Open Access
VOL. 8 | 2012 Accurate approximations to the distribution of a statistic testing symmetry in contingency tables
John E. Kolassa, Hema Gayat Bhagavatula

Editor(s) Dominique Fourdrinier, Éric Marchand, Andrew L. Rukhin

Inst. Math. Stat. (IMS) Collect., 2012: 181-189 (2012) DOI: 10.1214/11-IMSCOLL812


This manuscript examines this task of approximating significance levels for a test of symmetry in square contingency tables. The null sampling distribution of this test statistic is the same as that of the sum of squared independent centered binomial random variables, weighted by their separate sample size; each of these variables may be taken to have success probability half. This manuscript applies an existing asymptotic correction to the standard chi-squared approximation to the distribution of the quadratic form of a random vector confined to a multivariate lattice, when the quadratic form is formed from the inverse variance matrix of the random vector. This manuscript also investigates non-asymptotic corrections to approximations to this distribution, when the separate binomial sample sizes are small.


Published: 1 January 2012
First available in Project Euclid: 14 March 2012

zbMATH: 1326.62033
MathSciNet: MR3202510

Digital Object Identifier: 10.1214/11-IMSCOLL812

Primary: 60K35 , 62E17
Secondary: 62H17

Keywords: Bowker’s test of symmetry , conditional inference , Yarnold approximation

Rights: Copyright © 2012, Institute of Mathematical Statistics

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