What is a good effect size?

Cohen (1988) suggested d = 0.2 small, 0.5 medium, and 0.8 large; for η², .01, .06, and .14; for r, .1, .3, and .5. These are rough guides, so compare with typical effects in your own field.

Should I use Cohen's d or Hedges' g?

They are nearly identical with more than about 20 per group. With smaller samples, Hedges' g is preferred because it corrects the slight overestimate in d.

Can I calculate an effect size from a p value alone?

Not reliably. You need the test statistic (t, F, or z) and the sample sizes, or the means and SDs.

EFFECT SIZE CALCULATOR

Effect size calculator: Cohen's d, Hedges' g, eta squared, and r.

Calculate the effect size your results chapter needs, from means and SDs or straight from a t, F, or z value, with confidence intervals, benchmarks, and an APA-style sentence.

INPUT

Means & SDs

5 METHODS

Two independent groups: Cohen's d, Hedges' g, and Glass's Δ with a 95% CI.

GROUP 1 MEANGROUP 2 MEAN

GROUP 1 SDGROUP 2 SD (CONTROL)

GROUP 1 nGROUP 2 n

Effect size formulas, interpretation, and reporting

Why report an effect size?

A p value only says whether a difference is likely to be real. The effect size says how big it is. APA 7 asks for an effect size with every main result, and supervisors and journals expect it.

Cohen's d and Hedges' g

d = (M₁ − M₂) ÷ SD_pooled,   SD_pooled = √[((n₁−1)s₁² + (n₂−1)s₂²) ÷ (n₁+n₂−2)],   g = d × (1 − 3 ÷ (4df − 1))

Example: M₁ = 82.3 (SD 7.4) and M₂ = 76.1 (SD 8.9), 30 per group. SD_pooled = 8.18, so d = 6.2 ÷ 8.18 = 0.76, a medium-to-large effect. Hedges' g (0.75) corrects the small upward bias of d in small samples.

Eta squared from ANOVA

partial η² = (F × df_effect) ÷ (F × df_effect + df_error)

From F(2, 57) = 6.42: η² = 12.84 ÷ 69.84 = .18, so the grouping explains about 18% of the variance, a large effect.

Which effect size goes with which test?

t-tests → Cohen's d (independent) or dz (paired); Hedges' g for small samples
ANOVA → eta squared or partial eta squared
Mann-Whitney U and Wilcoxon → r = z ÷ √N
Correlation → r itself (r² for variance explained)
Chi-square → Cramér's V (shown in the chi-square calculator)

How to report it (APA style)

Put the effect size after the p value: “t(58) = 2.94, p = .005, d = 0.76, 95% CI [0.23, 1.28].” For ANOVA: “F(2, 57) = 6.42, p = .003, partial η² = .18.” Drop the leading zero only for values that cannot exceed 1 (η², r), not for d.

References

Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Lawrence Erlbaum.
Hedges, L. V., & Olkin, I. (1985). Statistical Methods for Meta-Analysis. Academic Press.
Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science. Frontiers in Psychology, 4, 863.

Effect Size Calculator

Get the effect size for any common test in seconds, from raw summary statistics or from a reported t, F, or z value, with benchmarks and APA wording.

Report Cohen's d alongside a t-test

Get partial eta squared from an ANOVA F value

Compute r for Mann-Whitney or Wilcoxon results

KEY FUNCTIONS

Cohen's d with 95% confidence intervalHedges' g and Glass's Δd or dz from independent or paired tPartial η² and Cohen's f from Fr from z, and r ↔ d conversion

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