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Testing for independence in a two-way table: New interpretations of the chi-square statistic. (English) Zbl 0593.62040
This paper is concerned with \(\chi^ 2\)-tests for the independence in contingency tables. In particular, it deals with the problem how to analyse a contingency table if the \(\chi^ 2\)-test rejects independence. The authors propose to consider the single alternative, consisting of the uniform distribution. They connect the hypothesis of independence and the hypothesis of uniformity by means of a one-parameter exponential family, and consider the statistical analysis of the parameter of this family.
The paper is followed by a number of discussions by other authors, most of them criticize the approach proposed in this paper.
Reviewer: H.Strasser

MSC:
62G10 Nonparametric hypothesis testing
62F05 Asymptotic properties of parametric tests
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