Interaction
One important reason for using a factorial experimental design is to obtain more accurate parameter estimates, but equally important is to detect interaction between the effects of the factors. This arises when the effect of changing the level of one factor may be different for different levels of the second factor.
A factorial experiment is needed to look for interaction.
The results of experiments are easier to summarise 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
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.