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Biometrika 1976 63(1):33-37; doi:10.1093/biomet/63.1.33
© 1976 by Biometrika Trust
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Improved likelihood ratio tests for complete contingency tables

D. A. WILLIAMS

Department of Statistics, University of Edinburgh

Lawley (1956) describes how asymptotic likelihood ratio tests can in general be improved by multiplying the –2log{lambda}test statistic by a multiplier chosen so that the null distribution of the modified statistic is better approximated by its asymptotic X2 distribution. This paper applies this technique to asymptotic likelihood ratio tests of hypotheses concerning complete contingency tables. Improved tests are derived for hypotheses with closed form maximum likelihood estimators.

Key Words: Asymptotic likelihood test • Log linear model • Multidimensional contingency table


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