Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)




Pinyuen Chen


Binomial Distribution, Clinical Trial Design, Experimental Design, Probability of Correct Selection, Ranking and Selection, Two-stage Design


In this thesis, we consider the problem of selecting a preassigned number t (>= 1) of k (>= t) experimental binomial populations in comparison to a control binomial population. A population associated with a larger success probability is considered "better". The goal is to select the t best experimental populations that are also sufficiently better than the control. An alternative goal considered in this thesis is to select any t acceptable (i.e., sufficiently better than the control) populations. We show that the two goals are equivalent at a particular parameter configuration of interest.

Selecting more than one best/acceptable populations may be useful in practice for a number of reasons. For instance, an experimenter may wish to identify more than one good populations, with confidence that all of these identified perform better than a control. In another situation, more than one good populations may be identified, from which a single population may be finally selected based on some other criterion, such as cost, availability, or safety.

All of the proposed procedures in this thesis are exact binomial procedures. That is, they are based on binomial distributions only, as opposed to many existing selection procedures that use normal approximation to binomial. We evaluate the exact probabilities of making a correct selection (P(CS)) and derive the least favorable configuration (LFC) which is the worst case scenario parameter vector for the corresponding P(CS). Due to the exact binomial probabilities, the proposed procedures do not need the large sample size assumption for normal approximation and can be applied to any sample size.


Open Access

Available for download on Thursday, June 12, 2025