Nonparametric multi-focus analysis for categorical variables

In this work, we present a new nonparametric procedure which is useful for testing independence in distribution for categorical variables between two or more populations. The classically adopted solution is the chi(2) test for the contingency table of observed frequencies; this solution is known to lack in power in case of cell with low expected frequences. The approach presented here, named Multi-focus, give a partial remedy to this problem; moreover, as peculiar characteristic, allow for an inferential inspection on the variable's categories which, more then others, contribute to this differentiation. This goal is reached starting from a decomposition of the global null hypothesis in sub-hypotheses, then testing them separately and, finally, combining the p-values in a global test via a permutation strategy; the control of the FWE is discussed and recommended. A comparative simulation study evaluating the power and an application to real data are shown.