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Exercises

Copy each block into your R session. Solutions are folded under Solution. Try the exercise first.

library(speed)

Every design is an answer to the same four questions (from the slides):

Question Argument
What moves? swap, linked_cols*
Where is it allowed to move to? swap_within
What should it be balanced across? spatial_factors
What counts as a ‘neighbour’? grid_factors

*: optional

Exercise 1: a spatially balanced block design with two-dimensional blocks (about 10 minutes)

Eight varieties, four replicates, in a 4 × 8 field. Instead of whole rows, each block is a 2 × 4 patch of plots.

  1. Set up the layout with initialise_design_df(). Look at the block column.
  2. Optimise it so that treatments only move within their block.
  3. Plot it, then check with table() that every block contains every variety once.

Before you run it, write down your answers to the four questions.

Solution 
sbbd <- initialise_design_df(
  items = paste0("V", 1:8), nrows = 4, ncols = 8,
  block_nrows = 2, block_ncols = 4
)
sbbd_opt <- speed(sbbd, swap = "treatment", swap_within = "block", seed = 1)
autoplot(sbbd_opt)
table(sbbd_opt$design_df$block, sbbd_opt$design_df$treatment)

If you finish early, compare how often a variety repeats in the same row or column (table(row, treatment)) with and without spatial_factors = ~ block + row + col.

Exercise 2: a split-plot (about 10 minutes)

Four tillage methods (whole plots, A to D) and three varieties (subplots, a to c), in three blocks. Each whole plot is a 1 × 3 strip of three subplots, and each block holds four whole plots in a 4 × 3 patch.

  1. Describe the structure with a splits list and build it with initialise_split_design_df(). The blocks are stacked on top of each other (rep_dim).
  2. Write the optimise list: one entry per level, answering the four questions for each. Whole plots must move as a unit.
  3. Plot both levels, then check with table() that every block has every tillage method once, and every whole plot has every variety once.

Hint: the slides’ example has the same shape. Which numbers change?

Solution 
splits <- list(
  subplot   = list(items = letters[1:3], nrows = 1, ncols = 1),
  wholeplot = list(items = LETTERS[1:4], nrows = 1, ncols = 3),
  block     = list(nrows = 4, ncols = 3)
)
sp <- initialise_split_design_df(splits = splits, rep_dim = c(3, 1))

optimise <- list(
  wp = list(
    swap        = "wholeplot_treatment",
    swap_within = "block",
    swap_all    = TRUE
  ),
  sp = list(
    swap        = "subplot_treatment",
    swap_within = "wholeplot"
  )
)
sp_opt <- speed(sp, optimise = optimise, seed = 1)

autoplot(sp_opt, treatments = "wholeplot_treatment")
autoplot(sp_opt, treatments = "subplot_treatment", block = "wholeplot")

table(sp_opt$design_df$block, sp_opt$design_df$wholeplot_treatment)
table(sp_opt$design_df$wholeplot, sp_opt$design_df$subplot_treatment)

If you finish early, add a column giving each variety a name (for example "Scepter", "Vixen", "Calibre") and use linked_cols so the names stay with their codes. See the linked_cols section of the main vignette.