The Development of New Statistic Testing for Homogeneity of Variance

Abstract

This study investigated the efficiency of two new proposed homogeneity of variance test statistics,!SA1" and !SA2", using Monte Carlo methods to compare results with those from Bartlett's, Levene's, and Cochran's tests. Experiments were conducted over normal and non-normal samples, with different variance ratios, using equal and unequal Ns. Each experimental condition was replicated 10,000 times. With regard to Type I error rates, it was found that SA2 provided the best control at the .05 level. The SA1 test was not as efficient at .05, but nonetheless showed better control than Levene and Cochran. On the other hand, at the .01 level, SA1 was found to be superior to SA2 and Cochran .

For normal distributions, Bartlett's test had the most power. SA1 and Levene were second best, with SA2 and Cochran coming last. With skewed distributions, Bartlett again had the most power, followed by SA1, then SA2, with Cochran having the least power. The SA1 test was found to have the highest power for platykurtic distributions, then Levene, then SA2. With leptokurtic distributions, Levene's test showed the most power, with SA1 second, followed by SA2.