blocks {blocksdesign}

Block designs for unstructured treatment sets

Description

Constructs randomized multi-level nested block designs for unstructured treatment sets.

Usage

blocks(
  treatments,
  replicates,
  blocks = NULL,
  searches = NULL,
  seed = NULL,
  jumps = 1
)

Arguments

treatments

the total required number of treatments partitioned into equally replicated treatment sets.

replicates

the replication numbers of the equally replicated treatment sets.

blocks

the number of nested blocks in each level of nesting from the top level down.

searches

the maximum number of local optima searched for a design optimization.

seed

an integer initializing the random number generator.

jumps

the number of pairwise random treatment swaps used to escape a local maxima.

Details

Constructs randomized multi-level nested block designs for any arbitrary number of unstructured treatments and any arbitrary feasible depth of nesting.

treatments is a partition of the number of treatments into equi-replicate treatment sets.

replicates is a set of replication numbers for the equi-replicate treatment sets.

blocks are the nested blocks levels in decreasing order of block size where each level defines the number of blocks nested within the blocks of the preceding level. The top-level block is assumed to be single super-block containing a full set of plots. The algorithm finds block sizes automatically for each level of nesting and the block sizes within each level of nesting will never differ by more than a single plot.

Unreplicated treatments are allowed and any simple nested block design can be augmented by any number of unreplicated treatments using the treatments and replicates formula. However, it may be preferable to find an efficient blocked design for the replicated treatment sets and then to add the unreplicated treatments heuristically.

The blocks function constructs all block designs algorithmically except for certain special block designs for r replicates of v x v treatments or r-1 replicates of v x (v-1) treatments in blocks of size v. Provided that a set of r-1 mutually orthogonal Latin squares of size v x v exists, these designs are constructed algebraically and are guaranteed to achieve optimality. See squarelattice and rectlattice for information about which design sizes are constructed algebraically.

Value

Replication

A table showing the replication number of each treatment in the design.

Design

Data frame giving the optimized block and treatment design in plot order.

Plan

Data frame showing a plan view of the treatment design in the bottom level of the design.

Blocks_model

The D-efficiencies and the A-efficiencies of the blocks in each nested level of the design together with A-efficiency upper-bounds, where available.

seed

Numerical seed used for random number generator.

searches

Maximum number of searches used for each level.

jumps

Number of random treatment swaps used to escape a local maxima.

References

Cochran, W.G., and G.M. Cox. 1957. Experimental Designs, 2nd ed., Wiley, New York.

Examples

## The number of searches in the following examples have been limited for fast execution.  
## In practice, the number of searches may need to be increased for optimum results.
## Designs should be rebuilt several times to check that a near-optimum design has been found.  

# Completely randomized design for 6 treatments with 2 replicates and 1 control with 4 replicates 
blocks(treatments=list(6,1),replicates=list(2,4))

# 12 treatments x 4 replicates in 4 complete blocks with 4 sub-blocks of size 3
# rectangular lattice see Plan 10.10 Cochran and Cox 1957.
blocks(treatments=12,replicates=4,blocks=list(4,4))

# 3 treatments x 2 replicates + 2 treatments x 4 replicates in two complete randomized blocks
blocks(treatments=list(3,2),replicates=list(2,4),blocks=2)

# 50 treatments x 4 replicates with 4 main blocks and 5 nested sub-blocks in each main block
blocks(treatments=50,replicates=4,blocks=list(4,5))

# as above but with 20 additional single replicate treatments, one single treatment per sub-block
blocks(treatments=list(50,20),replicates=list(4,1),blocks=list(4,5))

# 6 replicates of 6 treatments in 4 blocks of size 9 (non-binary block design)
blocks(treatments=6,replicates=6,blocks=4)

# 128 treatments x 2 replicates with two main blocks and 3 levels of nesting
 blocks(128,2,list(2,2,2,2))

# 64 treatments x 4 replicates with 4 main blocks, 8 nested sub-blocks of size 8
# (lattice), 16 nested sub-sub blocks of size 4 and 32 nested sub-sub-sub blocks of size 2
 blocks(64,4,list(4,8,2,2))

# 100 treatments x 4 replicates with 4 main blocks nested blocks of size 10 (lattice square)
blocks(100,4,list(4,10))