#### Date of Award

12-1992

#### Degree Name

Doctor of Philosophy

#### Department

Mathematics

#### First Advisor

Dr. Michael Stoline

#### Abstract

The purpose of this dissertation was to explore the appropriateness of testing the equality of two means using either a *t* test, the Welch test, or the Mann-Whitney-Wilcoxon test for two independent samples based on the results of using two classes of preliminary tests. One class of preliminary tests determines whether the population variances differ, and the other class ascertains if the underlying distributions are symmetric or skewed. The F-ratio test and the Levene test (using the median) were compared as preliminary tests for variance homogeneity; and the DAgostino Sy and the Triples tests were also compared as preliminary tests of symmetry/asymmetry. The simulation results were used in the formulation of an expert system procedure in which both classes of preliminary tests were incorporated in the test of equality of two means. Depending on the results of the two preliminary tests, the *t* test, Welch test, or Mann- Whitney-Wilcoxon test of means was selected. The performance of the expert system was evaluated relative to Type I error only. No power results were reported.

The performance of an expert system was also evaluated with respect to robustness and the frequency at which the expert system selected the most appropriate means test.

The results reported here indicate that a preliminary test procedure for equality of variance should be used rather than using the Mann- Whitney-Wilcoxon test or* t* test for cases where nothing is known a priori about variance equality. A second conclusion is that a preliminary test procedure should be urn at a significance level > 0.25.

Finally, suggestions for improvements in the overall expert system are given.

#### Access Setting

Dissertation-Open Access

#### Recommended Citation

Perry, Kimberly Tucker, "A Critical Examination of the Use of Preliminary Tests in Two-Sample Tests of Location" (1992). *Dissertations*. 1971.

http://scholarworks.wmich.edu/dissertations/1971