Treatments and factors
The earlier sections of this chapter have concentrated on randomised block experiments in which a single factor is varied. However the same design concepts also hold when the treatments are combinations of levels for two or more factors. Whatever the treatment structure,
In a randomised block design, the treatments are randomly allocated to the experimental units separately within each block.
By grouping similar experimental units into blocks and using a randomised block design, the main effects of the factors and their interactions can be estimated more accurately.
Illustration of randomisation
The scenario below relates to an experiment about the effects of two factors A (with two levels A1 and A2) and B (with three levels B1, B2 and B3). There are therefore six possible treatments corresponding to the combinations of levels for the two factors.
The diagram initially ignores any blocking of the experimental units and clicking Allocate treatments randomly allocates eight of each of the treatments to the 48 experimental units in a completely randomised design.
Select Randomised block from the pop-up menu then click Allocate treatments again. The randomisation now ensures that each treatment is used in exactly four of the experimental units in each block.
Change the number of blocks to four and repeat the randomisation, noting that there are always exactly two experimental units getting each treatment in every block.