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. ISSN 1017-0405

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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
Date:	April 2008
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
URI:	http://wrap.warwick.ac.uk/id/eprint/30050

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