Using information about the experimental units
In a completely randomised experiment, variability in the experimental units lowers the accuracy of the estimated factor effects. Although it is occasionally possible to conduct an experiment with very similar experimental units, some variation in the experimental units is unavoidable in most experiments.
If we have information about differences between the experimental units before the start of the experiment, we can use this information to design an experiment that more accurately estimates the factor effects.
The main way to improve accuracy involves grouping the experimental units into blocks of similar units.
Randomised block design
An efficient way to conduct an experiment in which the experimental units are grouped into blocks is to separately conduct a completely randomised experiment within each block. The results from the different blocks are combined in the analysis of the data.
Since randomisation occurs separately within each block, this is called a randomised block design.
Blocks of size two — pairs
Analysis of randomised block experiments in their full generality is fairly difficult, so we will start with a special case whose analysis is much easier to understand. This section restricts attention to:
In a randomised block design, both treatments are used within each pair and randomisation involves randomly deciding which of the two units gets which of the two treatments.
Illustration of randomisation
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.
Select Randomised block (paired) from the pop-up menu to group the children into pairs with the same gender and similar weight and muscular strength at the start of the experiment.(in vertical columns). Click Randomise to randomly select one child from each pair to get the new exercise programme.
Twin studies
Much of the variability between animals and people is caused by differences in genetic makeup. Dizygotic (fraternal) twins have the same parents and are therefore genetically similar. However monozygotic (identical) twins have identical genes and there is even less variation between their characteristics. Many animal experiments are conducted with identical twins since the genetic similarity within each pair of twins allows the effect of treatments to be more accurately estimated.
Human studies have also been conducted with identical twins. The table below shows the IQs of ten pairs of twins who were raised apart, one in a 'good' environment and the other in a 'poor' one. It can be assumed that the twins were randomly placed in these two environments.
IQ | |||||
---|---|---|---|---|---|
Family | Poor environment | Good environment | |||
|
|
|
The genetic influence on IQ is evident — when one twin has high IQ, the other often does too. However we can also ask...
Do the twins raised in a 'good' environment have a different mean IQ from those raised in a 'poor' environment?