الفهرس 
Nonparametric tests of heteroscedastic ANOVA
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Abstract
Analysis of variance (ANOVA) is generally regarded as one of the most powerful and flexible methods for testing null hypotheses about means of populations. However, the violation of one of the essential prerequisites to ANOVA which is homogeneity of variances in underlying populations may lead to a F-test that is not robust to all degrees of unequal variances, and the actual significance level and power can be distorted even when sample sizes are equal. In fact, the conventional ANOVA F provides generally poor control over both Type I and Type II error rates under a wide variety of variance heterogeneity conditions. Therefore, the problem of homogeneity of variances has to be settled before conducting an ANOVA. In the first part of this thesis, the ANOVA model and its classification, underlying assumptions, and consequences of the assumption violation will be discussed and presented. The second part offers a comprehensive review of the different approaches and tests, parametric and non parametric, discussed in literature to overcome the problem of heterogeneity is presented. Finally, a simulation study using SAS is conducted to compare the performance of the conventional ANOVA F Test, Welch{u2019}s F and Kruskal Wallis tests, in terms of Type I error controlling and the power of the test. The comparison was conducted for both balanced and unbalanced designs