Defense Date

2015

Document Type

Thesis

Degree Name

Master of Science

Department

Biostatistics

First Advisor

Dr. Wen Wan

Second Advisor

Dr. Donna McClish

Third Advisor

Dr. Qin Wang

Abstract

Analysis of variance (ANOVA) is a robust test against the normality assumption, but it may be inappropriate when the assumption of homogeneity of variance has been violated. Welch ANOVA and the Kruskal-Wallis test (a non-parametric method) can be applicable for this case. In this study we compare the three methods in empirical type I error rate and power, when heterogeneity of variance occurs and find out which method is the most suitable with which cases including balanced/unbalanced, small/large sample size, and/or with normal/non-normal distributions.

Comments

F-test in analysis of variance is unsuitable in three-group heterogeneity cases, even though it is a robust test when data are homogeneous, normal and equal/unequal sample sizes.

Welch’s test performs the best in three-group heterogeneity cases when data are normal and equal and unequal sample sizes. And this result is consistent with the results from Moder (2010) that Welch’s F-test is useful for a small number of group cases.

Kuskal-Wallis test is acceptable in mild heterogeneity cases when data are normal and equal sample sizes.

Rights

© The Author

Is Part Of

VCU University Archives

Is Part Of

VCU Theses and Dissertations

Date of Submission

8-4-2015

Included in

Biostatistics Commons

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