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

A. Cohen, J. Kolassa and H.B. Sackrowitz

Statistics & Probability Letters, 2004, vol. 70, issue 3, 223-234

Abstract: Consider a 2xJ 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.

Keywords: Contingency; table; Stochastic; ordering; Fisher's; statistic; Wilcoxon-Mann-Whitney; statistic; Chi-square; statistic; Bayes; procedure; Concordance; monotonicity (search for similar items in EconPapers)
Date: 2004
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