Testing for Independence in a Two-Way Table: New Interpretations of the Chi-Square Statistic
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.
Permanent link to this document: http://projecteuclid.org/euclid.aos/1176349634
Digital Object Identifier: doi:10.1214/aos/1176349634
Mathematical Reviews number (MathSciNet): MR803747
Zentralblatt MATH identifier: 0593.62040