Z-Test Calculator for 2 Population Proportions

This calculator performs a Z-test to compare the proportions of two independent populations or groups.

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When to Use

Use the Z-test for proportions when you want to compare the proportion of successes in two independent groups (e.g., proportion of patients responding to treatment in two different drug groups).

Requirements

  • Two independent samples
  • Binary outcome (success/failure)
  • Sufficient sample size (typically np > 5 and n(1-p) > 5 for both groups)

Null Hypothesis

H₀: p₁ = p₂ (the two population proportions are equal)

Formula

Z = (p₁ - p₂) / SE

where SE = √[p̂(1-p̂)(1/n₁ + 1/n₂)]

and p̂ = (x₁ + x₂) / (n₁ + n₂)

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