Blocks of similar experimental units

The previous section showed that the effect of a factor with two levels can be estimated more accurately if the experimental units are grouped into pairs and the two factor levels are randomly allocated within each pair. This design can be generalised to experiments in which there are more than two experimental units per block and more than two different treatments.

Consider an experiment in which the experimental units can be grouped into blocks of similar units.

A randomised block design is equivalent to a separate completely randomised design within each of the blocks.

To simplify the design, we initially restrict attention to situations where the block sizes are all equal and are multiples of the number of treatments. All treatments can therefore be used the same number of times within each block.

Random allocation of treatments to the experimental units within each block is essential.


Illustration of randomisation

The diagram below shows 48 experimental units on the right. The background shading shows possible grouping of the units into blocks.

The experimental design is initially a completely randomised one that ignores the blocks. Click Allocate treatments to randomly allocate the 48 treatments (12 of each type) to the units.

Select Randomised block from the pop-up menu. The 48 treatments are split into two groups (both containing 6 of each type). Click Allocate treatments to randomise the treatments separately within both blocks.

Now use the second pop-up menu to change the number of blocks and repeat. Observe that:

The randomisation always ensures that each treatment is applied to the same number of units within each block.

In practice, there is often flexibility in how the experimental units are grouped into blocks.

A large number of small blocks is best if this results in more homogeneous experimental units within each block.