Exact unconditional inference for analyzing contingency tables in finite populations

With recent developments in computer power the application of exact inferential methods has become more feasible which has resulted in increasing popularity of these approaches. However, there is a lack of such methodology for populations with more complex structure, such as finite populations. When a small sample is drawn from a finite population, the number of individuals with a specific characteristic of interest follows hypergeometric distribution. In order to test for the comparison of two proportions in finite populations we develop an exact unconditional test. We utilize the information gained from the sample to restrict our search for the maximum p-value. Our proposed test has power equal to its competitors while maintains the pre-specified nominal significance level.