The F – distribution is used mainly for testing the hypothesis that the variances of two populations are the same. It has two parameters
and
where
and
are the sample sizes of the samples from populations 1 and 2 respectively and is usually denoted
Some typical F – distributions are shown below.
We can derive the F – distribution from the
distribution. If a sample of sizeis taken from
a population with normal distribution
and a sample of sizeis taken from a second population with normal distribution
then
and
It follows by division that
and thence
Since 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 that
then we have