## 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) |
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Pages (from-to) | 223-234 |

Number of pages | 12 |

Journal | Statistics and Probability Letters |

Volume | 70 |

Issue number | 3 |

DOIs | |

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