basic

Two-Proportion Z-Test Calculator

z = (p̂₁ − p̂₂) / √(p̄(1 − p̄)(1/n₁ + 1/n₂)).

Test whether two independent sample proportions differ significantly. Pooled estimate p̄ = (x₁ + x₂)/(n₁ + n₂); z = (p̂₁ − p̂₂) / √(p̄(1−p̄)(1/n₁ + 1/n₂)). Reports the standardised statistic and its absolute value (compare to 1.96 for two-sided 5 %).

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

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Results

Enter values and click Calculate to see results.
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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

z = (p̂₁ − p̂₂) / √(p̄(1−p̄)(1/n₁ + 1/n₂))

In depth

Test whether two independent sample proportions differ significantly. Pooled estimate p̄ = (x₁ + x₂)/(n₁ + n₂); z = (p̂₁ − p̂₂) / √(p̄(1−p̄)(1/n₁ + 1/n₂)). Reports the standardised statistic and its absolute value (compare to 1.96 for two-sided 5 %).