Accurate approximations to the distribution of a statistic testing symmetry in contingency tables. (English) Zbl 1326.62033

Kolassa, John E.; Bhagavatula, Hema Gayat

Fourdrinier, Dominique (ed.) et al., Contemporary developments in Bayesian analysis and statistical decision theory. A festschrift for William E. Strawderman. Beachwood, OH: IMS, Institute of Mathematical Statistics (ISBN 978-0-940600-81-2). Institute of Mathematical Statistics Collections 8, 181-189 (2012).

Summary: 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.
For the entire collection see [Zbl 1319.62003].

MSC:

62E17	Approximations to statistical distributions (nonasymptotic)
62H17	Contingency tables

Keywords:

conditional inference; Bowker’s test of symmetry; Yarnold approximation