AN ASYMPTOTICALLY DISTRIBUTION-FREE MULTIPLE COMPARISON METHOD WITH APPLICATION TO THE PROBLEM OF n RANKINGS OF m OBJECTS

The statistic known as Hotelling's T2 is shown to be asymptotically distribution-free and thus to provide a multi-dimensional confidence ellipsoid for the joint population means which enables multiple comparisons of sample means to be made. If m objects are ranked in order by each of n judges, Friedman's test is usually used to test the hypothesis that the judges rank the objects at random. It is of interest, however, to enquire which of the objects are ranked significantly higher than others, in which case Hotelling's T2 may be used to provide asymptotically distribution-free multiple comparisons.