Document Type thesis Author Name zhou, jingran Email Address bestzhoujr at hotmail.com URN etd-121911-152204 Title a Bayesian test of independence of two categorical variables obtianed from a small area : an application to BMD and BMI Degree MS Department Mathematical Sciences Advisors Balgobin Nandram, Advisor Keywords small area categorical variables independence Bayesian test Date of Presentation/Defense 2011-12-05 Availability unrestricted
Scientists usually need to understand the extent of the association of two attributes, and the data are typically presented in two-way categorical tables. In science, the chi-squared test is routinely used to analyze data from such tables. However, in many applications the chi-squared test can be defective. For example, when the sample size is small, the chi-squared test may not be applicable. The terms small area" and local area" are commonly used to denote a small geographical area, such as a county. If a survey has been carried out, the sample size within any particular small area may be too small to generate accurate estimates from the data, and a chi-squared test may be invalid (i.e., expected frequencies in some cells of the table are less than ve). To deal with this problem we use Bayesian small area estimation. Because it is used toorrow strength" from related or similar areas. It enhances the information of each area with common exchangeable information. We use a Bayesian model to estimate a Bayes factor to test the independence of the two variables. We apply the model to test for the independence between bone mineral density (BMD) and body mass index (BMI) from 31 counties and we compare the results with a direct Bayes factor test. We have also obtained numerical and sampling errors; both the numerical and sampling errors of our Bayes factor are small. Our model is shown to be much less sensitive to the specication of the prior distribution than the direct Bayes factor test which is based on each area only.
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