Simple model for three factors

The simplest model for data from a factorial experiment assumes that there is no interaction between the effects of any of the factors — each acts additively on the response. For an experiment with 3 factors, this implies that...

(mean response)   =   (base value)   +   (effect of factor A)   +   (effect of factor B )

+   (effect of factor C)

It must be stressed that the no-interaction assumption does not always hold. Indeed, one of the main attractions of factorial experiments is the ability to assess interactions between the factors.

Randomisation

As in all other experiments, it is important to remember that the treatments (factor combinations) should be randomly allocated to the experimental units — randomisation of the experiment.

Legume germination

This example was presented earlier in this section. A greenhouse experiment was conducted to determine the rate of emergence of seeds of three species of legumes, treated and not treated with a fungicide, and planted in three soil types. The response is the number of plants emerging out of 300 seeds.

The diagram below allows models with the different main effects to be fitted.

Note that the residuals for Alfalfa on Clay soils are large for the model with all main effects. (The residuals are the differences between actual numbers germinating and those predicted by the model, shown as red lines in the diagram.) This could be caused by...