Comparing k Population Means with No Assumption about the Variances

<p>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.</p>

Name thesis:degree_name

Master of Science in Mathematics (M.S.)

Level thesis:degree_level

Thesis (open access)

Discipline thesis:degree_discipline

Department of Mathematical Sciences

Year dc:date.available

2014

Author dc:creator

• Yaacoub, Tony

Contributors dc:contributor

• Hani Samawi
• Broderick O. Oluyede

• ETD
• ANOVA
• fixed effects one-way design
• likelihood ratio test
• orthogonal designs
• statistically designed experiments
• Design of Experiments and Sample Surveys
• Statistical Theory

Repository record dc:identifier

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

OAI identifier oai:identifier

oai:digitalcommons.georgiasouthern.edu:etd-2111