Enter two proportions (P1 and P2) — values between 0 and 1 — and this Cohen's H Calculator computes the effect size h for comparing two proportions. You get the Cohen's H value, its magnitude interpretation (small, medium, or large), and the individual arcsine-transformed values (φ1 and φ2) used in the calculation.
Cohen's H Effect Size
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Effect Size Magnitude
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Arcsine Transform φ₁ (P₁)
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Arcsine Transform φ₂ (P₂)
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|h| (Absolute Value)
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Cohen's H is a measure of effect size used when comparing two proportions. It was developed by Jacob Cohen to quantify the practical significance of the difference between two proportions, beyond just statistical significance. The formula involves an arcsine transformation: h = 2·arcsin(√P₁) − 2·arcsin(√P₂).
By Cohen's (1988) conventions, an |h| of 0.20 is considered a small effect, 0.50 is a medium effect, and 0.80 or greater is a large effect. These thresholds are guidelines only and should be interpreted in the context of the specific research domain.
Proportions are bounded between 0 and 1, which makes their distribution non-normal and their variance unstable across the range. The arcsine square-root transformation (φ = 2·arcsin(√P)) stabilises the variance and normalises the distribution, allowing meaningful comparison of differences across different baseline proportions.
Cohen's d is used to measure effect size when comparing two means (continuous outcomes), while Cohen's H is specifically designed for comparing two proportions (binary outcomes). Both use the same small/medium/large thresholds (0.2, 0.5, 0.8), but their formulas and use cases are different.
Yes. Cohen's H can be negative when P₁ is smaller than P₂, since h = φ₁ − φ₂. In practice, most researchers report the absolute value |h| to describe effect magnitude, regardless of direction. The sign simply indicates which proportion is larger.
A Cohen's H of exactly 0 means the two proportions are identical — there is no effect. As |h| increases, the practical difference between the two proportions becomes more substantial, even if both proportions look similar in raw terms (e.g., comparing 0.01 vs 0.04 yields a larger h than comparing 0.50 vs 0.53).
Cohen's H is commonly used in power analysis to determine the sample size needed to detect a difference between two proportions. You specify the expected proportions (P₁ and P₂), compute h, then use a power analysis tool with the desired significance level (α) and power (1−β) to find the required N.
Enter proportions as decimal values between 0 and 1. For example, if 45% of Group 1 responded positively, enter 0.45 for P₁. If 30% of Group 2 responded positively, enter 0.30 for P₂. Do not enter percentages (like 45 or 30) — use their decimal equivalents.