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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. 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 | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > 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: |
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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 |
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