Date of Award

1990

Degree Type

Dissertation

Degree Name

Ph.D.

Department

Mathematics and Statistics

First Advisor

Tracy, D. S.,

Keywords

Statistics.

Rights

CC BY-NC-ND 4.0

Abstract

The assumption of normality in general and homogeneity of variance for two or more populations is required in the classical approach of hypothesis testing. The ideas of robustness and nonparametric tests were introduced to avoid these assumptions. Mielke, Berry and Johnson introduced a class of tests based on permutation procedures and the assumptions required in the application of these tests are minimal. Some well known test statistics are also special cases of this test. Mielke and others compared the power performance for two special cases of this test statistic for two equal sized samples by using the approximate distributions based on three moment results. Later Tracy and Tajuddin obtained the fourth moment of this test statistic and compared the power performance for these tests for two equal sized samples based on four moment approximations. In this dissertation we extend these studies to the case of two unequal sized and three equal sized samples based on three and four moment results. In addition we compare their empirical powers with some standard nonparametric tests considered suitable for these situations. Later the modified version of this test statistic was also introduced to take into account the effect of blocking. The three moments of this test statistic were obtained to approximate its distribution. In this dissertation we have obtained the fourth moment of this test statistic to find better approximating distributions. The simplified forms of this fourth moment are also obtained for some special cases of this test statistic. Then we compare the power performance for these tests by using the approximate distribution based on three and four moment results. Source: Dissertation Abstracts International, Volume: 52-11, Section: B, page: 5914. Supervisor: D. S. Tracy. Thesis (Ph.D.)--University of Windsor (Canada), 1990.

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