# Sample size calculation: Comparison of two means

Command: | Sampling Comparison of two 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 (see Sampling: Introduction).

## 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 of means: the hypothesized difference (considered to be
*biologically*significant). - Standard deviation in group 1 : hypothesized standard deviation in the first sample.
- Standard deviation in group 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.

### Correction for unequal variances

When you enter the same standard deviation for both samples, it is assumed that the data will be analysed using the Independent samples t-test with the option "Assume equal variances". When you enter two different standard deviations, it is assumed that the data will be analysed using the Independent samples t-test with the option "Assume unequal variances". See Independent samples t-test.

## Example

In the example you are interested in detecting a difference between the sample means of a least 10. You expect the standard deviations in the two studies to be equal to 16. You expect to include twice as many cases in group 1 as in group 2.

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

After you click the Calculate button the program displays 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.

## Literature

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