Rectangular Lattices Revisited

Summary

The intrablock analysis of rectangular lattices can be clarified by knowledge of the canonical structure of block and treatment subspaces. In this case there are natural canonical subspaces in block space having factorial structure, in contrast to the situation e.g. of balanced incomplete block designs, lattice desings and group divisible or Latin square type PBIB designs, where canonical factorial subspaces arise in treatment space. This factorial structure for the dual of a rectangular lattice and the associated canonical efficiency factors lead to a simple explicit general expression for the treatment estimator and the efficiency factor at each type of treatment comparison. Recovery of interblock information requires only slight modifications.