Interaction
One important reason for assessing the effects of two factors in a factorial experiment is that it allows you to assess whether the factors interact in their effect on the response. Interaction occurs when the effect of changing the level of one factor is different for different levels of the second factor.
In separate experiments for the two factors, we do not have information about the effects of factor A at different levels of factor B, so we cannot assess whether there is interaction.
A factorial design is needed to look for interaction.
Summarising the results of experiments is usually easier if there is no interaction between the factors. However if interaction exists, it is important that it is discovered and described. Interaction will be described more fully in a later section of this chapter.
Texture of a dairy product
Consider 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.
The diagram above initially shows typical results from a factorial experiment for storage time and temperature. The values on the right are differences between the mean texture at 1 day and 2 weeks. They are shown separately for the samples stored at low temperature, at high temperature and overall.
If there is no interaction between the factors, the decrease in texture between 1 day and 2 weeks should be approximately the same whatever the storage temperature. The actual data show a decrease in mean texture of about 3 at 10°C but about 11.5 at 20°C.
There is interaction — the decrease in texture (from 1 day to 2 weeks) is greater at high than low temperature.
Now consider the results that would have been obtained if two separate experiments had been conducted, one to assess the effect of temperature on texture and the other to assess the effect of storate time. Select Experiment for storage from the pop-up menu to see typical results from an experiment conducted at 10°C to assess the effect of storage time. From it and the corresponding experiment for temperature:
We would have no idea that the combination of high temperature and long storage time is particularly bad.
Since there is interaction:
A single value is not enough to describe how texture decreases between storage of 1 day and 2 weeks.
Because of the interaction between temperature and storage time, we must separately report the mean decreases at both 10°C and 20°C to fully describe how storage time affects texture.