Variability in a completely randomised design
In a completely randomised design, it is possible that one treatment may, by chance, be over-represented in a block whose response, Y, is naturally high, inflating its apparent effect. For example, treatment A would appear to have too high a response mean in the example below.
Block 1 (high Y) |
Block 2 (low Y) |
|||||
---|---|---|---|---|---|---|
C | A | A | B | B | A | |
A | C | B | C | C | B | |
B | C | A | B | A | C |
Of course, treatment A could also be under-represented in the first block, resulting in high variability in its estimated effect.
A randomised block design would ensure that treatment A is used for exactly 3 units in each block, so the high response values in Block 1 could not distort its effect relative to the other treatments. Therefore its estimated effect would be less variable (and hence more accurately estimated).