Examples

Many experiments involve experimental units that are variable but can be grouped into blocks that are relatively similar. Randomised block designs are therefore very common.

The following data sets arise from randomised block experiments. In the first example, there are two replicates for all treatments within each block; in the other two, there is only a single replicate.

Effect of cultivar on plant height

An experiment was conducted to compare the differences in growth among four different cultivars of a house plant. The greenhouse had three benches in different locations which form natural blocks. Two pots of each cultivar were randomly assigned to each bench for a total of six pots per cultivar and eight pots per bench.

In this experiment, the benches are blocks and there are two replicates — each treatment (cultivar) was used twice on each bench.

  Cultivar
       Bench           A       B       C       D   
1
19.3
17.2
20.1
19.4
17.4
16.6
16.6
15.7
2
16.7
15.5
21.2
20.8
14.4
13.6
13.5
12.9
3
17.7
19.8
21.0
21.9
15.8
17.4
12.8
14.7

It is important to note that:

The layout of experimental data presented in the table is different from the physical layout of the experiment.

The cultivars on each bench were grouped in the table to make the data easier to read — the physical layout might have been as follows:

       Bench                   
1 B
19.4
D
16.6
D
15.7
C
17.4
A
17.2
B
20.1
C
16.6
A
19.3
2 A
15.5
C
14.4
B
20.8
A
16.7
B
21.2
D
12.9
C
13.6
D
13.5
3 C
17.4
D
12.8
A
17.7
B
21.9
C
15.8
D
14.7
A
19.8
B
20.0

Acupuncture and Codeine for dental pain relief

An anaesthetist conducted an experiment to assess the effects of codeine and acupuncture for relieving dental pain. The experiment used 32 subjects who were grouped into blocks of 4 according to an initial assessment of their tolerance to pain.

The four treatments used in the experiment were the four combinations of (codeine or a sugar capsule) and (active or inactive acupuncture points) and these were randomly applied to the four subjects in each block. Pain relief scores were recorded from each subject two hours after dental treatment. The experiment was double blind since neither the subjects nor the person assessing pain relief knew which treatment had been administered.

  Pain relief score
Tolerance
group
  Control   Codeine
only
Acupuncture
only
Codeine +
Acupuncture
1
2
3
4
5
6
7
8
0.0
0.3
0.4
0.4
0.6
0.9
1.0
1.2
0.6
0.7
0.8
0.9
1.5
1.6
1.7
1.6
0.5
0.6
0.8
0.7
1.0
1.4
1.8
1.7
1.2
1.3
1.6
1.5
1.9
2.3
2.1
2.4

In the above experiment the tolerance groups are matched blocks of subjects.

Clotting time of plasma

The table below gives the clotting times (mins) of plasma that was taken from eight subjects. Four samples of plasma were obtained from each subject and they were treated in four different ways before the clotting time was measured.

  Clotting time (min)
Subject   Treatment  
1
  Treatment  
2
  Treatment  
3
  Treatment  
4
1
2
3
4
5
6
7
8
8.4
12.8
9.6
9.8
8.4
8.6
8.9
7.9
9.4
15.2
9.1
8.8
8.2
9.9
9.0
8.1
9.8
12.9
11.2
9.9
8.5
9.8
9.2
8.2
12.2
14.4
9.8
12.0
8.5
10.9
10.4
10.0

In this experiment, the four plasma samples from one subject form a block.