#### Date of Award

4-2013

#### Degree Name

Doctor of Philosophy

#### Department

Statistics

#### First Advisor

Dr. Gerald L. Sievers

#### Second Advisor

Dr. Jung Chao Wang

#### Third Advisor

Dr. Jeff Terpstra

#### Fourth Advisor

Dr. Ala Al-Fuqaha

#### Abstract

Testing equality of variances between two samples is applied in various fields. However, in the absence of non-normal assumptions, equality of variance tests would not yield robust results. In real life situation, the absence of such assumptions is even evident, which calls for more reliable tests to accommodate for the lack of these assumptions. There are abundant parametric and nonparametric methods for estimating the scale parameter; yet a distribution-free method for estimating and finding the confident interval ratio of scale parameters in the two-sample problem would be a reliable alternative. A comparison between existing parametric and non-parametric rank tests for the two-sample scale problem will be investigated which include linear rank tests and folded rank tests with different score functions, Lehmann test, jackknife test, Sukhatme test, placement tests, permutations tests and the classical Levene tests. The developed algorithm of estimation and finding the confidence interval of the scale parameters will be examined. A Monte Carlo simulation will be used to study the performance of our algorithm under symmetric and asymmetric distributions for different sample sizes. Also, the efficiency of the proposed confidence interval will be analyzed by computing the length of the interval and its probability of coverage. In general, our algorithm performed better than the available methods for estimating the ratio of the scale parameter in the two-sample problem. This work suggests the robustness of Lehmann test and Folded Klotz test for testing equality of variances. This suggestion is supported by the proposed algorithm, which asserts that the estimator and the confidence intervals of Lehmann test and Folded Klotz test are superior compared to other tests in estimating the ratio of scale parameters in the two-sample problem. Finally, real data from a cloud-based computing environment will be analyzed.

#### Access Setting

Dissertation-Open Access

#### Recommended Citation

Alduailij, Mona Abdullah, "A Computational Method for Estimating and Finding the HConfidence Interval of the Ratio Scale Parameters in the Two-Sample Problem" (2013). *Dissertations*. 132.

https://scholarworks.wmich.edu/dissertations/132