Permutation Approaches for Stochastic Ordering

In many application problems, when dealing with comparisons between two or more groups, the classical parametric inferential statistical methods are used, although in real problems the quite stringent assumptions required by such methods are rarely satisfied. In particular a parametric approach to the test on ordering of C > 2 populations is very difficult. In order to tackle this problem two alternative methods are proposed in the present paper. Both the methods consist in permutation combination based tests: the first is supposed to be more powerful and it is suitable when the main goal of the study is related to the global ordering of the populations; the second is useful when the interest is in the pairwise comparisons between the populations.