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Exact Tests for Trends in Ordered Contingency Tables

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  • W. M. Patefield

Abstract

In an r × c table the probability of a particular outcome conditioned on fixed marginal totals depends on v = (r – 1) (c – 1) odds‐ratio parameters and hence tests of H0 no association against a general alternative have 2v “tails”. Exact conditional tests are developed for alternatives in which the odds‐ratios take restricted values according to the practical context. Use of the appropriate test can lead to substantial increases in power. An exact test based on the χ2 trend statistic is recommended on the grounds of power and computational feasibility.

Suggested Citation

  • W. M. Patefield, 1982. "Exact Tests for Trends in Ordered Contingency Tables," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 31(1), pages 32-43, March.
    • Handle: RePEc:bla:jorssc:v:31:y:1982:i:1:p:32-43
    DOI: 10.2307/2347072
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    Cited by:

    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.
    2. Agresti, Alan & Coull, Brent A., 1998. "Order-restricted inference for monotone trend alternatives in contingency tables," Computational Statistics & Data Analysis, Elsevier, vol. 28(2), pages 139-155, August.
    3. Park, Chul Gyu, 2002. "Testing for Ordered Trends of Binary Responses between Contingency Tables," Journal of Multivariate Analysis, Elsevier, vol. 81(2), pages 229-241, May.
    4. Bhaskar Bhattacharya & Richard Dykstra, 1997. "A Fenchel Duality Aspect of Iterative I-Projection Procedures," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(3), pages 435-446, September.
    5. Park, Chul Gyu, 1998. "Testing for unimodal dependence in an ordered contingency table with restricted marginal probabilities," Statistics & Probability Letters, Elsevier, vol. 37(2), pages 121-129, February.

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