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December, 1989 Bounds on the Size of the $\chi^2$-Test of Independence in a Contingency Table
Wei-Yin Loh
Ann. Statist. 17(4): 1709-1722 (December, 1989). DOI: 10.1214/aos/1176347389


Bounds are obtained on the limiting size of the level-$\alpha \chi^2$-test of independence in a contingency table, as the sample size increases. The situations considered include (a) sampling with one or both sets of marginal totals random, (b) performing the test with or without the continuity correction and (c) with or without conditioning on the event $\mathscr{E}_k$ that the minimum estimated expected cell count is greater than a given $k \geq 0$. Bounds for both the unconditional and conditional (on $\mathscr{E}_k$) size are derived. It is shown, for example, that the limiting conditional size of the test is unity for all $\alpha$ if the continuity correction is used with $k = 0$ and sampling is done with both margins random. The same conclusion holds if sampling is done with one set of margins fixed and the dimensions of the table are not too small.


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Wei-Yin Loh. "Bounds on the Size of the $\chi^2$-Test of Independence in a Contingency Table." Ann. Statist. 17 (4) 1709 - 1722, December, 1989.


Published: December, 1989
First available in Project Euclid: 12 April 2007

zbMATH: 0695.62063
MathSciNet: MR1026307
Digital Object Identifier: 10.1214/aos/1176347389

Primary: 62F05
Secondary: 62H17

Keywords: continuity correction , multinomial sampling

Rights: Copyright © 1989 Institute of Mathematical Statistics


Vol.17 • No. 4 • December, 1989
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