We test A formal test is based on sums of squares. Then, is always an unbiassed estimator for , while is an unbiassed estimator for only if is true. Further, under , the ratio has an F distribution with and degrees of freedom. Thus, we reject if the observed value of F is sufficiently large. In fact, it is easy to see that .
Diagnostic procedures are essential.
In these cases, the transformations or frequently result in making both the group standard deviations more nearly equal and the observations more nearly normal. A test for equality of variances is not recommended, as it lacks robustness against nonnormality.