Power Analysis Calculator: Two Proportions
Comparing two conversion rates, success rates or prevalences? Enter the two proportions you expect (say 40% vs 60%), your alpha and target power, and get the required sample size per group. The calculator converts the proportions to Cohen's effect size h using the arcsine transformation — exactly the parametrization G*Power and R's pwr.2p.test use — so results match those tools to at least six significant digits. It works for classic hypothesis tests and for planning A/B tests alike: the 'find power' mode shows what difference your traffic can realistically detect. Note that proportions near 0 or 1 are easier to distinguish than the same absolute difference near 50% — h captures this automatically.
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Frequently asked questions
How many users do I need per variant in an A/B test?
Enter your baseline rate (e.g. 0.40) and the rate you hope to reach (e.g. 0.50), keep α = .05 and power = 80%, and read off n per group — about 387 per variant in this example (h = 0.20). Halving the detectable difference roughly quadruples the requirement.
What is Cohen's h?
h = 2·arcsin(√p₁) − 2·arcsin(√p₂) — an effect size for proportions that makes power calculations accurate across the whole 0–1 range. Benchmarks: 0.2 small, 0.5 medium, 0.8 large. The calculator computes it from your proportions automatically.
How do I report this power analysis in APA format?
For example: "An a priori power analysis for a two-proportion z-test (p₁ = .40, p₂ = .60, h = 0.41, α = .05, two-tailed, power = .80) indicated 48 participants per group." The AI Report formats the full justification paragraph.
Does this assume equal group sizes?
Yes — the classic design with equal n per group, which is also the most efficient. For planned unequal allocation, a rough approach is to power for the harmonic mean of the group sizes.