Type I error rate and test power for different approaches to factorial designs when normality and homogeneity of variances assumptions are not satisfied

In this study, it was aimed to compare type I error rate and test power of Fisher?s factorial ANOVA-F test to the some alternatives namely Welch-James (WJ) test, permutation tests (FP), analysis of variance based on logarithmic transformation (FL) and rank transformation (FR) tests by Monte Carlo simulation technique under normality and variance homogeneity of variances assumptions were not satisfied. As a result of the simulation trials, it was seen that generally all tests displayed similar results in the terms of type I error rate and test power as long as the variances are homogeneous. In these experimental conditions, type I error rates which occur in terms of F, FL, FR, FP tests were not affected from the shape of the distrubution regardless of the sample size when the variances are homogeneous. However, type I error rates which occur in terms of WJ test were affected from the shape of the distrubution especially when n<5. Considering all experimental conditions together, unless the shape of distrubition was extrem tailed (chi square and exponential) and the number of observations in subgroups was very small (n=3), it was seen that WJ test gives the most reliable results in terms of keeping the agreed type I error rate on the same level. As a result of the simulation trials, it was seen that value of test power of all tests and mainly value of test power of FR test were pretty influenced by the lack of homogeneity of variances in a negative way. This negative impact became to be more crystallized in cases when the distrubitions of the population worked on were heavy taied (chi square and exponantial) and the number of observations in subgroups was very small (n=3). In general, however, it was seen that according to the other tests F and FP tests were more powerful. Considering all the tests together, it was concluded that under many experimentation conditions WJ test can be chosen according to the other tests.