# 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

Buy from Amazon US - CA - UK - DE - FR - ES - IT

Sample Sizes for Clinical, Laboratory and Epidemiology Studies includes the sample size software (SSS) and formulae and numerical tables needed to design valid clinical studies. The text covers clinical as well as laboratory and epidemiology studies and contains the information needed to ensure a study will form a valid contribution to medical research.

The authors, noted experts in the field, explain step by step and explore the wide range of considerations necessary to assist investigational teams when deriving an appropriate sample size for their when planned study. The book contains sets of sample size tables with companion explanations and clear worked out examples based on real data. In addition, the text offers bibliography and references sections that are designed to be helpful with guidance on the principles discussed.