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

Sonja Kuhnt and Anne Krampe

No 2005,29, Technical Reports from Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen

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.

Keywords: Computational commutative algebra; Diaconis-Sturmfels algorithm; matched-pairs data; MCMC; Metropolis-Hastings algorithm; test for symmetry (search for similar items in EconPapers)
Date: 2005
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