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For any class of one-sided $1-\alpha$ confidence intervals with a certainmonotonicity ordering on the random confidence limit, the smallest interval, inthe sense of the set inclusion for the difference of two proportions of twoindependent binomial random variables, is constructed based on a directanalysis of coverage probability function. A special ordering on the confidencelimit is developed and the corresponding smallest confidence interval isderived. This interval is then applied to identify the minimum effective dose(MED) for binary data in dose-response studies, and a multiple test procedurethat controls the familywise error rate at level $\alpha$ is obtained. Ageneralization of constructing the smallest one-sided confidence interval toother discrete sample spaces is discussed in the presence of nuisanceparameters.

On construction of the smallest one-sided confidence interval for the difference of two proportions