Interaction

The increased accuracy of the parameter estimates is an important reason for using a factorial experimental design.

However an equally important reason is that the effect of changing the level of one factor may be different for different levels of the second factor. If this occurs, there is said to be an interaction between the effects of the two factors.

If there are no runs of the experiment for some combinations of factor levels, we cannot assess whether there is interaction.

A factorial experiment 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.

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 an experiment that only keeps samples at low temperature for 2 weeks. From it, we might estimate that texture decreases by 2.96 between 1 day and 2 weeks from manufacture.

Now select Factorial experiment from the pop-up menu at the top of the diagram. This adds some extra observations when samples are stored for 2 weeks at 20°C to complete the factorial design. With these extra observations, it can be seen that the deterioration in texture from 1 day to 2 weeks is much greater when the temperature is 20°C than when it is 10°C. This is called an interaction between the effects of storage time and temperature.

In conclusion,

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 provide the mean decreases at both 10°C and 20°C to fully describe how storage time affects texture.