Comparison of some parametric and nonparametric K-sample test procedures' performances as an alternative to one-way analysis of variance

The one-way analysis of variance, which is a parametric test, is used to compare the mean of more than two populations and is one of the most important statistical methods used for this purpose. The assumptions necessary for the application of variance analysis are that the data follows to the normal distribution, the homogeneity of the group variances to be compared and the independence of the observations; if these assumptions are violated, it is considered an alternative strategy for researchers to turn to use different test procedures rather than analysis of variance. In this thesis, Welch, Alexander-Govern, Brown-Forsythe, James Second-Order, Kruskal-Wallis, modified version of Kruskal-Wallis test based on permutation test, Mood's Median, Van der Waerden and Savage tests in terms of maintaining the probability of Type-Ⅰ error determined at the beginning of the experiment was compared with the F test. The performance of the tests in terms of to protect Type I error; the variances are homogeneous and heterogeneous, the sample size is not balanced and balanced, the distribution of the data is appropriate to the normal distribution and abnormal distribution in the number of groups to be compared with how the change is affected by simulation scenarios. As indicated in the literature, the F test tended to maintain its robustness in the even of a violation of the normal distribution, whereas it was found that the homogeneity of the variances was more affected by the assumption of a violation. In this respect, if the homogeneity of variances is neglected, Welch, Alexander-Govern and James Second-Order tests, which are not affected by the equal or differentiation of the number of units in the groups within the framework of the findings of the thesis, are the tests that can be proposed as an alternative to the F test.