Year

2020

Season

Spring

Paper Type

Master's Thesis

College

College of Arts and Sciences

Degree Name

Master of Science in Mathematical Sciences (MS)

Department

Mathematics & Statistics

NACO controlled Corporate Body

University of North Florida. Department of Mathematics and Statistics

First Advisor

Dr. Elena Buzaianu

Second Advisor

Dr. Ping Sa

Third Advisor

Dr. Yisu Jia

Abstract

We propose a method for comparing success rates of several populations among each other and against a desired standard success rate. This design is appropriate for a situation in which all experimental treatments have only two outcomes that can be considered “success”and “failure” respectively. The goal is to identify which treatment has the highest rate of success that is also higher than the desired standard. The design combines elements of both hypothesis testing and statistical selection. At the first stage, if none of the samples have a number of successes above the appropriate standard for the design, the experiment is terminated before the second stage. If one or more of the samples do exceed the standard, we continue to the second stage and take another sample from the population with the highest success rate in stage one. If the second stage produces a test statistic that is greater than the cutoff value for the second stage, we conclude that its associated treatment group/population has the highest success rate, which is also higher than the standard. Since this procedure is not a pure hypothesis testing procedure, power and size are redefined in order to account for the hybrid selection and hypothesis testing nature of the design. We determine the design parameters for any given size and power of the procedure. When multiple designs meet the requirements we will recommend the design that has the lowest expected sample size.

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