# interaction and significance

How do you interpret interaction terms between two categorical variables if Y is significant, Z is not significant, but Y*Z is significant. Do you include the interaction term in the model, or do you eliminate the variable that is not significant (in this case Z) and therefore also the interaction term?

• In addition to Ben's answer; making a quick graph of the means of the dependent in all categories for the interaction, Y x Z, might help you with interpreting the result. You can do this on paper no code needed. – stijn Apr 30 '15 at 2:24

If the interaction is significant, interpreting either main effect, whether significant or not, is basically pointless (and misleading). The reason is that when $A$ and $B$ are involved in an interaction, the coefficient for $A$ is the effect of $A$ when $B=0$; in other words, the effect is conditional on the value of $B$, and is not a main effect. Similarly, the coefficient for $B$ is the effect of $B$ when $A=0$.
• Since the variables are categorical in this place, replace "$= 0$" in that answer with "equal to the baseline," but it's the same idea. – Ben Kuhn Apr 30 '15 at 5:58