Serial dependence of observations leading to contingency tables, and corrections to chi-squared statistics

SUMMARY The asymptotic behaviour of the Pearson goodness-of-fit test and of the test of independence in 2 x 2 tables is examined when the data are generated by Markov dependent sequences. The results allow simple quantification of the effects of such serial dependence on some standard test statistics. Some key wrords: (hi-squared tests: Contingency tables; Dependence; Goodness of fit; Markov chains; Reversibilitv. 1. INTROI)UCTION In this paper, we discuss the asymptotic behaviour of some standard test statistics in the presence of Markov dependence in a sequence of observations. In particular, we examine the standard Pearson x2 goodness-of-fit test, and the 2 x 2 contingency table test for independence.