Importance of randomisation

The most important aspect of a paired experimental design is that:

The two factor levels should be allocated at random to the two experimental units in each pair.

If the factor levels are allocated in a subjective way within each pair, it is possible for the treatment allocation to be associated with some lurking variable that will bias the results.

Illustration of pairing

Consider an experiment that is conducted to assess whether a new exercise programme for broken legs aids recovery over the standard method. A group of 20 children with broken legs is used (the experimental units) and the response measurement will be the strength of the leg muscles three weeks after the break.

In a completely randomised experiment, 10 children are randomly picked from the 20 for the new exercise programme. Click Randomise to show this.

In a paired experiment, the 20 children might be grouped into pairs of the same gender who had similar weight and muscular strength at the start of the experiment. Select Paired from the pop-up menu. One child from each pair will be randomly selected for the new exercise programme. Click Randomise to see this randomisation.