Free statistical calculators

Test for one proportion calculator

Observed proportion


Null hypothesis value



The Test for one proportion in the Tests menu can be used to test the hypothesis that an observed proportion is equal to a pre-specified proportion.

This test is not performed on data in the data table, but on statistics you enter in a dialog box.

Required input

  • Observed proportion (%): the observed proportion, expressed as a percentage.
  • Sample size: the sample size or total number of observations.
  • Null Hypothesis value (%): the pre-specified proportion (the value to compare the observed proportion to), expressed as a percentage.

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

If the P-value is less than 0.05, the hypothesis that the observed proportion is equal to the pre-specified proportion value is rejected, and the alternative hypothesis that there is a significant difference between the two proportions can be accepted.

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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