Free statistical calculators
Test for one proportion calculator
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.
- 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.
The significance level, or P-value, is calculated using a general z-test (Altman, 1991):
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:
The P-value is the area of the normal distribution that falls outside ±z (see Values of the Normal distribution table).
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.
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)
- Binomial proportion confidence interval on Wikipedia.