A permutation test for effects in an unreplicated factorial design

A permutation test is proposed for examining the significance of effects in unreplicated factorial experiments. The procedure tests each effect with a separate sampling distribution using a test statistic that is equivalent to the optimal invariant decision rule of Birnbaum. The proposed test is more flexible than other methods proposed for the same situation because it requires no a priori assumptions regarding the underlying distribution of the data nor does it impose any practical restriction on the number of potentially significant effects present.