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Test for one proportion calculator

Observed proportion

Null hypothesis value

Computational notes


The significance level, or P-value, is calculated using a general z-test (Altman, 1991):

z-value for single proportion

where p is the observed proportion; pexp is the Null hypothesis (or expected) proportion; and se(p) is the standard error of the expected proportion:

Standard error of a proportion

The P-value is the area of the normal distribution that falls outside ±z (see Values of the Normal distribution table).

Normal distribution

Confidence interval

MedCalc calculates the "exact" Clopper-Pearson confidence interval for the observed proportion (Clopper & Pearson, 1934; Fleis et al., 2003).


  • Altman DG (1991) Practical statistics for medical research. London: Chapman and Hall.
  • Clopper C, Pearson ES (1934) The use of confidence or fiducial limits illustrated in the case of the binomial. Biometrika 26:404–413.
  • Fleiss JL, Levin B, Paik MC (2003) Statistical methods for rates and proportions, 3rd ed. Hoboken: John Wiley & Sons. (p. 26)

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