# How to interpret interaction effects when main effect is not significant?

I ran a linear mixed model in R and included an interaction effect between two predictors. The main effect was not significant, but the interation effect was. Is it possible to interpret this interaction effect? Or should it be ignored, because of the missing main effect?

• What do you mean by "interpret" the effect? Whether the p-value is large or small, the predicted impact on the response variable is the same. – Dave Jun 29 at 12:10
• Hi Dave, thank you very much for your response! What I mean is, if I have a significant interaction effect and a non-significant main effect, would you interpret the interaction effect? – Martha Jun 29 at 12:16
• At its base, this is a theoretical question about which there is considerable controversy. The consensus opinion is that, when testing interactions, main effects associated with that interaction are to be included in the model but are of secondary importance. In other words, your interest should be focused solely on the interaction(s) and any hypotheses about that. – user332577 Jun 29 at 13:17
• Consider this scenario. Generally speaking, corn yields improve as irrigation levels go from Low to Med to High. Generally speaking, yields improve as fertilizer levels go from Low to Med to High. But there is interaction. Everything dies with Low irrigation and High fertilizer, which happens to render both main effects non-significant. But there is still important info in the results. // If you can't untangle it any other way, look at one-way ANOVA, one main effect w/ $3 \times 3 = 9$ levels of the factor. Which of 9 is best? – BruceET Jun 29 at 17:45