MedCalc

# Free statistical calculators

## Description

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

### P-value

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.

### 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.

• MedCalc Software Ltd. Test for one proportion calculator. https://www.medcalc.org/calc/test_one_proportion.php (Version 20.008; accessed June 20, 2021)