Nonparametric Analysis of Ordinal Data in Designed Factorial Experiments

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Abstract
Plant disease severity often is assessed using an ordinal rating scale rather than a continuous scale of measurement. Although such data usually should be analyzed with nonparametric methods, and not with the typical parametric techniques (such as analysis of variance), limitations in the statistical methodology available had meant that experimental designs generally could not be more complicated than a one-way layout. Very recent advancements in the theoretical formulation of hypotheses and associated test statistics within a nonparametric framework, together with development of software for implementing the methods, have made it possible for plant pathologists to analyze properly ordinal data from more complicated designs using nonparametric techniques. In this paper, we illustrate the nonparametric analysis of ordinal data obtained from two-way factorial designs, including a repeated measures design, and show how to quantify the effects of experimental factors on ratings through estimated relative marginal effects.