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

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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.

Original languageEnglish (US)
Pages (from-to)223-234
Number of pages12
JournalStatistics and Probability Letters
Volume70
Issue number3
DOIs
StatePublished - 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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