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
First Advisor
Dr. Ping Sa
Second Advisor
Dr. Pali Sen
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