Page 91 - Contributed Paper Session (CPS) - Volume 8

CPS2202 Oladugba Abimibola Victoria et al.
4. Discussion and Conclusion
Having observed the type-one-error rate and power of each HOV test, the
following deductions were made from this study: All the HOV tests perform
optimally under the condition of normality and equal sample sizes. This shows
that population distribution and unequal sample sizes significantly affects
type-one-error control and power of HOV tests. The Bartlett and Levene tests
maintained the highest power for one-way ANOVA under normality and non-
normality respectively with equal and unequal sample sizes. Under normality
and non-normality with equal and unequal sample sizes, the O’Brien and
Brown-Forsythe tests committed the least type I error for one-way ANOVA.
Nevertheless, they also have the lowest powers for one-way ANOVA. Under
normality with equal and unequal sample sizes, the Bartlett test committed no
type-one-error for two-way ANOVA. It is very robust. Under non-normality
with equal and unequal sample sizes, the O’Brien committed the least type-
one-error for two-way ANOVA. Under normality and non-normality with equal
and unequal sample sizes, the Bartlett, Levene and Z-variance maintained the
highest power for two-way ANOVA. In order to achieve better results in terms
of statistical power and type-one-error in testing for HOV when the data set
are either normal or non-normal with equal and unequal sample sizes based
on the results obtained from this study, we recommended that the Bartlett
and O’Brien tests should be used to test for HOV under normality with equal
and unequal sample sizes for one-way and two-way ANOVA. The Levene and
Brown-Forsythe tests should be used to test for HOV under non-normality
with equal and unequal sample sizes for one-way and two-way ANOVA.

References
1. Garbunova A. A. & Lemeshko B. Y. (2012). Application of variance
homogeneity tests under violation of normality assumption. Applied
Methods of Statistical Analysis 6, 28-36.
2. Howard B., Gary S., Kalz & Restori F. A. (2010). A Monte Carlo study of
seven homogeneity of variance tests. Journal of Mathematics and
Statistics, 6, 359-366.
3. Koning, A. J. (2014). Homogeneity of variances. In Wiley statsref:
Statistics Reference Online. John Wiley & Sons Online library.
4. Parra-Frutos I. (2012). Testing homogeneity of variance with unequal
sample sizes. Computational Statistics. 28, 1269-1297
5. Peter, S. (2013). Data assumption: Homogeneity of variance (univariate
tests). Blog post:
6. Vanhove, J. (2018). Causes and consequences of unequal sample sizes.
blog post: https://janhove.github.io/design/2015/11/02/unequal-
sample-sized.

80 | I S I W S C 2 0 1 9