# Sample size: Single proportion

## Description

Calculates the required sample size for the comparison of a proportion with a given proportion. The sample size takes into account the required significance level and power of the test.

## Required input

- Type I error - alpha: the probability of making a Type I error (α-level, two-sided), i.e. the probability of rejecting the null hypothesis when in fact it is true.
- Type II error - beta: the probability of making a Type II error (β-level), i.e. the probability of accepting the null hypothesis when in fact it is false.
- Proportion (%): the hypothesized proportion (considered to be
*biologically*significantly different from the null hypothesis value), expressed as a percentage. - Null hypothesis value (%): the null hypothesis value (a proportion, expressed as a percentage).

## Example

If the null hypothesis value is 50%, and you consider a proportion of at least 70% to be significantly different, then you enter the numbers 70 and 50 in the dialog box. For α-level you select 0.05 and for β-level you select 0.20 (power is 80%).

## Results

After you click the OK button the program will display the required sample size (47 in the example).

A table shows the required sample size for different Type I and Type II Error levels.

## Reference

- Machin D, Campbell MJ, Tan SB, Tan SH (2009) Sample size tables for clinical studies. 3
^{rd}ed. Chichester: Wiley-Blackwell.