Information about treatment effects
In a randomised block experiment, there are two potential sources of information about differences between the treatments.
These two sources of information are independent. The relative amounts of information of the two types depend on the design of the experiment.
Orthogonal randomised blocks
In Chapter 4, we described randomised block designs in which the treatments were used in the same proportions within each block. In these designs, the treatments were orthogonal to the blocks.
Nested experiments
The first section of this chapter described experiments in which the treatments are varied at block level. In such experiment,
Other designs
In many experiments, the treatments are neither orthogonal to the blocks nor varied at block level. This may occur by design (e.g. lattice designs) or accident (e.g. missing values).
In these designs, some information about the treatments is available both from differences within blocks and from the block means.
A continuum of designs
The diagram below shows possible allocation of 5 treatments (A, B, C, D and E) to 50 experimental units in 10 blocks.
The diagram initially shows treatments allocated in a randomised block experiment with all treatments used once per block. The average responses in the 10 blocks are all averaged over all 5 treatments, so the block averages can hold no information about treatment differences.
Drag the slider to the right to change the design to a nested design in which the treatments are allocated at block level. Since all units in a block get the same treatment, differences between units in a block hold no information about treatment differences.
At intermediate slider positions,