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Two-Sample Z-Test Statistic Calculator

Z-statistic for comparing two independent population means.

Calculates the z-statistic for comparing two sample means when population variances are known: z = (x̄₁ − x̄₂) / √(σ₁²/n₁ + σ₂²/n₂). Provides the standard error of the difference.

Marcus Laurent By Marcus Laurent
Published Last reviewed 1 min read

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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 = (x̄₁ − x̄₂) / √(σ₁²/n₁ + σ₂²/n₂)

In depth

Calculates the z-statistic for comparing two sample means when population variances are known: z = (x̄₁ − x̄₂) / √(σ₁²/n₁ + σ₂²/n₂). Provides the standard error of the difference.