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Test for one proportion

The Test for one proportion calculator is used to test the hypothesis that an observed proportion is equal to a prespecified proportion.

 

Observed proportion
: 
: 
Null hypothesis value
: 

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 prespecified proportion (the value to compare the observed proportion to), expressed as a percentage.
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Computational notes

P-value

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

$$ z = \frac {p - p_{exp}} { se(p)} $$

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:

$$ se(p) = \sqrt{ \frac {p_{exp} (1 - p_{exp})} {n}} $$

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 prespecified 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).

Literature

  • 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)
  • Kirkwood BR, Sterne JAC (2003) Essential medical statistics, 2nd ed. Oxford: Blackwell Science.

How to cite this page

  • MedCalc Software Ltd. Test for one proportion. https://www.medcalc.org/en/calc/test_one_proportion.php (Version 23.6.1; accessed June 15, 2026)

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See also

https://www.medcalc.org/en/calc/test_one_proportion.php

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