A critical review and a comparative study on conditional permutation tests for two-way ANOVA

Two-way ANOVA methodology is surely one of the most important models in the framework of the experimental design theory, as suggested by the great number of proposed solutions given in literature. Among these, some solutions are nonparametric and particularly, thanks to the availability of modern powerful computing equipments, those based on conditional on observations permutation test have gained great interest. The aim of this work is to present and compare such proposals and to illustrate their possible advantages and disadvantages when applied to some real data-sets.