Nonparametric Analysis of Ordinal Categorical Response Data with Factorial Structure

Abstract
SUMMARY: A simple nonparametric method of analysis for contingency tables with an ordinal response and factorial treatment structure is described. The method involves a partition of Pearson’s X2P-statistic by using orthogonal polynomials so that location and dispersion effects are estimated for each level of the explanatory variable. Analyses of variance are then performed on these effects to determine the important factors. The methods are applied to two examples, where consumers rate their liking for a product on an ordered categorical scale, one of which highlights the need to look at dispersion as well as location effects.

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