# Transformed tests for homogeneity of variances and means

Abstract (Summary)

Hanfeng Chen, Advisor
The analysis of variance (ANOVA) is one of the most important and useful techniques for
variety of fields such as agriculture, sociology and medicine for comparing different groups
or treatments with respect to their means. A set of assumptions such as normal error
distribution, homogeneity of variances and independence of observations, has to be made
to employ an F test for equality of the treatment means. It is now well established that
the violation of the assumption of homogeneity of variances can have severe effects on the
inference of the population means, especially in the case of unequal sample sizes. In fact,
the conventional ANOVA F provides generally poor control over both Type I and Type II
error rates under a wide variety of variance heterogeneity conditions. Therefore, the problem
of homogeneity of variances has to be settled before conducting an ANOVA. While a good
number of tests are available for testing homogeneity of variances, Bartlett test and four
versions of Levene tests are still popular for testing homogeneity of variances in the case of
one-way ANOVA setting. It is evident that the Bartlett test is not as robust as Levene tests
against the violation of the normality assumption. On the other hand, Levene tests are less
powerful than the Bartlett test. In this dissertation, we proposed a transformed version of
Bartlett test where the transformation is intended to achieve the normality of the data and
independence of the observations to some extent. It is evident from the simulation that the
transformed Bartlett test is more robust than the untransformed Bartlett test against the
iii
violation of the normality assumption. It also follows that the transformed Bartlett test is a
balance between the Bartlett test and the four versions of the Levene tests in terms of Type
I error rate and power concern.
While, the estimation of location parameter is of concern, a modified version of trimmed
mean has been proposed as an alternative to trimmed mean when the distribution is skewed
or contains outliers. It is evident from the simulation study that modified trimmed mean
outperform trimmed mean in terms of coverage probability of interval estimate. It is also
evident that the test based on the modified version of trimmed mean is suitable for estimating
Type I error rate and is more powerful than the tests based on the mean and the trimmed
mean in the presence of the outliers.
Finally, an alternative method of estimating transformation parameter has been proposed
by using the chi-squared goodness of fit criteria which could be useful for testing
equality of two population means.
iv
Bibliographical Information:

Advisor:

School:Bowling Green State University

School Location:USA - Ohio

Source Type:Master's Thesis

Keywords:analysis of variance

ISBN:

Date of Publication: