The Mesh Adaptive Direct Search algorithm (MADS) algorithm is designed for nonsmooth blackbox optimization problems in which the evaluation of the functions defining the problems are expensive to compute. The MADS algorithm is not designed for problems with a large number of variables. The present paper uses a statistical tool based on variance decomposition to rank the relative importance of the variables. This statistical method is then coupled to the MADS algorithm so that the optimization is performed either in the entire space of variables or in subspaces associated to statistically important variables. The resulting algorithm is called STATS-MADS and is tested on bound constrained test problems having up to 500 variables. The numerical results show an important improvement in the objective function value after a fixed budget of function evaluations.