Rejecton of a single outiier in two- or three-way layouts

Accurate bounds are presented for the fractiles of the maximum normed residual (which is often used to test for a single outlier) for two- and three-way layouts. It is shown that the second Bonferroni bound of the critical value, while not conservative, is an excellent approximation to the critical value, being much more accurate than the first Bonferroni upper bound. The third Bonferroni (upper) bound, which, although conservative, is expensive to calculate, agrees with the second bound to at least four decimal places for all factor combinations considered in this paper.