= Missing cells can destroy factor orthogonality in two-way ANOVA
{title2=$C^{\mathsf T}(I-P_{\mathbf1})J\ne0$}
In a fully balanced crossed design, centered indicator columns for the two factors are orthogonal because each pair of levels occurs equally often. Missing cells can change the level-pair counts so that the displayed cross-product becomes nonzero. Then <sequential sums of squares> depend on term order, although the final additive fit is unchanged. Testing either factor conditional on the other requires its <extra sum of squares> from the appropriate reduced model.
Back to article page
