Blocks next

Revisit the rooms

Seed 123 was balanced overall, but not within rooms.

Why room might matter

Rooms may differ in:

• temperature or ventilation
• routine or staff access
• light, noise or disturbance
• equipment and measurement conditions

If those differences may affect the response, room is a plausible source of nuisance variation.

Restrict the draw

Instead of shuffling all 24 labels together:

• place eight pens in each room group
• provide two labels for each diet in each room
• shuffle those eight labels within that room
• repeat independently for all rooms

The restriction fixes within-room replication; chance still fixes pen positions.

The R structure

library("tibble")
library("dplyr")

pens <- tibble(
  pen_id = sprintf("P%02d", 1:24),
  room = rep(c("North", "Central", "South"), each = 8),
  position = rep(1:8, times = 3)
)

set.seed(123)
allocation_blocked <- pens |>
  group_by(room) |>
  mutate(diet = sample(rep(
    c("Control", "Diet A", "Diet B", "Diet C"), each = 2
  ))) |>
  ungroup()

Name the design

Block: a group of experimental units expected to be relatively similar.

Randomised complete block design:

• room is the block
• pen remains the experimental unit
• every block contains all four diet treatments
• treatments are randomised among pens within each block

Not a fixed pattern

Both arrangements could place two labels per diet in each room:

• randomly shuffle the eight labels within the room
• repeat Control, A, B, C, Control, A, B, C

Only the first is randomised. The second may align treatment with a position pattern and is predictable.

A trade-off

Blocking is helpful when blocks capture important variation.

It also:

• adds structure to allocation and analysis
• needs enough units for treatment replication within blocks
• can be inefficient if blocks are not informative
• must be planned before looking at outcomes

Next class

In the Lego activity, you will:

• build blocked designs physically
• distinguish blocks from treatment factors
• construct factorial treatment combinations
• inspect what can be estimated from each design

For now, remember: restrict for a stated design reason, then randomise within the restriction.

Sources

Ruxton, Graeme D., and Nick Colegrave. 2016. Experimental Design for the Life Sciences. 4th ed. Oxford: Oxford University Press. Chapter 7, sections 7.1–7.4, pp. 101–108. ISBN 978-0-19-871735-5. Publisher page.

R Core Team. 2026. R: A Language and Environment for Statistical Computing. Vienna: R Foundation for Statistical Computing. R project.

Wickham, Hadley, et al. 2019. “Welcome to the tidyverse.” Journal of Open Source Software 4 (43): 1686. doi:10.21105/joss.01686.