An example of what is meant by an interaction Suppose you have data showing that males are better than females at spatial cognitive tasks, but females are better than males at verbal cognitive tasks. You cannot give a direct answer to this question. By saying this, you are saying that there was an interaction between gender and type of cognitive task.
Theories often imply the existence of interactions.
Whether smoking causes cancer probably depends on how much you smoke and perhaps on genetic factors which interact with effects of smoking, rather than simply on whether you do or do not smoke. We begin with a two-factor design. The effects of each factor are called main effects and one, both, or neither may turn out to be significant. The MS for the interaction is also divided by the MS within treatments to yield an F value which is tested for significance. However, a significant interaction does not rule out the possibility of significant main effects.