Date of Award
Bachelor of Science (B.S.) in Mathematics and University Honors
Analysis of variance -- Testing, Multivariate analysis, Mathematical statistics
Studies have shown that ANOVA F-test has a lower performance against heterogeneity of variances. It is important to provide more information on its alternatives and other methods that can prove useful. As a general guideline, Welch’s ANOVA is a perfect alternative with low type 1 error in all cases of different population variances. An addition to Welch’s ANOVA, Marascuilo’s alternative to this test gives a less accurate result but provides simpler calculation methods. Similar to Moder K. (2010) , Kruskal Wallis test and Hotelling’s T2 test were taken into consideration. Kruskal Wallis test had higher type 1 errors similar to the ANOVA F-test. Hotelling’s T2 test had significantly lower type 1 errors in comparison to the ANOVA F-test and the Kruskal Wallis test. Depending on the amount of observations different studies may have, a multivariate analysis of variance using Hotelling’s T2 test is advisable. Otherwise Welch’s ANOVA is a perfect choice for a test with lower type 1 errors.
Lopez, Jay, "Effect of Heterogeneity of Variance on the performance of ANOVA F-test and its Alternatives: Simulation Based Study" (2019). University Honors Theses. Paper 788.