The Annals of Statistics

Testing for Independence in a Two-Way Table: New Interpretations of the Chi-Square Statistic

Persi Diaconis and Bradley Efron

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Abstract

The classical chi-square test for independence in a two-way contingency table often rejects the independence hypothesis at an extremely small significance level, particularly when the sample size is large. This paper proposes some alternative distributions to independence, to help interpret the $\chi^2$ statistic in such situations. The uniform alternative, in which every possible contingency table of the given dimension and sample size receives equal probability, leads to the volume test, as originally suggested in a regression context by H. Hotelling. Exponential family theory is used to generate a class of intermediate alternatives between independence and uniformity, leading to a random effects model for contingency tables.

Article information

Source
Ann. Statist. Volume 13, Number 3 (1985), 845-874.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176349634

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aos/1176349634

Mathematical Reviews number (MathSciNet)
MR803747

Zentralblatt MATH identifier
0593.62040

Subjects
Primary: 62F05: Asymptotic properties of tests
Secondary: 62G10: Hypothesis testing

Keywords
Chi-square test for independence overdispersion volume tests random effects for exponential families

Citation

Diaconis, Persi; Efron, Bradley. Testing for Independence in a Two-Way Table: New Interpretations of the Chi-Square Statistic. Ann. Statist. 13 (1985), no. 3, 845--874. doi:10.1214/aos/1176349634. http://projecteuclid.org/euclid.aos/1176349634.


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