SUGGESTED BAYESIAN MODELS TO TEST THE INDEPENDENCE HYPOTHESIS IN 2X2 CONTINGENCY TABLES

Abstract

In this paper, the Bayesian approach was used to test the independence hypothesis in the 2x2 contingency tables, considering that the data in the cells of the contingency table follow a probability distribution and through it the prior distribution of the parameters is found for the purpose of calculating the joint posterior probability of the difference between the two parameters in the table, and then finding the probability of the difference between them and comparing it with a significance level value 0.05. We used four Bayesian models that depend on prior distribution, which are the binomial - beta model, the Poisson - gamma model, the geometrical - beta model and the normal – standard normal model, and by using simulation and an algorithm written in the R program, the required probabilities were found for the purpose of testing the independence hypothesis. The results showed that significance of all the models that used.