In other situations, the experimental units naturally separate into groups. For example,
If the number of experimental units in each block is a multiple of the number of factor levels in the experiment, it is possible to randomly allocate each factor level the same number of times within each block. The resulting experiment is called a randomised block design.
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 treatment combinations of (codeine or a sugar capsule) and (active
or inactive acupuncture points) were randomly given 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 |
|
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. In the following examples, the blocks occur naturally.
Measuring sulphur in soils
Measurements were made on the amount of sulphur (in parts per million) in soil samples using four different solvents. The soil samples were collected from five different geographical locations in Florida, USA, and represented different soil types. The soil samples are the blocks in this experiment:
- Troup, Jackson Co. (Paleudults soil)
- Lakeland,Walton Co. (Quartzipsamments soil)
- Leon, Duval Co. (Haplaquads soil)
- Chipley, Jackson Co. (Quartzipsamments soil)
- Norfolk, Alachua Co. (Paleudults soil)
The solvents used to analyse the each of the five soils were:
- Calcium Chloride, CaCl2
- Ammonium Acetate, NH4OAc
- Mono-Calcium Phosphate, Ca(H2PO4)3
- Water, H2O
Each soil sample was split into four and the solvents were randomly allocated to them.
|
Soil sample |
Solvent |
Troup |
Lakeland |
Leon |
Chipley |
Norfolk |
CaCl2
NH4OAc
Ca(H2PO4)3
H2O |
|
|
|
|
|
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 |
|
|
|
|
2 |
|
|
|
|
3 |
|
|
|
|