A four action problem with ordered categorical data: are two distributions the same, ordered, or otherwise?

• Published in: Statistics & probability letters Vol. 70; no. 3; pp. 223 - 234
• Main Authors: Cohen, A., Kolassa, J., Sackrowitz, H.B.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.12.2004; Elsevier
• Series: Statistics & Probability Letters
• Subjects: Applications; Bayes procedure; Chi-square statistic; Concordance monotonicity; Contingency table; Contingency table Stochastic ordering Fisher's statistic Wilcoxon-Mann-Whitney statistic Chi-square statistic Bayes procedure Concordance monotonicity; Distribution theory; Exact sciences and technology; Fisher's statistic; Insurance, economics, finance; Mathematics; Multivariate analysis; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Statistics; Stochastic ordering; Wilcoxon–Mann–Whitney statistic; Fisher's statistic; Wilcoxon–Mann–Whitney statistic; Concordance monotonicity; Stochastic ordering; Chi-square statistic; Contingency table; Bayes procedure; Bayes estimation; Economics; Data analysis; Conditional distribution; Probability theory; Wilcoxon Mann Whitney statistics; Chi square test; Fisher statistics; Statistical method; Categorical data; Marginal distribution; Distribution function; Multinomial distribution
• ISSN: 0167-7152; 1879-2103
• DOI: 10.1016/j.spl.2004.10.012

Consider a 2 × J contingency table under the product multinomial model when the J categories are ordered. We compare the two distributions by deciding among the following four choices: (i) distributions are the same; (ii) distribution 1 is stochastically larger than distribution 2; (iii) distribution 2 is stochastically larger than distribution 1; (iv) neither (i), (ii), or (iii). A four action problem is posed and two procedures are considered. One ad hoc and the second procedure is a conditional Bayes procedure, where the conditioning is on the marginal row and column totals. The problem was motivated by a data set comparing survey methods dealing with economic damage to farms by deer.