UNIVARIATE RANDOM CUT-POINTS THEORY FOR THE ANALYSIS OF ORDERED CATEGORICAL-DATA

A new theory is developed for nonparametric analyses of r x k continge ncy tables, where the columns correspond to k ordered categories. The work is motivated by concern that conventional nonparametric theory yi elds inferences concerning the given categories, but results are often interpreted as if for a continuum. Asymptotic distributions are deriv ed under random cut-points models for the Mann-Whitney (-Wilcoxon) U s tatistic. A model is recommended under which the exact moments of U ar e simple functions of k and the two sample sizes. For two more general models, the asymptotic variance is given for k less than or equal to 12 and k = 20, 30. Tables of empirical critical values show that the r ecommended model yields P values very close to P values under the gene ral models.