Evaluation of transformation methods in terms of type I error rate and power of the test when assumptions are not satisfied in group comparisons

In this thesis, some transformation methods that can be applied when the assumptions of analysis of variance are not satisfied are evaluated in terms of the probability of type I error rate and the power of the test, with the different distributions, number of groups, number of observations, variance ratios, and standard deviation differences. The materials used in this study are consist of random numbers drawn from N(0, 1),χ2(3), t(10) and β(15, 5) distributions using the random function of the Numpy library in the Python language. Simulation designs were set up for each of these distributions with 3, 4, and 5 groups, with the number of observations in each group as 3, 5, 10, 15, 30, and the variance ratio between groups as 1, 3, 5 and 10 times the variance ratio of the other groups, and the standard deviation differences between means as 0, 0.5, 1, 1.5 and 2. As a result of the study, it was observed that the transformation techniques of taking the square root by adding 0.5 and 0.375 to the data are relatively more reliable compared to other transformation techniques in terms of the probability of type I error, but in every case, the probability of type I error determined at the beginning of the experiment increases both before and after the transformation is applied. In particular, it was observed in an interesting way that the third and fourth degree root transformations gave higher results in the power of the test in the right skewed distribution.