## The F Distribution

The F – distribution is used mainly for testing the hypothesis that the variances of two populations are the same. It has two parametersandwhereandare the sample sizes of the samples from populations 1 and 2 respectively and is usually denotedSome typical F – distributions are shown below.

We can derive the F – distribution from thedistribution. If a sample of sizeis taken from

a population with normal distributionand a sample of sizeis taken from a second population with normal distributionthenandIt follows by division thatand thenceSince all the factors on the left hand side are positive,is always positive. By interchanging samples 1 and two we see that

If we assume thatthen we have