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


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


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.

Suggested Citation

  • Cohen, A. & Kolassa, J. & Sackrowitz, H.B., 2004. "A four action problem with ordered categorical data: are two distributions the same, ordered, or otherwise?," Statistics & Probability Letters, Elsevier, vol. 70(3), pages 223-234, December.
  • Handle: RePEc:eee:stapro:v:70:y:2004:i:3:p:223-234

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    References listed on IDEAS

    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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