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.

Surface treatment and abrasion

This example was presented earlier in this section. For illustration, we will combine the two replicates and treat the cell means as a single replicate. (This has only been done to halve the number of crosses in the diagram.)

  No surface treatment   Surface treatment
Percentage
Filler
Filler A Filler B   Filler A Filler B
25% 544 416.5   470.5 310.5
50% 642.5 451   550.5 268
75% 733.5 443   654 313

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

Initially the diagram shows only the mean response. Use the checkboxes to fit models with different combinations of factors. Observe that using all three factors allows the mean responses to be close (but not identical) to the corresponding observed responses.

Note how the diagram displays the two levels of Surface treatment with a green and a purple grid when its main effect is in the model.