Chapter 5 Comparing Two Groups 187 arise in subsequent chapters where the Storer­Kim method has less power than Beal's method when comparing multiple groups of individuals. But when comparing two groups only, we find situations where the Storer­Kim method rejects and Beal's method does not. In terms of controlling the probability of a type I error when testing the hypothesis that the two binomial distributions have the same probability of success, all three methods appear to ensure that the actual level will be less than or equal to the nominal level. Limited comparisons indicate that typically the level of the Storer­Kim method is closest to the nominal level, when testing at the 0.05 level, suggesting that in general it will have the highest power. Reiczigel, Abonyi-T´ th, and Singer (2008) generalized results derived by Sterne (1954) that o yields a minimum volume confidence region for the two probabilities of success. Their method can be used, among other things, to compute a p-value when testing the hypothesis that two probabilities are equal. However, the Storer­Kim method appears to have a slight edge in terms of power, at least when testing at the 0.05 level. A more systematic study is needed to resolve this issue. The involved computational details are not described, but an R function for computing the confidence region derived by Reiczigel et al. is provided in Section 5.8.4. 5.8.1 Storer­Kim Method