Efficiency Comparison of Statistic for Testing Three Population Means in Case of Homogeneity of Variance

Abstract

The objective of this research is to compare the efficiency comparison of test statistic for testing three population means in case of hemogeneity and heterogeneity of variance. In analysis of variance using F-test 1(F), Brown-Forsythe's test (BF), modified Brown-Forsythe's test (MBF), and Welch's test (W) are test statistic for computing probability of type 1 error and power of a test. The Bradley's is a criterion to control the probability of type I error at 0.01 and 0.05 significance level. The data of this research is simulated by using the Monte Carlo technique and each case is replicated 1,000 times from normal and gamma distributions base on equal and unequal sample size. For homogeneity of variance, most of F, BF, MBF are test statistical efficiency with respect to probability of type I error and power of the test in normal distribution. For gamma distribution, F and BF perform very satisfactorily in almost all case at significance level 0.01, while F and W exhibit a good power of a test at significance level 0.05. In case of heterogeneity of variance, W perform better than F, Bf, and MBF at sigificance levels 0.01 but F,BF, and MBF are reasonable working as good as W at significance levels 0.05.