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

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.


Department of Mathematical Sciences

Committee Chair

Charles Champ

Committee Member 1

Andrew Sills

Committee Member 2

Zheni Utic


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.

Research Data and Supplementary Material