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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?

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  • $\begingroup$ 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. $\endgroup$ – stijn Apr 30 '15 at 2:24
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Keep both the interaction term and the main effects.

Because Z influences the model both through the main Z term and the interaction term Y*Z, it's not very meaningful to look at the significance of the main effect on its own. See for instance this answer:

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 $A=0$.

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  • $\begingroup$ So making sure I understand you correctly, even though Z is not significant, I should still keep it in the model because it is part of a significant interaction term? $\endgroup$ – stats123 Apr 30 '15 at 2:31
  • $\begingroup$ Yes, that's correct. $\endgroup$ – Ben Kuhn Apr 30 '15 at 5:43
  • $\begingroup$ Since the variables are categorical in this place, replace "$= 0$" in that answer with "equal to the baseline," but it's the same idea. $\endgroup$ – Ben Kuhn Apr 30 '15 at 5:58

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