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Bowker's Test for Symmetry and Modifications within the Algebraic Framework

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  • Kuhnt, Sonja
  • Krampe, Anne

Abstract

Categorical data occur in a wide range of statistical applications. If the data are observed in matched pairs, it is often of interest to examine the differences between the responses. We concentrate on tests of axial symmetry in two-way tables. A commonly used procedure is the Bowker test which is a generalization of the McNemar test. The test decision is based on a x2-approximation which might not be adequate, for example if the table is sparse. Therefore modifications of the test statistic have been proposed. We suggest a test of symmetry based on Bowker's test and Markov Chain Monte Carlo methods following the algorithm of Diaconis and Sturmfels (1998). We carry out a simulation study to determine and com- pare the performance of the simulation test, the Bowker test and two modifications.

Suggested Citation

  • Kuhnt, Sonja & Krampe, Anne, 2005. "Bowker's Test for Symmetry and Modifications within the Algebraic Framework," Technical Reports 2005,29, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200529
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    References listed on IDEAS

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    1. Allen Edwards, 1948. "Note on the “correction for continuity” in testing the significance of the difference between correlated proportions," Psychometrika, Springer;The Psychometric Society, vol. 13(3), pages 185-187, September.
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