Krampe, AnneKuhnt, Sonja2005-10-122005-10-122005-10-12http://hdl.handle.net/2003/2164910.17877/DE290R-14477Categorical 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 di®erences 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 compare the performance of the simulation test, the Bowker test and two modifications.enComputational commutative algebraDiaconis-Sturmfels algorithmmatched-pairs dataMCMCMetropolis-Hastings algorithm004report