Admissible statistical tests of fixed level are derived for the hypotheses (a) of statistical independence and (b) of Markov dependence, against the alternative of a higher-order Markov dependence. The tests, which are related to the run test and to contingency tests, are conditional procedures given a complete sufficient statistic. Comparisons are made with chi-squared tests for independence using computer simulation.
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Denny et al. (1978) studied this question.
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