Sample Size for Mean Difference

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Formula

Sample Size for Difference in Means of Two Normally Distributed

Samples of Equal Size

n=(σ12+σ22)×(Zα/2+Zβ)2(μ1−μ2)2n = \frac{(\sigma_1^2 + \sigma_2^2) \times (Z_{\alpha/2} + Z_{\beta})^2}{(\mu_1 - \mu_2)^2}

Where:

  • n = required sample size (for each group)
  • Zα/2Z_{\alpha/2} = Z-score for confidence level
  • ZβZ_{\beta} = Z-score for power
  • σ12,σ22\sigma_1^2, \sigma_2^2 = variances of the two respective groups
  • (μ1−μ2)(\mu_1 - \mu_2) = difference in means to detect