#### Article Title

Identifying Which of *J* Independent Binomial Distributions Has the Largest Probability of Success

#### Abstract

Let *p*_{1},…, *p _{J}* denote the probability of a success for

*J*independent random variables having a binomial distribution and let

*p*

_{(1)}≤ … ≤

*p*

_{(J)}denote these probabilities written in ascending order. The goal is to make a decision about which group has the largest probability of a success,

*p*

_{(J)}. Let

*p̂*

_{1},…,

*p̂*

_{J}denote estimates of

*p*

_{1},…,

*p*, respectively. The strategy is to test

_{J}*J*− 1 hypotheses comparing the group with the largest estimate to each of the

*J*− 1 remaining groups. For each of these

*J*− 1 hypotheses that are rejected, decide that the group corresponding to the largest estimate has the larger probability of success. This approach has a power advantage over simply performing all pairwise comparisons. However, the more obvious methods for controlling the probability of one more Type I errors perform poorly for the situation at hand. A method for dealing with this is described and illustrated.

#### DOI

10.22237/jmasm/1604190960

#### Recommended Citation

Wilcox, R. (2019). Identifying which of J independent binomial distributions has the largest probability of success. Journal of Modern Applied Statistical Methods, 18(2), eP3359. doi: 10.22237/jmasm/1604190960

#### Included in

Applied Statistics Commons, Social and Behavioral Sciences Commons, Statistical Theory Commons