Publication Date

12-2025

Date of Final Oral Examination (Defense)

10-17-2025

Type of Culminating Activity

Dissertation

Degree Title

Master of Science in Mathematics

Department

Mathematics

Supervisory Committee Chair

Kyungduk Ko, Ph.D.

Supervisory Committee Member

Michael Perlmutter, Ph.D.

Supervisory Committee Member

Juna Goo, Ph.D.

Abstract

Understanding variability is fundamental to knowledge advancement across various disciplines, including manufacturing, clinical research, biology and genetics. Population variances play a crucial role in processes such as quality control, treatment evaluation and the interpretation of biological mechanisms. However, statistical procedures for comparing variances across multiple populations remain less developed than those for comparing means. Classical omnibus tests, such as Bartlett's and Levene's, can detect overall variance heterogeneity but fail to identify which populations differ, thereby limiting their usefulness in multi-population analyses and increasing the risk of inflated family-wise error rates through repeated testing.

This thesis develops and evaluates three multiple comparison procedures designed to overcome these limitations. The Levene–Tukey-type procedure integrates absolute deviations from population means with Tukey’s multiple comparison framework. The F-ratio-type procedure extends the conventional F-test to multi-population contexts, enhancing sensitivity while maintaining control of type I error. The Hartley’s F-max -type procedure employs a ratio-based and stepwise elimination approach to identify groups contributing to variance heterogeneity.

The proposed methods are assessed through extensive simulation studies under varying sample sizes, variance structures, and distributional assumptions, including non-normal data. Their practical relevance is further demonstrated using real-world data. Collectively, these procedures advance statistical methodology by providing robust, interpretable, and accessible tools for analyzing variance across populations, thereby improving the reliability of applied statistical inference.

DOI

https://doi.org/10.18122/td.2464.boisestate

Download

Included in

Mathematics Commons

Share

COinS