Nested and Crossed Block Designs for Factorial and Unstructured Treatment Sets
Efficiency bounds
Block designs for unstructured treatment sets
Blocks design package
General block and treatment designs.
Optimum treatment set from a candidate set of treatments
Graeco-Latin squares
Finds hcf of any set of positive integers
Prime number test
Finds a prime power solution for N, if available.
Prime power MOLS from finite fields
nestedBlocks
Rectangular lattice designs
Square lattice designs
Constructs treatment and block designs for linear treatment models with crossed or nested block factors. The treatment design can be any feasible linear model and the block design can be any feasible combination of crossed or nested block factors. The block design is a sum of one or more block factors and the block design is optimized sequentially with the levels of each successive block factor optimized conditional on all previously optimized block factors. D-optimality is used throughout except for square or rectangular lattice block designs which are constructed algebraically using mutually orthogonal Latin squares. Crossed block designs with interaction effects are optimized using a weighting scheme which allows for differential weighting of first and second-order block effects. Outputs include a table showing the allocation of treatments to blocks and tables showing the achieved D-efficiency factors for each block and treatment design. Edmondson, R.N. Multi-level Block Designs for Comparative Experiments. JABES 25, 500–522 (2020) <doi:10.1007/s13253-020-00416-0>.