K Bağımsız Grubu Karşılaştırmak İçin Dayanıklı Yöntemler

Abstract

Objective: One-way ANOVA-F test is the most common test to examine whether there is a statistically significant difference between population means of more than two independent groups or not. However, ANOVA-F test can give misleading results when normality and homoscedasticity assumptions are violated. In order to get reliable results, robust methods can be preferred instead of ANOVA-F test. The purpose of this study is comparing six different methods including ANOVA-F test in terms of controlling actual Type I error rates under 28 different experimental conditions. These experimental conditions comprise of the combinations of the components which are symmetric and asymmetric distributions, homoscedasticity and heteroscedasticity, equal and unequal sample sizes and positive and negative pairings of variances with sample sizes. Furthermore, these six different methods were compared for two real data sets which were obtained from speech exercises of Parkinson’s patients. Material and Methods: Compared methods are ANOVA-F test, Welch test, Welch test with trimmed mean, Welch test with trimmed mean and a bootstrap-t, Box method, and Kruskal-Wallis test. Results: After computing actual Type I error rates of the methods with a simulation study, power rates are calculated for the four methods which controlled the actual Type I error rate according to a robustness criterion. Conclusion: Based on all results obtained from this study, Welch test is recommended when the assumptions are satisfied whereas Welch test with trimmed mean is recommended when the assumptions are violated.