# Test for one proportion

## Description

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.

## Results

The program calculates:

- the 95% Confidence Interval (CI) for the observed proportion
- z statistic and associated P-value.

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.

## 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; *p*_{exp} 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).

### Confidence interval

SciStat.com 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, 3
^{rd}ed. Hoboken: John Wiley & Sons. (p. 26)

## External links

- Binomial proportion confidence interval on Wikipedia.

## Link

Go to Test for one proportion.