Page 84 - Contributed Paper Session (CPS) - Volume 8

CPS2202 Oladugba Abimibola Victoria et al.

A comparative study of test statistics for testing
homogeneity of variances in analysis of variance
models
1
Oladugba Abimibola Victoria , Okiyi Bright Chiamaka , Caroline Ogbonne
1
Odo
2
1 Department of Statistics, University of Nigeria, Nsukka
2 Department of Agricultural Economics, Michael Okpara University of Agriculture Umudike,
Abia State

Abstract
This study compared seven methods of testing homogeneity of variances in
one-way and two-way analysis of variance models under the assumptions of
normality and non-normality distributions when the sample sizes are equal
and unequal using type-one-error and power of the test. The methods
compared were: Bartlett test, Levene test, Brown-Forsythe test, O’Brien test, Z-
variance test, Hartley’s F-max test and Cochran’s G-test. Monte Carlo
simulation was used to generate response observations for normality and
non-normality distributions (Chi-square). The result from the analysis showed
that under normality and non-normality distributions, the Brown-Forsythe and
O’Brien tests committed the least type-one-error while the Levene and Bartlett
test maintained the highest power respectively with equal and unequal sample
sizes in one-way analysis of variance. The Bartlett, Levene and Z-variance
maintained the highest powers while the O’Brien committed the least type-
one-error under non-normality with equal and unequal sample sizes in two-
way analysis of variance.

Keywords
Type-one-error; Power; Bartlett; Levene test; Normality and Non-normality

1. Introduction
In many experimental data, the first thing one noticed in the data set is
that the observed values are not all the same even under the same condition
or subject. This shows that there is variability in the data set. The statistics that
deals with variability in a data set is called variance. Variance is the expectation
of the squared deviation of a random variable from its mean that is variance
measures how far each observation in the data set was from their mean
Vanhove (2018). When all the observed values in a data set are identical, the
variance will be zero but when they are not all identical, the variance will be
greater than zero; a large variance indicates that most of the observed values
in the data set are far from each other while a small variance indicates the
opposite Peter (2013).

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