Statistical Inference for the Cross-Product Ratio under Different Sampling Schemes

The problem of comparing Bernoulli trial success probabilities comes up in biological and medical research. In this article, we examine how well the cross-product ratio of Binomial proportions performs hypothesis testing for various sample designs. The main criterion is the probability of types I and II errors. To ascertain the precision of the hypothesis testing procedure under the various sampling schemes, Monte Carlo simulations will be used. Other related results, including the probability of types I and II errors, will be compiled in tables for various levels of samples and probabilities. We determine the sample plan that performs the best when testing a hypothesis about the cross-product ratio of probabilities for each set of parameter choices.