A Bayesian Test of Independence in a Two-Way Contingency Table Under Two-Stage Cluster Sampling

• Activity Number: 16
• Type: Topic Contributed
• Date/Time: Sunday, July 29, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Survey Research Methods
• Author(s): Dilli Bhatta*+
• Companies: Worcester Polytechnic Institute
• Keywords: Bayes factor ; Chi-squared test ; Cluster table ; Rao-Scott approximation ; Surrogate samples ; Total table

Abstract

We consider a Bayesian approach to study independence in a two-way contingency table which is obtained from a two-stage cluster sampling design with simple random sampling at both stages. For many large complex surveys, the Rao-Scott corrections to the standard chisquared (or likelihood ratio) statistic is appropriate. If a procedure, based on simple random sampling rather than cluster sampling, is used to test for independence, the p-value can be too small resulting in significant evidence against the null hypothesis when there may be no such evidence. For smaller surveys, the Rao-Scott corrections are not accurate, partly because the chi-squared test is inaccurate. In this article, we use a hierarchical Bayesian model to convert the cluster samples to simple random samples. This provides surrogates which can be used to construct a distribution of the Bayes factor. We demonstrate our procedure on an example and also provide a simulation study which establishes our methodology as a viable alternative to the Rao-Scott approximation for relatively small two-stage cluster samples.