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.
OCLC Number
1608234239
Catalog Permalink
https://galileo-georgiasouthern.primo.exlibrisgroup.com/permalink/01GALI_GASOUTH/c9nn09/alma9916670545202950
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)
