A Comparison of the Efficiency of Nonparametric Test Statistics For Testing Homogeneity of Variances

Abstract

The objectives of this study were to calculate the probability of type I error, power of a test, and to compare the efficiency of two statistics tests: Klotz’s test and Mood’s test, including the recommending the appropriate test statistic. Classification of the population with the distribution 5 format. Study three and four populations, including the sample sizes were equal and unequal. Sample sizes were divided into small, medium, and large size. Defined the difference of the population variances into three levels: low, moderate, and high difference. The significance levels to study were 0.01 and 0.05. The data were simulated by using Statistical programming with 1,000 replicates. Results of the research were as follows. Small sample size case for all distributions and medium sample size for left- or right-skewed with leptokurtic kurtosis distribution, Mood’s test was more appropriate than Klotz’s test. But, when the difference of the population variances was low (noncentrality parameter  in the range 0 to 1.5) or the medium and equal sample size case for left- or right-skewed with platykurtic kurtosis distribution and large sample size case for normal distribution, left- or right-skewed with platykurtic kurtosis distribution, Klotz’s test was more appropriate than Mood’s test. For other cases, two statistic tests were not significantly different.