Interaction in statistics

Interaction in statistics can be defined as the effect of one independent variable may depend on the level of the other independent variable. In statistics, an interaction may arise when considering the relationship among three or more variables, and describes a situation in which the simultaneous influence of two variables on the third is not additive. In order to find an interaction, you must have a factorial design, in which the two or more independent variables are “crossed” with one another so that there are observations at every combination of levels of the two independent variables.

The presence of interaction can have important implications for the interpretation of statistical models. If two variables of interest interact, the relationship between each of the interacting variables and a third “dependent variable” depends on the value of the other interacting variables and this makes it hardest to anticipate or predict the consequences of the value of variable that changes particularly if the variable it interacts with are difficult to control. (Eastern & McColl 2016)

Example is if we want to examine the effect of two variables, gender and premature birth on health outcomes, we would first of all outline any differences in health outcome score among gender as a main effect.  Similarly, we will describe any difference in the scores of full term/premature as a main effect.  The presence of an interaction effect shows that the effect of gender on health outcome varies as a function of premature birth status.


Easton J.C & McColl 2016: Design of Experiments and Anova.  Retrieved August 17, 2018 from