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))