Introduction to Equal Variance Assumption

Still, it is good practice to check for radical departures from the equal variance assumption. In order to do so you must remember one thing – it is the variances of the residuals that are assumed to be equal, not the variances of the Y values. This means that you would need to organize the residuals into groups based upon the values of the factors, one group for each term in the model, and then get an estimate of the variance from each group. For a one-way ANOVA this is not too hard to do. For a two-way ANOVA, it is still not difficult. But, for more than two factors, this becomes increasingly difficult to do. An alternative would be to examine the residuals for extreme outliers, or plot the residuals against each factor as well against the fits. These plots will at least show whether any of the factors have main effects on the variability of the residuals, as well as determining whether the residual variance is correlated with the response.

Also, bear in mind that the p-values in the ANOVA table may be slightly underestimated, and that the cutoff line in the Pareto chart is slightly higher than it should be. In other words, some effects that are observed to be marginally statistically significant could actually be marginally insignificant. In any case where an effect is marginally significant, or marginally insignificant, from a statistical point of view, one should always ask whether it is of practical significance before passing final judgement.