Lawley (1956) describes how asymptotic likelihood ratio tests can in general be improved by multiplying the −2logλtest 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.

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