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Sample size: Confidence Interval for a difference between proportions

Command: Sample size
Next selectConfidence Interval estimation & Precision
Next selectDifference between proportions


Calculates the required minimum sample size for the estimation of a confidence interval with a required width for the difference between two independent proportions (Machin et al., 2009).

Note that the calculation does not include a null hypothesis value or a factor for power (1−β). Therefore the estimated sample size does not give a certainty that a particular value will fall inside or outside the confidence interval. The number of cases is only the number required to attain a specified confidence interval width.

Required input

  • Confidence level (%): select the confidence level: 90, 95 or 99%. A 95% confidence level (the value for a 95% Confidence Interval) is the most common selection. You can enter a different confidence level if required.
  • Proportion in group 1 (%): hypothesized proportion (expressed as a percentage) in the first sample.
  • Proportion in group 2 (%): hypothesized proportion (expressed as a percentage) in the second sample.
  • Confidence interval width (2-sided): this is the required total width of the confidence interval. For example when a difference is 40% with 95% Confidence Interval 35 to 45, then the confidence interval width is 10.
  • Ratio of sample sizes in Group 1 / Group 2: enter 1 for equal sample sizes in both groups. Enter 2 if the number of cases in group 1 must be double of the number of cases in group 2.


Sample size for the confidence interval of a difference between two proportions


  • Machin D, Campbell MJ, Tan SB, Tan SH (2009) Sample size tables for clinical studies. 3rd ed. Chichester: Wiley-Blackwell.

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