Nonparametric directional tests in the presence of confounding factors and categorical data
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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.
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