Ensuring that results hold more generally
Even for experiments in which it is possible to use very similar experimental units, it is not always desireable to do so. If all experimental units are identical, it is difficult to generalise the results to other kinds of experimental units.
Using a variety of different experimental units (but grouped into blocks) allows results to be generalised more easily — we can be more confident that the results will hold for a variety of different types of experimental unit.
Blocks for accuracy and generality
In a completely randomised experiment, intentional variation in the experimental units would result in less accurate estimates for the factors of interest. However grouping these experimental units into blocks can result in estimates that have similar accuracy to those that would arise from homogeneous experimental units.
On-station and on-farm experiments
Crop trials are often initially conducted at research stations where the different varieties can be grown under well controlled conditions. However the results that are (accurately) determined from an experiment in a single research station may not hold in the same way on real farms in which there are a multitude of different farm types and farmer practices. For example, the most productive variety of maize in the research station may not perform well in particular soils or with particular cultivation practices that are used by some farmers.
Before recommendations are made about the best varieties, on-farm experiments are often conducted involving this extra variation. In these experiments, a few plots of land or animals are used in each of several farms. The experimental units in each farm would be considered to be a separate block.
Penicillin production
In the example below, a process for manufacture of penicillin was being investigated. Four variants of the basic process (A, B, C and D) were being studied and the response measurement was the yield of penicillin.
An important raw material for the process was corn steep liquor, and this was quite variable. Instead of conducting the experiment with only one blend of corn steep liquor, it was therefore decided to use five different blends (blocks) in order to ensure that the results were not specific to one particular blend. Four different runs of the experiment were used with each blend, with the four process variants randomly allocated to the runs. The resulting yields are shown in the diagram below.
Process variant | ||||
---|---|---|---|---|
Corn blend | A | B | C | D |
1 | 89 | 88 | 97 | 94 |
2 | 84 | 77 | 92 | 79 |
3 | 81 | 87 | 87 | 85 |
4 | 87 | 92 | 89 | 84 |
5 | 79 | 81 | 80 | 88 |