Rank-based procedures for analysis of factorial effects

Traditional analysis of variance procedures for analyzing factorial experiments assume that the error variables are a random sample from a normal distribution. When normality cannot be verified, a nonparametric analysis should be considered. This paper highlights some nonparametric procedures for the analysis of multi-factor experiments, and presents new procedures for testing for non-additivity in the two-way layout with one observation per cell. The new techniques address the asymmetry of the procedures presented by Hartlaub, Dean, and Wolfe (1999). Their approach was to align the observations within levels of one factor, rank within levels of the second factor, and use a test procedure based on the maximum of all crossed comparisons with these aligned ranks. The resulting test procedure is not invariant with respect to which factor is ranked and which is aligned. The new symmetric test procedures proposed are evaluated via an extensive Monte Carlo simulation study. The new procedures exhibit robustness with respect to maintenance of the nominal significance level over a broad class of continuous distributions and with respect to power against a wide variety of non-additive alternatives. Simulated critical values for most practical situations are provided for the recommended new procedures.