• The Pure and Applied Mathematics
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• v.4 no.1
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• pp.7-18
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• 1997

Consider an $r\;\times\;c$ contingency table under the full multinomial model in which each classification is ordered. The problem is to test the null hypothesis of independence. A number of tests have been proposed for this problem. In this article we show that all of these tests can be improved on in some sense for most cases. In fact the preceding tests sometimes are inadmissible in a strict sense. Furthermore, we show by example that in some cases improved tests can yield substantially improved power functions.