Comparison of proportions


Performs a Chi-squared test for the comparison of proportions observed in two independent samples. Proportions are expressed as a percentages.

Required input

For both samples, you enter:

  • Observed proportion (%): the observed proportion, expressed as a percentage.
  • Sample size: the sample size or total number of observations in the sample.


The program calculates:

  • the difference between the two proportions and a 95% confidence interval for this difference;
  • Chi-squared test and P value.

If the P-value is less than 0.05, the conclusion is that the two proportions indeed differ significantly.

Computational notes uses the "N-1" Chi-squared test as recommended by Campbell (2007) and Richardson (2011).

The confidence interval is calculated according to the recommended method given by Altman et al. (2000).


  • Altman DG, Machin D, Bryant TN, Gardner MJ (Eds) (2000) Statistics with confidence, 2nd ed. BMJ Books. (p. 49)
  • Campbell I (2007) Chi-squared and Fisher-Irwin tests of two-by-two tables with small sample recommendations. Statistics in Medicine 26:3661-3675. PubMed
  • Richardson JTE (2011) The analysis of 2 x 2 contingency tables - Yet again. Statistics in Medicine 30:890. PubMed


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