Design principle
The varying characteristics of the experimental units only result in misleading estimates for the factors of interest if they are associated with the allocation of treatments to the experimental units (e.g. if variety A is used on wet plots). To avoid this, ...
An important goal of experimental design is to minimise association between allocation of the treatments and characteristics of the experimental units.
The method depends on whether these varying characteristics of the experimental units are understood and measured before the experiment is conducted.
Randomisation
When the differing characteristics of the experimental units are unmeasured, the best way to avoid association between them and the treatments is to randomly allocate treatments to the experimental units. This is called randomisation of the treatments and the experimental design is called a completely randomised design.
Randomisation does not guarantee that there will be no association between the treatments and characteristics of the experimental units — by chance, there may be some association. However...
Randomisation means that is unlikely that such lurking variables will affect the conclusions.
There is no better way to allocate treatments if the varying characteristics of the experimental units are unmeasured before the experiment is conducted.
Effect of a feed supplement on weight gain of calves
Earlier in this section we described an experiment in which a feed supplement was given to the first nine calves from a group of 18 that entered a barn. This resulted in older and heavier calves getting the supplement, so the effect of the supplement was over-estimated.
Randomising the allocation of the supplement to 9 of the 18 calves reduces the chance of any association between the treatment and the age and weight of the calves. The simulation below increases the weight gain of calves getting the supplement by exactly 5.0.
Click Allocate treatments to randomly pick calves to get the supplement then click Run experiment to find their weight gains and estimate the effect of the supplement.
Repeat a few times and observe that the effect of the supplement is usually estimated to be between 2 and 8. The results are therefore consistent with the true effect that was built into the simulation, 5.0.
With randomisation, there is no tendency to over- or under-estimate the effect of the feed supplement.
Mechanics of randomisation
There are several different ways to randomise allocation of treatments to the experimental units. These all use random numbers either from printed tables or, preferably, generated by a computer. The simplest method is to use a spreadsheet such as Microsoft Excel.
If there are n available experimental units,
This creates a random permutation of the numbers 1 to n. If there are two treatments, allocate the first to the experimental units in the top half of the list.
The table below illustrates this method.
The first column shows twelve random numbers, each between 0 and 1, and the list of unit numbers. Click Sort random numbers to sort the rows of the table into ascending order of the random numbers. This randomly permutes the unit numbers.