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

Art Cohen; John Kolassa; Harold Sackrowitz

doi:10.1016/j.spl.2004.10.012

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

Art Cohen, John Kolassa, Harold Sackrowitz

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	223-234
Number of pages	12
Journal	Statistics and Probability Letters
Volume	70
Issue number	3
DOIs	https://doi.org/10.1016/j.spl.2004.10.012
State	Published - Dec 1 2004

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

Keywords

Bayes procedure
Chi-square statistic
Concordance monotonicity
Contingency table
Fisher's statistic
Stochastic ordering
Wilcoxon-Mann-Whitney statistic

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10.1016/j.spl.2004.10.012

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abstract = "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.",

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