ABSTRACT
You may recall that one of the assumptions in analysis of variance is normality; that is, the scores for the subjects in each group are normally distributed. Why should we be interested in studying assumptions in ANOVA and MANOVA? Because, in ANOVA and MANOVA, we set up a mathematical model based on these assumptions, and all mathematical models are approximations to reality. Therefore, violations of the assumptions are inevitable. The salient question becomes: How radically must a given assumption be violated before it has a serious effect on type I and type II error rates? Thus, we may set our α = .05 and think we are rejecting falsely 5% of the time, but if a given assumption is violated, we may be rejecting falsely 10%, or if another assumption is violated, we may be rejecting falsely 40% of the time. For these kinds of situations, we would certainly want to be able to detect such violations and take some corrective action, but all violations of assumptions are not serious, and hence it is crucial to know which assumptions to be particularly concerned about, and under what conditions.
