Year
2025
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
Committee Chairperson
Dr. Elena Buzaianu
Second Advisor
Dr. Yisu Jia
Rights Statement
http://rightsstatements.org/vocab/InC/1.0/
Third Advisor
Dr. Fei Heng
Department Chair
Dr. Richard Patterson
College Dean
Dr. Kaveri Subrahmanyam
Abstract
A two-stage design is developed for comparing the means of multiple normally distributed treatment groups under a known common variance, with the aim of identifying the treatment with the highest mean while minimizing the expected sample size, a crucial consideration in clinical trials. The proposed methodology integrates elements of both hypothesis testing and selection procedures to achieve greater efficiency and decision-making power. In the initial stage, if no treatment exhibits a mean surpassing a predefined efficacy threshold, the trial is terminated early, conserving resources. If one or more treatments exceed the threshold, the procedure advances to a second stage, where additional data is collected for the treatment group with the highest observed mean, followed by a formal hypothesis test against a control to determine its effectiveness. The design is optimized through the principle of the least favorable configuration (LFC), which focuses on minimizing expected sample size under the most challenging conditions for detection. As this approach blends selection and testing, conventional definitions of type I error and power are modified to suit the hybrid framework. For any given significance level and target power, the procedure outlines how to derive suitable design parameters, ultimately selecting the design with the lowest expected sample size from among feasible candidates.
Suggested Citation
Senaratne, Samarasuriyage Sayura Sankalpa, "A two-stage design for choosing among several normal treatments in comparison with a control: The case of common, known variance" (2025). UNF Graduate Theses and Dissertations. 1338.
https://digitalcommons.unf.edu/etd/1338
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