College of Graduate Studies: Theses & Dissertations
Term of Award
Summer 2026
Degree Name
Master of Science in Mathematics (M.S.)
Document Type and Release Option
Thesis (open access)
Copyright Statement / License for Reuse
This work is licensed under a Creative Commons Attribution 4.0 License.
Department
Department of Mathematical Sciences
Committee Chair
Arpita Chatterjee
Committee Member 1
Divine Wanduku
Committee Member 2
Ionut Iacob
Abstract
Traditional factorial analysis often relies on ANOVA, which assumes normality and equal variances. This thesis presents a nonparametric approach for assessing main and interaction effects in a 2 × 2 factorial design using the overlap coefficient, estimated through kernel density methods. A bootstrap procedure is used to approximate its sampling distribution for hypothesis testing. Simulation studies compare the overlap-based test with the ANOVA F-test, permutation F-test, and the Kruskal–Wallis test under heteroskedasticity and non-normal conditions. Results show that the overlap measure is highly sensitive to differences in spread and shape, detecting effects that traditional methods frequently miss.
Recommended Citation
Liebenow, Sarah W., "Factorial Design: A New Look Through Overlap Measures" (2026). College of Graduate Studies: Theses & Dissertations. 3189.
https://digitalcommons.georgiasouthern.edu/etd/3189
Research Data and Supplementary Material
Yes
Mixed Controls.R (7 kB)
Full Main Effect perm ovr with perm F.R (7 kB)
interaction _CDF.R (3 kB)
simulation test.xlsx (24 kB)
