Summarising the main effects and interactions
In factorial experiments with four or more factors, it is impossible to plot the raw data in a way that shows the main effects and interactions. It is therefore essential that the effects are summarised in plots of the mean response against each factor. If there are interactions between a factor and another, the fitted response must be plotted separately for each level of the other factor.
Pilot plant filtration
In the pilot plant filtration experiment, only three main effects and two 2-factor interactions were significant. The diagram below shows this model and plots the mean filtration rate against the four factors. Because of the interactions between temperature and both stir rate and formaldehyde, the effects of stir rate and formaldehyde must be shown separately for both temperatures.
At high temperature, increasing the stirring rate increases the mean filtration rate, but the stirring rate does not seem to have much effect at low temperature.
At low temperature, increasing the formaldehyde level increases mean filtration rate, but this possibly even decreases the filtration rate at high temperature.
Sugar reduction study
In the sugar reduction study, three 2-factor interactions are significant at the 5% level, as shown below.