Strength of asphaltic concrete
Use this diagram to explain both how a factorial experiment is necessary in order to assess whether there is any interaction, and also to explain the meaning of the interaction.
The diagram initially shows results from an experiment in which there are no replicates when both factors are at their high level. From this experiment, it is possible to estimate 'main effects' for the two factors.
Now select Factorial experiment to complete the factorial design. Explain that the effect of storage time is different for the different temperatures, and that the effect of temperature is different for different storage times. In other words, there is interaction between the effects of the factors.
Mention that the 'overall' effects of the factors (averaging the effects at the two levels of the other factor) are an incomplete description of their effects — we must also describe the interaction.
The context is an experiment in which the main aim is to assess how the texture of a dairy product deteriorates between 1 day and 2 weeks after manufacture. It is also known that the storage temperature affects deterioration, so the experiment will attempt to discover the effects of both factors on texture.