Page 85 - Contributed Paper Session (CPS) - Volume 8

CPS2202 Oladugba Abimibola Victoria et al.
The assumption of homogeneity of variance (HOV) also known as
homoscedasticity implies that the variance within each of the population
groups are equal. This is one of the assumptions of analysis of variance
(ANOVA). When this assumption is violated, there is a greater probability of
falsely rejecting the null hypothesis. Lack of homoscedasticity is known as
heteroscedasticity. The statistical validity of many commonly used tests such
as the t-test and ANOVA depend on the extent to which the data conform to
the assumption of HOV. Accessing HOV is of paramount importance to many
researchers as they are concerned with whether the dispersion of the
dependent variable is similar across multiple groups. When comparing groups,
their dispersion on the dependent variable should be relatively equal at each
level of the independent (factor or grouping) variable (and neither should their
sample sizes vary greatly across the groups), this implies that the dependent
variable should exhibit equal levels of variance across the range of groups.
Furthermore, violation of the assumption of HOV distort the F-distribution in
ANOVA to such an extent that the critical F-value no longer corresponds to
the chosen level of significance, this leads to a serious type-one-error Peter (
2013). Heteroscedasticity may not only affect the validity test, it may also have
a negative effect on the coverage of the confidence intervals and the accuracy
of the estimator Koning (2014).
According to Parra-Frutos (2012) problems of heteroscedasticity of data
set arise when the sample sizes are unequal. Usually unequal sized groups are
common in research and may be as a result of simple randomization. In test
like ANOVA, having both unequal sample sizes and variance dramatically
affects statistical power and type-one-error rates Vanhove (2018). Test
statistics is relatively insensitive to small departures from the assumption of
equal variances for the treatments if the sample sizes are equal, this is not the
case for unequal sample sizes; Also, power of the test is maximized if the
samples are of equal sizes Montgomery (2013).
One of the basic assumptions to formulate classical tests for comparing
variances is normal distribution of samples Garbunova & Lemeshko (2012). It
is well known that classical tests are very sensitive to departures from
normality. Therefore, the application of classical criteria always involves the
question of how valid the obtained results are when the data are non-normal.
Testing for the equality of variance is a difficult problem due to the fact that
many tests are not robust to non-normality and are affected by sample sizes
Vanhove (2018). Therefore, given that there are several methods available in
testing for HOV, it would be of interest to determine which of them perform
best under normality and non-normality when the sample sizes are equal and
unequal. In this work, seven HOV tests using one-way and two-way ANOVA
models were compared when the data are normal and non-normal for equal
and unequal sample sizes. They are Bartlett test, Levene’s Test, Z-Variance test,

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