Known differences between the experimental units
When nothing is known about the differences between the experimental units before the experiment is conducted, we can do no better than to randomise allocation of treatments to the units.
This design can be improved when more is known about the differences between the experimental units.
Randomised block designs
Ideally all experimental units are virtually identical (minimum random variation) but in practice they are often highly variable. A better design groups similar experimental units into blocks.
In a randomised block design, a separate experiment is conducted within each block with treatments randomly allocated to its experimental units. Although all data are analysed together, the lower random variation within each block means that differences between the treatments can be more accurately estimated.
Simple block design
Although it is not essential,
If possible, researchers usually try to define blocks that have the same size and use each treatment the same number of times within each block.
With equal replicates for all treatments in every block, each treatment mean uses the same number of values in each block, so comparisons between treatment means are not affected by differences between the blocks.
Block 1 | Block 2 | Block 3 | Block 4 | Mean | |||||
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Treatment A |
|
|
|
|
2.608 | ||||
Treatment B |
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|
|
|
2.116 |
In the example above, the experimental units were grouped into blocks of six, with each treatment randomly allocated to three within each block. Even though the response values are much higher in Block 1, this affects both treatment means equally, so the difference between them is unaffected.
Comparison of completely randomised and randomised block designs
Grouping experimental units into blocks of similar units and using a randomised block design gives more accurate estimates of the treatment effects than a completely randomised design that ignores the blocks.