Confidence Estimation of a Ratio of Binomial Proportions for Dependent Populations

In this article, we investigate the confidence estimation of the ratio of Binomial proportions. Contrary to the previous research, where independent Bernoulli samples were considered, here we concentrate on the confidence estimation of dependent (correlated) samples. We use data from two dependent samples to explore general problem of the estimating a ratio of two proportions. Each sample is obtained in the framework of direct binomial sampling. Our goal is to show that the normal approximation (which is relatively simple) for estimates of the ratio are reliable for the construction of confidence estimators. The main criterion of our judgment is the coverage probability and the width of the corresponding confidence interval. The main characteristics of confidence estimators are investigated by the Monte-Carlo method. Coverage probability and width of the confidence intervals are collected in tables, and some recommendations for an application are presented.