COMPARISON OF EXACT CONFIDENCE INTERVALS FOR THE DIFFERENCE BETWEEN TWO INDEPENDENT BINOMIAL PROPORTIONS

The confidence interval for the difference between two independent binominal proportions has been frequently discussed in recent conferences or papers. This interest arises from the fact that the actual confidence level does not correspond to the nominal confidence level. The major problems are the collapse of the assumption of asymptotic normality with small sample size and the fact that it has been pointed out that the actual confidence level of approximate confidence interval using this assumption is less than the nominal confidence level. In this paper, we focus on a construction method for the exact confidence interval that directly uses the probability of a binominal distribution, and presented both of the existing methods and the new method using new test statistics. Further, we compare the existing and new methods using a simulation. We also propose an exact confidence interval that does not need repetitive calculations, and shows the usability of this method.