Sample Size for Proportion Difference

50%
50%

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Formula

Sample Size for Difference in Proportions

n=(ZΞ±/2+ZΞ²)2[p1(1βˆ’p1)+p2(1βˆ’p2)](p1βˆ’p2)2n = \frac{(Z_{\alpha/2} + Z_{\beta})^2 [p_1(1 - p_1) + p_2(1 - p_2)]}{(p_1 - p_2)^2}

Where:

  • n = required sample size (for each group)
  • ZΞ±/2Z_{\alpha/2} = Z-score for confidence
  • ZΞ²Z_{\beta} = Z-score for power
  • p1p_1 and p2p_2 = the two proportions