Effect Size Calculator

Cohen's d ยท Pearson r ยท ฮทยฒ ยท odds ratio

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Compute effect sizes for Cohen's d, Pearson's r, Eta-squared, or Odds/Risk Ratio.

Effect Size Visualization

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What Is Effect Size?

Effect size is a quantitative measure of the magnitude of a phenomenon. Unlike p-values which only indicate whether an effect exists, effect size tells you how large the effect is โ€” making it essential for practical significance, meta-analysis, and power analysis.

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Practical Significance

Effect size quantifies how meaningful a result is in practice, beyond statistical significance alone.

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Meta-Analysis

Effect sizes allow combining and comparing results across different studies with different scales and sample sizes.

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Power Planning

Knowing the expected effect size is essential for calculating the sample size needed to detect it reliably.

Effect Size Measures & Formulas

Cohen's d:  d = (Mโ‚ โˆ’ Mโ‚‚) / SDpooled
Standardized mean difference between two groups
Pearson's r:  r = t / โˆš(tยฒ + df)
Correlation coefficient or converted from t-statistic
Eta-squared:  ฮทยฒ = SSB / SST
Proportion of variance explained in ANOVA
Odds Ratio:  OR = (a ร— d) / (b ร— c)   |   Risk Ratio:  RR = (a/(a+b)) / (c/(c+d))
Association measures for 2ร—2 contingency tables

Interpretation Guidelines

MeasureSmallMediumLargeVery Large
Cohen's d0.20.50.81.2
Pearson's r0.10.30.50.7
Eta-squared (ฮทยฒ)0.010.060.140.20
Odds Ratio1.52.54.310+

Note: These benchmarks are from Cohen (1988) and are general guidelines. The practical significance of an effect size depends on the research context. A โ€œsmallโ€ effect can be highly meaningful in some domains.

Why Effect Size Matters

๐Ÿ“‰ Beyond p-values

A statistically significant p-value with a tiny effect size means the result is real but practically meaningless. Effect size tells you whether it matters.

๐Ÿ“ Publication Standards

APA, CONSORT, and major journals now require effect sizes. Reporting only p-values is increasingly seen as incomplete statistical practice.

๐Ÿ” Cross-Study Comparison

Effect sizes allow you to compare findings across studies that used different scales, measures, or sample sizes โ€” essential for systematic reviews.

๐Ÿ“‹ Sample Size Planning

Power analysis requires an expected effect size. Knowing whether you expect a small or large effect determines how many participants you need.

Converting Between Measures

d โ†’ r:  r = d / โˆš(dยฒ + 4)
Convert Cohen's d to Pearson's r
r โ†’ d:  d = 2r / โˆš(1 โˆ’ rยฒ)
Convert Pearson's r to Cohen's d
d โ†’ ฮทยฒ:  ฮทยฒ = dยฒ / (dยฒ + 4)
Approximate eta-squared from Cohen's d (equal groups)
OR โ†’ d:  d = ln(OR) ร— โˆš3 / ฯ€
Convert log Odds Ratio to Cohen's d (Hasselblad & Hedges)
Worked Example: Convert Cohen's d = 0.5 to Pearson's r.
r = 0.5 / โˆš(0.5ยฒ + 4)
r = 0.5 / โˆš(0.25 + 4)
r = 0.5 / โˆš4.25
r = 0.5 / 2.062 = 0.243

Frequently Asked Questions

Use Cohen's d for comparing two group means. Use Pearson's r for correlations. Use Eta-squared for ANOVA with multiple groups. Use Odds or Risk Ratio for categorical outcomes in 2ร—2 tables.
For Cohen's d: small is 0.2, medium is 0.5, and large is 0.8. For Pearson's r: small is 0.1, medium is 0.3, and large is 0.5. For Eta-squared: small is 0.01, medium is 0.06, and large is 0.14. These are Cohen (1988) benchmarks.
P-values only tell you if an effect exists, but not how large it is. A tiny effect can be statistically significant with a large enough sample. Effect size quantifies practical significance and allows comparison across studies.
Hedges' g applies a small-sample bias correction to Cohen's d. For samples larger than about 20 per group, the difference is negligible. Use Hedges' g when reporting in meta-analyses or with small samples.
If the 95% CI for an OR includes 1.0, the association is not statistically significant. An OR of 2.5 with CI [1.2, 5.2] means the odds are significantly 2.5 times higher in the exposed group.
Yes. Cohen's d can be converted to r using r = d / โˆš(dยฒ + 4). Eta-squared can be derived from d using ฮทยฒ = dยฒ / (dยฒ + 4). Odds Ratio can be converted to d using d = ln(OR) ร— โˆš3 / ฯ€.

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