Permutation Tests for Unreplicated Factorial Designs

In experimental design, wide use is made of screening comparative experiments to compare the effects of treatments on a given number of experimental units. In this type of experimentation, designing the experiment in such a way as to obtain all pertinent information in the related field of research is of fundamental importance, especially for costly or complicated experiments. Screening designs very often represent the first approach to experimental situations in which many explanatory factors are available and we are interested in establishing which ones are significant. In this field, the two-level factorial designs represent an instrument that is easy to use and interpret. When considering complete unreplicated designs, it is not possible to obtain an estimate of the variance of the errors, and therefore the usual inferential techniques, aimed at identifying the significantly active factors, are unsuitable. Various solutions to this problem have been proposed in the literature. Some, such as the normal plot (Daniel, 1959) normal plot, prove not to be very objective; others presuppose assumptions, such as normality of errors, even when little or nothing is known about the phenomenon being analyzed. (1998) propose a review of existing parametric and nonparametric tests conceived for unreplicated two-level factorial designs.