Term of Award
Master of Science in Mathematics (M.S.)
Document Type and Release Option
Thesis (open access)
Department of Mathematical Sciences
Charles W. Champ
Committee Member 1
Committee Member 2
Broderick O. Oluyede
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.
Yaacoub, Tony, "Comparing k Population Means with No Assumption about the Variances" (2014). Electronic Theses & Dissertations. 1079.