Farklı Dağılımlar İçin Varyans Homojenlik Testlerinin Karşılaştırılması

Abstract

Objective: The reliability of the hypothesis tests to be performed using variance analysis depends on the holding of the assumptions. In the analysis of variance, the sensitivity of the results obtained for the test statistic is most influenced by the heterogeneity of the variances. In this study, it is aimed to compare the variance homogeneity tests widely used in different literature for different distributions in terms of type-I error level and power. Material and Methods: 1000 repetitive simulations were performed for the Levene median, Levene mean, Levene trimmed mean, bootstrap Levene median, Bartlett and Cochran tests. Four cases where the sample sizes are equal were taken as n₁=n₂=n₃=15; n₁=n₂=n₃=30; n₁=n₂=n₃=45; n₁=n₂=n₃=100 and the two cases where the sample sizes are not equal were taken as n₁=15, n₂=30, n₃=45; n₁=15, n₂=30, n₃=100. For different distributions, the data were generated by taking into account the skewness and kurtosis coefficients. For power, the variance ratios of 1:1:2, 1:2:4, 1:2:2 and 1:4:4 were taken and different variances were corresponded to different sample sizes. Results: In terms of type-I error rates, the bootstrap Levene median test gave the best result for all distributions. For power; if the sample sizes were equal, for medium and large sample sizes bootstrap Levene median and Levene median tests gave the best results. For large sample sizes Bartlett test gave similar results to these two tests. Conclusion: It was seen that, while the performances of the tests were affected from the distribution, the best result against the deviations from normality was obtained for the bootstrap Levene median test and the performance of the tests was affected from the variance-sample size combination.