Analysis of contingency tables under cluster sampling

doi:10.1093/biomet/67.3.591

Biometrika 1980 67(3):591-596; doi:10.1093/biomet/67.3.591
© 1980 by Biometrika Trust

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Analysis of contingency tables under cluster sampling

STEPHEN S. BRIER

Department of Statistics, University of Iowa Iowa City

The Dirichlet-multinomial distribution is formulated as a modelfor contingency tables generated by cluster sampling schemes.This model provides an alternative justification for some resultsof Altham (1976) and enables an extension of her results tothe case of unequal cluster sizes. The model also provides aconvenient framework for the fitting and testing of generallog linear models in contingency tables. The asymptotic distributionsof the Pearson and likelihood ratio chi-squared statistics areshown to be multiples of chi-squared random variables and thisresult permits a simple modification of the usual procedureswhen faced with a cluster sample.

Key Words: Cluster sample • Contingency table • Dirichlet-multinomial distribution • Goodness-of-fit test • Log linear model

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