Construct an Augmented Randomised Complete Block Design Layout

Generates an augmented block design layout (Federer, 1956; Federer, 1961) in which test treatments are divided into blocks of a specified size. A set of check treatments can be randomly positioned among the test treatments, while another set of check treatments can be placed at fixed positions at the end of each block.

Usage

construct.augmentedRCBD(
  block.size,
  test.treatments,
  check.treatments,
  randomize.test = FALSE,
  random.checks = check.treatments,
  fixed.checks = NULL
)

Arguments

block.size

Integer specifying the number of test treatments assigned to each block. Check treatments are added in addition to this number.

test.treatments

A vector containing the test treatment identifiers.

check.treatments

A vector containing all available check treatment identifiers.

randomize.test

Logical indicating whether the test treatments should be randomized before being divided into blocks. Defaults to FALSE.

random.checks

A vector containing the check treatments to be randomly positioned within each block. Defaults to all check.treatments.

fixed.checks

A vector containing check treatments to be placed at the end of each block. Defaults to NULL.

Value

A data frame with three columns:

Block

The block number.

Plot

The plot position within the block.

Treatment

The treatment assigned to the plot.

Details

By default, test treatments retain their supplied order. When randomize.test = TRUE, the test treatments are randomized before being divided into blocks. The relative order of test treatments within each block is otherwise preserved; only the positions of the random.checks are randomized.

The number of blocks is determined by dividing the number of test treatments by block.size and rounding up. The final block may therefore contain fewer test treatments than the specified block.size.

Within each block, the test treatments occupy all positions not assigned to random.checks. The order of the test treatments is preserved. The positions of the random checks are selected randomly from the combined set of test-treatment and random-check positions. The fixed.checks, when supplied, are appended to the end of the block in their supplied order.

The elements of random.checks and fixed.checks must be distinct, and all must be present in check.treatments.

References

Federer WT (1956). “Augmented (or Hoonuiaku) designs.” The Hawaiian Planters' Record, LV(2), 191–208.

Federer WT (1956). “Augmented (or Hoonuiaku) Designs.” Technical Report BU-74-M, Cornell University, New York.

Federer WT (1961). “Augmented designs with one-way elimination of heterogeneity.” Biometrics, 17(3), 447–473.

Examples

checks <- paste0("C", 1:6)
tests <- paste0("T", sprintf("%03d", 1:100))

design <-
  construct.augmentedRCBD(block.size = 20,
                          test.treatments = tests,
                          check.treatments = checks,
                          random.checks = checks[1:4],
                          fixed.checks = checks[5:6])

head(design)
#>   Block Plot Treatment
#> 1     1    1      T001
#> 2     1    2      T002
#> 3     1    3      T003
#> 4     1    4      T004
#> 5     1    5        C4
#> 6     1    6      T005