The LATTICE procedure computes the analysis of variance and analysis of simple covariance for data from an experiment with a lattice design. PROC LATTICE analyzes balanced square lattices, partially balanced square lattices, and some rectangular lattices.

In balanced square lattices, the number of treatments is equal to the square of the number of units per block. Incomplete blocks are grouped to form mutually orthogonal replications. The number of replicates in the basic plan is always 1 plus the number of units per block.

Partially balanced square lattices are similar to balanced lattices, although the number of replicates can vary. Partially balanced designs are constructed of the replicates in the basic plan, but not all replicates are included the same number of times, and some might not be included at all.

In rectangular lattices, there are *k* units per block and *k* (*k* +1) treatments. As in square lattices, blocks are grouped to form mutually orthogonal replicates in the basic plan. PROC LATTICE can analyze simple rectangular lattices (two orthogonal replications) and triple rectangular lattices (three orthogonal replications). The experiment can include several repetitions of the basic plan.

The LATTICE procedure determines from the data set which type of design has been used. It also checks to see whether the design is valid and displays an appropriate message if it is not.