# Sample size: Single mean

## Description

Calculates the required sample size for the comparison of a sample mean with a given value. 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.
- Mean: the hypothesized mean (considered to be
*biologically*significantly different from the null hypothesis value). - Standard deviation: hypothesized standard deviation (known from previous studies or from the literature).
- Null hypothesis value: the null hypothesis value.

## Example

If the null hypothesis value is 50, and you consider a value of at least 60 to be significantly different, then you will enter these numbers for Null hypothesis value and Mean. If from a previous study, you expect the standard deviation of the sample to be 14, you enter 14 for the Standard deviation. 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.

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.

## Link

Go to Sample size: Single mean.