EFFECT OF DEPARTURES FROM STANDARD ASSUMPTIONS USED IN ANALYSIS OF VARIANCE

Abstract

In this paper the effect of non-normality and non-homogeneity on the Analysis of Variance is investigated. Three non-normal distributions have been selected (Poisson, Exponential and Lognormal) for the assessment of such effect. The empirical distributions of MST, MSE and F are obtained when the samples are generated from these non-normal distributions and then these are compared with corresponding results obtained under the normal distribution assumption. The variances of the empirical distributions of MST, MSE and covariance of MST and MSE have been also computed under the assumption of these non-normal distributions and comparison was made with normal case of equal variances and independence. These results show that non- normality and non-homogeneity have very little effect on the Analysis of Variance and correlation between MST and MSE tends to zero with the increase in the sample size per group. However the Analysis of Variance test is conservative and one has to provide more protection for non-normal distribution of larger peakedness, like Lognormal for the small size per group.