Term of Award
Spring 2024
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
Charles Champ
Committee Member 1
Andrew Sills
Committee Member 2
Zheni Utic
Abstract
Reporting the p-value is customary when conducting a test of hypothesis or significance. The likelihood of getting a fictitious second sample and presuming the null hypothesis is correct is the p-value. The significance level is a statistic that interests us to investigate. Being a statistic, it has a distribution. For the F-test in a one-way ANOVA and the t-tests for population means, we define the significance level, its observed value, and the observed significance level. It is possible to derive the significance level distribution. The t-test and the F-test are not without controversy. Specifically, we demonstrate that as sample size increases, the expectation of the T statistic in the t-test increases to infinity. The F statistic in the F-test is equivalent in this regard. Nonetheless, we demonstrate that the variance of these two test statistics is solely dependent on the total effect size in both scenarios.
Recommended Citation
Monnu, Paul O., "The Distribution Of The Significance Level" (2024). Electronic Theses and Dissertations. 2727.
https://digitalcommons.georgiasouthern.edu/etd/2727
Research Data and Supplementary Material
No
Included in
Applied Statistics Commons, Probability Commons, Statistical Methodology Commons, Statistical Theory Commons
