Thavatchai Vorapongsathorn, Sineenart Taejaroenkul and Chukiat Viwatwongkasem

pp. 537 - 547

Abstract

This study compared the probability of Type I error and the power of three statistical tests (Bartlett,
Levene and Cochran) by varying the sampling distribution, variances and sample sizes. Monte Carlo methods
were used to generate responses based on sample sizes and distributions 1,000 times. The sample sizes were
both equal and unequal: 15, 30 and 45. The data distributions were Normal, Gamma and Chi-square.
It was found that Bartlett’s test was sensitive to the normality assumption whereas Cochran’s test
and Levene’s test were robust when the normal assumption was violated. Moreover, Levene’s test was quite
good for both equal and small sample sizes. In the case of power, Bartlett’s test had the highest power in all
cases. When one variance was large, Cochran’s test was the best test. The recommendations from this study are that: Bartlett’s test is the best test for homogeneity of
variances since it is not affected by sample size. When data are non-normally distributed, Levene’s test is
a good choice for small equal sample sizes. Cochran’s test is best when sample size is large and unequal and
one variance is larger.

Keywords

• homogeneity of variance
• Bartlett’s test
• Levene’s test
• Cochran’s test
• simulation