Introduction    Types of Mistakes       Suggestions       Resources       Table of Contents     About    Glossary

Power and Sample Size

Power will depend on sample size as well as on the difference to be detected.

Example: The pictures below each show the sampling distribution for the mean under the null hypothesis µ = 0 (blue -- on the left in each picture) together with the sampling distribution under the alternate hypothesis
µ = 1 (green -- on the right in each picture), but for different sample sizes.

Sampling distributions for sample size n = 25 under the null and alternate hypotheses    Sampling distributions for sample size n = 100 under the null and alternate hypotheses

This illustrates the general situation: Larger sample size gives larger power. The reason is essentially the same as in the example: Larger sample size gives a narrower sampling distribution, which means there is less overlap in the two sampling distributions (for null and alternate hypotheses).


Choosing sample size

The dependence of power on sample size allows us (in principle) to figure out before doing a study what sample size is needed to detect a specified difference, with a specified power, at a given significance level, if that difference is really there. In practice, details on figuring out sample size will vary from procedure to procedure. Some considerations involved:

Last updated May 12, 2011