The Effect of Positive Dependence on Chi-Squared Tests for Categorical Data
Leon Jay Gleser, David S. Moore · Journal of the Royal Statistical Society Series B (Statistical Methodology) · 1985
SUMMARY We introduce a general definition of positive dependence for finite-state processes, and show that if successive observations are positively dependent, all tests that are asymptotically equivalent to standard Pearson chi-squared tests have asymptotic null distributions stochastically larger than those obtained under the usual independence assumptions. Ignoring positive dependence therefore leads to too frequent rejection of null hypotheses. This qualitative conclusion applies in particular to certain cases of Markov dependence, and of dependence induced by cluster sampling, that have been studied by previous authors.