Year
2016
Season
Summer
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. Ping Sa
Second Advisor
Dr. Pali Sen
Rights Statement
http://rightsstatements.org/vocab/InC/1.0/
Third Advisor
Dr. Donna Mohr
Department Chair
Dr. Scott Hochwald
College Dean
Dr. Daniel Moon
Abstract
When the variance of a single population needs to be assessed, the well-known chi-squared test of variance is often used but relies heavily on its normality assumption. For non-normal populations, few alternative tests have been developed to conduct left tailed hypothesis tests of variance. This thesis outlines a method for generating new test statistics using a saddlepoint approximation. Several novel test statistics are proposed. The type-I error rates and power of each test are evaluated using a Monte Carlo simulation study. One of the proposed test statistics, R_gamma2, controls type-I error rates better than existing tests, while having comparable power. The only observed limitation is for populations that are highly skewed with heavy-tails, for which all tests under consideration performed poorly.
Suggested Citation
Grimes, Tyler L., "A Saddlepoint Approximation to Left-Tailed Hypothesis Tests of Variance for Non-normal Populations" (2016). UNF Graduate Theses and Dissertations. 644.
https://digitalcommons.unf.edu/etd/644