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Compare two proportions (e.g., A/B test conversion rates) with z-statistic, p-value, and Python code.
Enter group data and click Run Test.
Tests H₀: p₁ = p₂ (no difference between proportions)
They are equivalent for 2×2 tables: z² = χ². The z-test gives a directional z-statistic (positive/negative) and supports one-tailed tests. Chi-square is always two-tailed. Use the z-test when direction matters.
The normal approximation requires n₁p̂₁ ≥ 5, n₁(1−p̂₁) ≥ 5, and same for group 2. For most practical A/B tests, this means at least 30-50 observations per group. For small counts, use Fisher's exact test.
Pooled SE assumes H₀: p₁ = p₂ and is used for the test statistic. Unpooled SE uses each sample's own proportion and is used for confidence intervals. The pooled version is standard for hypothesis testing.
Yes, if you have a directional hypothesis (e.g., "B is better than A"). A one-tailed test has more power but only tests in one direction. Use two-tailed when you want to detect differences in either direction.
Sample size calculators use this test's formula in reverse. Given desired power (80%), α (5%), and minimum detectable effect, they solve for the required n per group.