see the effect size. Standard deviations must be positive and sample sizes at least 2.
How to Use the Effect Size Calculator
- 1. Say what you have. Summary statistics for two independent groups, for two paired conditions, a t statistic, an ANOVA result, or an effect size you want to convert.
- 2. Fill in the fields. Means, standard deviations and sample sizes; or t and the n's; or F with its two degrees of freedom; or the sums of squares from an ANOVA table.
- 3. Read the effect sizes. Each card is labelled, and the formulas panel states exactly how each number was computed, with your values substituted.
- 4. Interpret with care. The benchmark line places the main result against Cohen's small, medium and large — useful as a rough guide, not a verdict.
Which Effect Size Should You Report?
| Situation | Effect size | Formula |
|---|---|---|
| Two independent groups | Cohen's d | (M₁ − M₂) ÷ sp, with the pooled SD sp |
| The same, small samples | Hedges' g | J × d, J = 1 − 3 ÷ (4(n₁ + n₂) − 9) |
| A treatment that changes the spread | Glass's Δ | (M₁ − M₂) ÷ SD of the comparison group |
| Paired or repeated measures | dz and dav | Mdiff ÷ sdiff; Mdiff ÷ ((s₁ + s₂) ÷ 2) |
| ANOVA | η², partial η², f | SSeffect ÷ SStotal; F·df₁ ÷ (F·df₁ + df₂); √(η² ÷ (1 − η²)) |
Hedges' g corrects the small upward bias of d in small samples; with 58 participants the correction factor is 0.9865, so the two barely differ, but with 10 participants per group it is about 0.96. Glass's Δ standardizes by the comparison group's SD alone, which is the safer choice when an intervention changes the variability as well as the mean.
Worked Examples
Two classes. A class taught with a new method averages 82.4 (SD 9.1, n = 30) against 76.8 (SD 10.3, n = 28) for the usual method. The pooled SD is 9.6971, so d = 5.6 ÷ 9.6971 = 0.5775. The correction factor J = 1 − 3 ÷ (4 × 58 − 9) = 0.9865 gives g = 0.5697, and dividing by the comparison class's SD instead gives Δ = 5.6 ÷ 10.3 = 0.5437.
Before and after. Twenty-five students score 24.6 (SD 5.2) before a workshop and 21.3 (SD 4.8) after, and the SD of their individual differences is 3.9. Then dz = 3.3 ÷ 3.9 = 0.8462, while dav = 3.3 ÷ 5 = 0.66. Both are legitimate but answer different questions: dz reflects how consistently individuals changed — it is what drives the power of a paired t-test — while dav is on the same scale as a between-groups d, so it is the one to compare with other studies (Lakens, 2013).
Converting Between Effect Sizes
Meta-analyses often need every study on one scale. A correlation converts to d with d = 2r ÷ √(1 − r²), so r = 0.3 becomes d = 0.629; the reverse is r = d ÷ √(d² + 4). Both assume two groups of equal size — with unequal groups use r = d ÷ √(d² + a), where a = (n₁ + n₂)² ÷ (n₁n₂). An odds ratio converts with Chinn's (2000) logit method, d = ln(OR) × √3 ÷ π: an odds ratio of 2.5 corresponds to d = 0.5052, and d = 0.629 corresponds to an odds ratio of 3.13.
Cohen's Benchmarks — and Their Limits
| Measure | Small | Medium | Large |
|---|---|---|---|
| d, g, Δ | 0.2 | 0.5 | 0.8 |
| r | 0.1 | 0.3 | 0.5 |
| η² | 0.01 | 0.06 | 0.14 |
| f | 0.10 | 0.25 | 0.40 |
Cohen (1988), Statistical Power Analysis for the Behavioral Sciences, 2nd ed.
Cohen offered these values as a fallback for when nothing better is known, and he warned against using them mechanically. What counts as large depends on the field and the outcome: Kraft (2020), for instance, argues that in education-intervention research effects of 0.05 to 0.20 SD are already medium. Partial η² is also inflated relative to η² in designs with several factors, so its benchmark labels flatter it. Compare your effect with similar studies and with what would matter in practice.
Frequently Asked Questions
- What is a good effect size?
- There is no universal answer. Cohen's benchmarks call d = 0.2 small, 0.5 medium and 0.8 large, but a d of 0.2 can be important for a cheap intervention affecting millions, and a d of 0.8 can be disappointing in a lab manipulation. Judge it against prior studies in your area and the practical stakes.
- What is the difference between Cohen's d and Hedges' g?
- Both divide the mean difference by a pooled standard deviation, but d is slightly biased upward in small samples. Hedges' g multiplies d by a correction factor J = 1 − 3 ÷ (4(n₁ + n₂) − 9), which matters with fewer than about 20 participants per group and is negligible beyond that. Many meta-analyses report g by default.
- How do I calculate Cohen's d from a t-test?
- For an independent-samples t-test, d = t × √(1 ÷ n₁ + 1 ÷ n₂); with t = 2.45 and groups of 30 and 28, d = 0.6438. For a paired t-test, dz = t ÷ √n, so t = 2.45 with 25 pairs gives dz = 0.49. Choose "A t statistic" above and the calculator applies the right one.
- Should I report eta squared or partial eta squared?
- In a one-way ANOVA they are identical. In factorial designs, partial η² removes the other effects from the denominator, which makes it comparable across studies with the same design but larger than η². Say which one you report, and prefer η² when you want the share of the total variance.
- How do I convert an odds ratio to Cohen's d?
- Use the logit method from Chinn (2000): d = ln(OR) × √3 ÷ π, about ln(OR) ÷ 1.81. An odds ratio of 2.5 gives d ≈ 0.51. The conversion assumes the binary outcome comes from an underlying continuous variable with a logistic distribution.
- Can Cohen's d be negative?
- Yes. The sign only shows which group has the larger mean: d is negative when the first group's mean is smaller. The benchmarks apply to the absolute value, so d = −0.6 is a medium-to-large effect in the opposite direction.