Two variables interact if a particular combination of variables leads to results that would not be anticipated on the basis of the main effects of those variables. For instance, it is known that both drinking alcohol and smoking increase the chance of throat cancer. However, people who both drink and smoke have a much higher chance of getting cancer than would be predicted if one knew only how much more likely smokers are than nonsmokers to get throat cancer and how much more likely drinkers are than nondrinkers to get throat cancer. The combination of smoking and drinking is particularly dangerous: these drugs interact.

This definition of interaction in terms of a particular combination of variables is consistent with the previously-given definition that there is an interaction if the effect of one variable differs depending on the level of another variable. In the tobacco and alcohol example, the effect of smoking on the probability of getting cancer is greater for people who drink than for people who do not drink: the effect of smoking differs depending on whether drinkers or nondrinkers are being considered. Similarly, the effect of drinking differs depending on whether smokers or nonsmokers are being considered.