Some hypothesis testing problems for categorical variables

This paper considers some testing problems for multivariate categorical variables within a conditional, or permutation, framework. The key idea is based on the decomposition of null and alternative hypotheses into a number of sub-hypotheses. For each sub-hypothesis it is assumed that a proper permutation partial test is available. Of course, these partial tests are assumed to be not independent. Then, the global testing solution is obtained by a nonparametric combination of resulting p-values. The theory of nonparametric combination and a computing algorithm to perform related calculations are outlined. As a particular result, a test analogous to Hotelling’s T2 for nominal and ordered categorical variables is obtained. Moreover, an analysis from the point of view of multiple testing is also outlined in order to inspect which variable or class or group is mostly responsible of a global significance