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

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

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 70 (2004)
    Issue (Month): 3 (December)
    Pages: 223-234

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    Handle: RePEc:eee:stapro:v:70:y:2004:i:3:p:223-234

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

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    1. Cohen Arthur & Sackrowitz Harold B., 2000. "Testing Whether Treatment Is “Better“ Than Control With Ordered Categorical Data: Definitions And Complete Class Theorems," Statistics & Risk Modeling, De Gruyter, vol. 18(1), pages 1-26, January.
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