# Sample size: Comparison of means

## Description

Calculates the required sample size for the comparison of two independent means. 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.
- Difference: the hypothesized difference (considered to be
*biologically*significant). - Standard deviation 1: hypothesized standard deviation in the first sample.
- Standard deviation 2: hypothesized standard deviation in the second sample.
- 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 the sample means of at least 10. You expect the standard deviations in the two study groups to be equal to 16. Enter the value 10 for difference, and enter 16 for both standard deviations.

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 the OK button the program will display the required sample size which is 61 for group 1 and 31 in group 2, or a total of 92 cases.

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

## Comparison of two paired samples

To calculate the sample size required for the comparison of two paired samples, see Sampling for single mean.

## Reference

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