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Information identities and testing hypotheses : power analysis for contingency tables

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Cheng, Philip E., Liou, Michelle, Aston, John A. D. and Tsai, Arthur C. (2008) Information identities and testing hypotheses : power analysis for contingency tables. Statistica Sinica, Vol.18 (No.2). pp. 535-558.

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Abstract

An information theoretic approach to the evaluation of 2 x 2 contingency tables is proposed. By investigating the relationship between the Kullback-Leibler divergence and the maximum likelihood estimator, information identities are established for testing hypotheses, in particular, for testing independence. These identities not only validate the calibration of p values, but also yield a unified power analysis for the likelihood ratio test, Fisher's exact test and the Pearson-Yates chi-square test. It is shown that a widely discussed exact unconditional test for the equality of binomial parameters is ill-posed for testing independence, and that using this test to criticize Fisher's exact test as being conservative is logically flawed.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH): Contingency tables, Chi-square test, Statistical hypothesis testing
Journal or Publication Title: Statistica Sinica
Publisher: Academia Sinica, Institute of Statistical Science
ISSN: 1017-0405
Official Date: April 2008
Dates:
DateEvent
April 2008Published
Volume: Vol.18
Number: No.2
Number of Pages: 24
Page Range: pp. 535-558
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access

Data sourced from Thomson Reuters' Web of Knowledge

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