## The F Distribution

The F – distribution is used mainly for testing the hypothesisthat the variances of two populations are the same. It has twoparametersandwhereandarethe sample sizes of the samples from populations 1 and 2 respectivelyand is usually denotedSometypical F – distributions are shown below.

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

a population with normal distributionanda sample of sizeistaken from a second population with normal distributionthenandItfollows by division thatandthenceSinceall the factors on the left hand side are positive,isalways positive. By interchanging samples 1 and two we see that

If we assume thatthenwe have