Nonparametric directional tests in presence of confounding factors and categorical data

In modern socio-economic systems, often the aim of a performance analysis or quality evaluation is to compare different products, different manufacturing plants or service centres, different actions or distinct treatments. The question is, ‘‘Which is better?’’ This is complicated because the considered aspects are often measured through categorical data and the results can be affected by confounding factors. To solve this problem we discuss some directional permutation tests based on the nonparametric combination of dependent permutation tests (NPC) for two-sample comparisons in the presence of ordinal categorical variables and confounding factors. In particular we present a new permutation test based on the combination of a finite number of sample moments. To reduce the confounding effects we consider the joint application of stratification and the NPC method. We also show the results of Monte Carlo simulations in order to compare permutation solutions with other nonparametric tests and to evaluate the robustness of the test based on moments.