Skip to main content
Mail a PDF copy of this page to:
(Your email address will not be added to a mailing list)
Download our user-friendly MedCalc statistical software for your Windows desktop. Download

Other calculators ...

Free statistical calculators

Test for one proportion calculator

Observed proportion

Null hypothesis value


The Test for one proportion 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. Buy from Amazon
  • 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) Buy from Amazon
  • Kirkwood BR, Sterne JAC (2003) Essential medical statistics, 2nd ed. Oxford: Blackwell Science. Buy from Amazon

How to cite this page

  • MedCalc Software Ltd. Test for one proportion calculator. (Version 20.008; accessed June 20, 2021)

See also

Recommended book

Essentials of Medical Statistics
Betty Kirkwood, Jonathan Sterne

Buy from Amazon US - CA - UK - DE - FR - ES - IT

Essential Medical Statistics is a classic amongst medical statisticians. An introductory textbook, it presents statistics with a clarity and logic that demystifies the subject, while providing a comprehensive coverage of advanced as well as basic methods.

The second edition of Essential Medical Statistics has been comprehensively revised and updated to include modern statistical methods and modern approaches to statistical analysis, while retaining the approachable and non-mathematical style of the first edition. The book now includes full coverage of the most commonly used regression models, multiple linear regression, logistic regression, Poisson regression and Cox regression, as well as a chapter on general issues in regression modelling. In addition, new chapters introduce more advanced topics such as meta-analysis, likelihood, bootstrapping and robust standard errors, and analysis of clustered data.