Tests of Independence in a Single 2x2 Contingency Table with Random Margins

In analysis of the contingency tables, the Fisher\u27s exact test is a very important statistical significant test that is commonly used to test independence between the two variables. However, the Fisher\u27 s exact test is based upon the assumption of the fixed margins. That is, the Fisher\u27s exact test uses information beyond the table so that it is conservative. To solve this problem, we allow the margins to be random. This means that instead of fitting the count data to the hypergeometric distribution as in the Fisher\u27s exact test, we model the margins and one cell using multinomial distribution, and then we use the likelihood ratio to test the hypothesis of independence. Furthermore, using Bayesian inference, we consider the Bayes factor as another test statistic. In order to judge the test performance, we compare the power of the likelihood ratio test, the Bayes factor test and the Fisher\u27s exact test. In addition, we use our methodology to analyse data gathered from the Worcester Heart Attack Study to assess gender difference in the therapeutic management of patients with acute myocardial infarction (AMI) by selected demographic and clinical characteristics