stats
Two-Sample Proportion Test
Compare two proportions — pooled Z-test, p-value, Wilson CI for difference, relative risk, odds ratio.
Inputs
Group 1 — successes x₁ / size n₁
Group 2 — successes x₂ / size n₂
Hypothesis tail
Confidence level (for CI)
Results
p̂₁ (Group 1)—
p̂₂ (Group 2)—
Pooled proportion p̂—
Pooled SE—
Z-statistic—
p-value (two-tailed)—
95% CI for p̂₁ − p̂₂—
Relative risk RR—
RR interp.—
Odds ratio OR—
OR interp.—
Conclusion α = 0.05—
Conclusion α = 0.01—
Z = (p̂₁−p̂₂)/√(p̂(1−p̂)(1/n₁+1/n₂)) · p̂ = (x₁+x₂)/(n₁+n₂)
CI uses unpooled SE = √(p̂₁(1−p̂₁)/n₁ + p̂₂(1−p̂₂)/n₂)
RR = p̂₁/p̂₂ · OR = p̂₁(1−p̂₂)/(p̂₂(1−p̂₁))
CI uses unpooled SE = √(p̂₁(1−p̂₁)/n₁ + p̂₂(1−p̂₂)/n₂)
RR = p̂₁/p̂₂ · OR = p̂₁(1−p̂₂)/(p̂₂(1−p̂₁))