Randomized Complete Block Designs
Last updated on 2024-05-14 | Edit this page
Overview
Questions
- What is randomized complete block design?
Objectives
- A randomized complete block design randomizes treatments to experimental units within the block.
- Blocking increases the precision of treatment comparisons.
Design issues
Imagine that you want to evaluate the effect of different doses of a new drug on the proliferation of cancer cell lines in vitro. You use four different cancer cell lines because you would like the results to generalize to many types of cell lines. Divide each of the cell lines into four treatment groups, each with the same number of cells. Each treatment group receives a different dose of the drug for five consecutive days.
Group 1: Control (no drug)
Group 2: Low dose (10 μM) Group 3: Medium dose (50 μM) Group 4: High
dose (100 μM)
R
# create treatment levels
f <- factor(c("control", "low", "medium", "high"))
# create random orderings of the treatment levels
block1 <- sample(f, 4)
block2 <- sample(f, 4)
block3 <- sample(f, 4)
block4 <- sample(f, 4)
treatment <- c(block1, block2, block3, block4)
block <- factor(rep(c("cellLine1", "cellLine2", "cellLine3", "cellLine4"), each = 4))
dishnum <- rep(1:4, 4)
plan <- data.frame(cellLine = block, DishNumber = dishnum, treatment = treatment)
plan
OUTPUT
cellLine DishNumber treatment
1 cellLine1 1 control
2 cellLine1 2 high
3 cellLine1 3 low
4 cellLine1 4 medium
5 cellLine2 1 high
6 cellLine2 2 medium
7 cellLine2 3 low
8 cellLine2 4 control
9 cellLine3 1 low
10 cellLine3 2 control
11 cellLine3 3 medium
12 cellLine3 4 high
13 cellLine4 1 low
14 cellLine4 2 control
15 cellLine4 3 high
16 cellLine4 4 mediumWhen analyzing a random complete block design, the effect of the block is included in the equation along with the effect of the treatment.