# Sample size calculation: Single mean

Command: | 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 (see Sample size calculation: 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.
- 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

In the example you consider a value of at least 60 to be significantly different from the null hypothesis value 50. From a previous study, you expect the standard deviation of the sample to be 14.

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

After you click Calculate the program displays the required sample size, which is 18 in the example.

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

## Literature

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

## See also

## Recommended book

## Sample Size Tables for Clinical Studies

David Machin, Michael J. Campbell, Say-Beng Tan, Sze-Huey Tan

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