A composite Latin rectangle and nonstandard strip block design

Considered is an unusual split plot design. The whole plot part is a Latin rectangle design, while the split plot part derives from a nonstandard strip block design. For the strip block part, there are two treatment factors that are randomized to strips across the whole plot experimental units, not to strips within each whole plot experimental unit. The result is five split plot error terms, not three as in a standard strip block design. The mixed model analysis and optimal exact tests for all treatment effects are developed geometrically. The analysis is illustrated by example and concluding remarks on replicated designs are offered.