#### Term of Award

Spring 2014

#### Degree Name

Master of Science in Mathematics (M.S.)

#### Document Type and Release Option

Thesis (open access)

#### Department

Department of Mathematical Sciences

#### Committee Chair

Charles W. Champ

#### Committee Member 1

Hani Samawi

#### Committee Member 2

Broderick O. Oluyede

#### Abstract

In the analysis of most statistically designed experiments, it is common to assume equal variances along with the assumptions that the sample measurements are independent and normally distributed. Under these three assumptions, a likelihood ratio test is used to test for the difference in population means. Typically, the assumption of independence can be justified based on the sampling method used by the researcher. The likelihood ratio test is robust to the assumption of normality. However, the equality of variances is often difficult to justify. It has been found that the assumption of equal variances cannot be made even after transforming the data. Our interest is to develop a method for comparing k population means assuming the data are independent and normally distributed but without assuming equal variances. This is the Behrens-Fisher problem for k=2. We propose a method that uses the exact distribution of the likelihood ratio (test) statistic. The data is used to estimate this exact distribution to obtain an estimated critical value or an estimated p-value.

#### Recommended Citation

Yaacoub, Tony, "Comparing k Population Means with No Assumption about the Variances" (2014). *Electronic Theses & Dissertations*. 1079.

https://digitalcommons.georgiasouthern.edu/etd/1079