Non-Orthogonal Designs of Even Resolution

Designs of even resolution have the property that a set of parameters, although themselves not estimable, do not appear as aliases of those which are estimable. The most important are designs of resolution 4, which are such that the main effects are estimable with no two-factor interactions as aliases. In this paper it is shown that the smallest resolution 4 designs for n factors at two levels must contain at least 2n runs, and that “foldover” designs are available with 2n runs. It is conjectured that the only minimal resolution 4 designs are foldover designs. The case of resolution 6 designs is also discussed.