Nonparametric Testing of Saturated D-Optimal Designs

We introduced a new permutation test as a modification of the well-known Loughin and Noble test by also taking into account an innovative permutation mechanism based on non-isomorphic designs which can be often available for a given model and a given number of runs by means of the algorithm proposed by Fontana [6]. As it is pointed out in [2] it is quite difficult to construct powerful permutation tests for unreplicated factorial designs. In particular the original Loughin and Noble test loses power when the number of active effects and/or the error distribution is heavy tailed. Our modified procedures seem to have a general better behaviour in terms of power especially in presence of heavy tailed error distributions.