ANOVA methods for the group means with unknown variances

Analysis of variance (ANOVA) is one of the most powerful tools while investigating the sources of variability in many disciplines like medicine, engineering, agriculture, education, psychology, sociology and biology. In ANOVA, variance of the distributions in which the samples are drawn should be homogeneous to validate the underlying probability distribution of the method and to confine the errors within the desired limits. Violation of this equality of variances assumption is called as heteroscedasticity in literature. In this study, after describing a general appearance of one-way ANOVA and effects of it?s inevitable assumptions, the results of heteroscedasticity in one-way fixed effects ANOVA have been examined with a close concern on large sample approximations of treatment and error mean sum of squares and distortion of the distribution of the F ratio. Then, two new and simple approximation procedures which intend to create an easy and applicable alternative under heteroscedasticity and nonnormality have been presented. The purpose of these new approximation procedures is to preserve the actual Type I error rate at a level determined by the researcher and to increase the power as well. Performance of these two new approximation procedures under different experimental patterns have been observed with two separate simulation studies and finally, some recommendations about the preference of these tests and further research topic were given.