Models with interaction
If it is concluded that there is interaction between the effects of the factors, we must graphically examine the data to ascertain the nature of this interaction. A 3-dimensional diagram such as that in the previous page can be used but it requires dynamic rotation to effectively describe the effect of the factors and it cannot be extended for experiments involving more than two factors.
It is therefore common to plot the mean responses for all combinations of the factor levels against a horizontal axis for one factor, with lines joining the means for the other factor. This corresponds to a rotation of the 3-dimensional diagram showing the model.
Although there is duplication of information, it often helps to plot these same means against both explanatory variables separately.
Models with no interaction
If it is concluded that there is no interaction between the two factors and there are the same number of replicates for each combination of factor levels, it suffices to separately graph the mean response for each value of X and separately plot the mean response for each Z.
These plots do not correspond to a rotation of the full model to Y vs X and Y vs Z, but average the parallel lines in such rotations of the full model.
It is not helpful to examine these diagrams if interaction is present.
Interaction means that the effect of X on Y is different for different values of Z, so it is not then meaningful to plot an 'overall' effect of X on Y.
Abrasion of coated fabric
The data below shows the abrasion loss from coated fabric that was treated with two types of filler at three different percentages.
The diagrams with blue background on the top right describe the nature of the models that can be fitted to these data.
Drag the red arrows down to add the two factors to the model, but no interaction. The diagrams on the top right summarise how changing filler type and filler percent alter mean abrasion loss in this model. Rotate the 3-dimensional diagram on the left to y-z and observe that the diagram showing the main effect of filler percent is the average of the two coloured lines on the left.
Drag the red arrows to add an interaction to the model. The nature of the interaction is described by the multiple coloured lines in the graphs on the right. There is duplication of information here since the same means are shown in both diagrams, sorted by a different explanatory variable. However it is often worthwhile to examine both.
Rotate the diagram on the left to y-x and y-z and observe that the two profile diagrams on the right correspond to these rotations.