# Sample size: Comparison of proportions

## Description

Calculates the required sample size for the comparison of two proportions. 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.
- First proportion (%): hypothesized proportion in the first sample.
- Second proportion (%): hypothesized proportion in the second sample (the hypothesized difference with the first proportion is considered to be
*biologically*significant). - Ratio of sample sizes in Group 1 / Group 2: the ratio of the sample sizes in group 1 and 2. Enter 1 for equal sample sizes in both groups. Enter 2 if the number of cases in group 1 must be double of the number of cases in group 2.

## Example

You are interested in detecting a difference between two proportions of at least 15. You expect the two proportions to be equal to 75 and 60, so enter these values in the dialog box.

You expect to include twice as many cases in group 1 as in group 2. Enter 2 for the ratio of sample sizes in Group 1 / Group 2.

For α-level you select 0.05 and for β-level you select 0.20 (power is 80%).

## Results

After you click OK, the program displays the required sample size, which is 244 in the first group and 122 in the second group, i.e. 366 cases in total.

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

## References

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