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September, 1985 Testing for Independence in a Two-Way Table: New Interpretations of the Chi-Square Statistic
Persi Diaconis, Bradley Efron
Ann. Statist. 13(3): 845-874 (September, 1985). DOI: 10.1214/aos/1176349634


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.


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Persi Diaconis. Bradley Efron. "Testing for Independence in a Two-Way Table: New Interpretations of the Chi-Square Statistic." Ann. Statist. 13 (3) 845 - 874, September, 1985.


Published: September, 1985
First available in Project Euclid: 12 April 2007

zbMATH: 0593.62040
MathSciNet: MR803747
Digital Object Identifier: 10.1214/aos/1176349634

Primary: 62F05
Secondary: 62G10

Rights: Copyright © 1985 Institute of Mathematical Statistics


Vol.13 • No. 3 • September, 1985
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