Recently, the class of experimental designs that are analyzable by permutation means (thus yielding exact p-values) was extended to the two-factor casethrough the use of synchronized permutations (Salmaso, 2003 and Pesarin 2001). The new tests achieve exact p-values through weak exchangeability(Good, 2002). By recognizing that synchronized permutations can be identified with similarities, these results can be extended to k-factor designs, balancedor not, complete or not.[full paper at: http://users.oco.net/drphilgood/synch02a.htm ]