An exact rank test for scale under normality using Helmert's transformation

Abstract

In the problem of testing equality of scale of two distributions a rank test should be preferred over the F-test if it is not sure that the distributions involved are normal. However, if in addition the distributions may also differ in location, it becomes necessary to first adjust the observations, and the rank test will then at best be asymptotically distribution-free, even if normality holds after all. In this paper it is demonstrated how using Helmert's transformation for the adjustment of the observations leads to a rank test which is exact under normality and asymptotically distribution-free otherwise.