Nonparametric Analysis of Ordered Categorical Data in Designs with Longitudinal Observations and Small Sample Sizes

For designs with longitudinal observations of ordered categorical data, a nonparametric model is considered where treatment effects and interactions are defined by means of the marginal distributions. These treatment effects are estimated consistently by ranking methods. The hypotheses in this nonparametric setup are formulated by means of the distribution functions. The asymptotic distribution of the estimators for the nonparametric effects are given under the hypotheses. For small samples, a rather accurate approximation is suggested. A clinical trial with ordered categorical data is used to motivate the ideas and to explain the procedures which are extensions of the Wilcoxon-Mann-Whitney test to factorial designs with longitudinal observations. The application of the procedures requires only some trivial regularity assumptions.