[1] This particular situation is of importance in mathematical statistics since it provides a basic exemplar case in which the F-distribution can be derived.
Then the test statistic has an F-distribution with n − 1 and m − 1 degrees of freedom if the null hypothesis of equality of variances is true.
The null hypothesis is rejected if F is either too large or too small based on the desired alpha level (i.e., statistical significance).
These F-tests are generally not robust when there are violations of the assumption that each population follows the normal distribution, particularly for small alpha levels and unbalanced layouts.
The immediate generalization of the problem outlined above is to situations where there are more than two groups or populations, and the hypothesis is that all of the variances are equal.