Bowker's test for symmetry and modifications within the algebraic framework

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 (1998). We carry out a simulation study to determine and compare the performance of the simulation test, the Bowker test and two modifications.

Asymmetry models for square contingency tables: exact tests via algebraic statistics

“…We use a slightly different sufficient statistic T S for the symmetry model than given in Krampe and Kuhnt (2007). In particular, we add N I I to T S .…”

“…as the cross-classified characteristics become too different) and thus the standard asymptotic chi-squared tests are not applicable. Exact inference for the S model based on the algebraic algorithm of Diaconis and Sturmfels (1998) is provided by Rapallo (2003) and Krampe and Kuhnt (2007), where the algebraic testing for the S model was developed. In the context of rater agreement, Rapallo (2005) provides algebraic testing procedures for Cohen's kappa, the quasi symmetry and quasi independence model.…”

A nonparametric symmetry test for absolutely continuous bivariate copulas

“…Among Bowker's test (1948) and two of its modifications, Edwards' test (1948) and Wald's modified test as introduced by May and Johnson (2001), we chose Edwards', which from now on we will just refer to as Bowker-Edwards test, since its asymptotic distribution works relatively better compared to the other two, see Krampe and Kuhnt (2007). The proposed test, which from now on we will refer to as the Trisymmetric test, rejects the null hypothesis of symmetry whenever |T i,n | > k α for an appropiate threshold k α depending on the test size α.…”

A short history of algebraic statistics

“…These include the Bowker test for matched pair data [41], rater agreement test [59], calibration of Fourier analysis of ranking data [23], in model selection [42], sequential sampling in multi-way contingency tables with given constraints [21], for quasi-independence [39] and weaken independence [18], to mention a few. The computation of Markov bases in special cases has received much attention e.g.…”