# Interpreting significant interactions when single effects are not significant

I am fitting a linear mixed effect model to my data, and I get the following results I cannot interpret.

I have two main effects (Force and frequency) and one interaction (Force:frequency). The Force main effect is significant ($p=0.046, \beta_F=0.004637$), the frequency effect is not ($p=0.243, \beta_f=0.99724$), and the interaction is ($p=0.038, \beta_{Ff}=-0.0060714$). I am not sure how to interpret this.

My understanding is that frequency let the effect of Force decrease. However, at which level of frequency does the effect of Force become non-significant?

## 1 Answer

I do not think there is a point in interpreting a single effect here. The effect of frequency varies according to the force, which is the reason why you cannot see it on its own, frequency does not have an overall effect. But then I don't understand your design... Look there: http://www.theanalysisfactor.com/interactions-main-effects-not-significant/

• The significance of the interaction term tells me that the effect of one variable depends on the value of the other. I could therefore immagine a situation in which at a certain level of force, frequency has a non-significant effect, and other levels of force at which frequency becomes significant (although it is not on its own). How to perform such an assessment? My design is a repeated measure in which each subject performs physical exercises at various level of Force and repetition frequency. I am studying the effects of such exercises on cardiovascular parameters. – Cristiano Sep 17 '16 at 5:21
• You mean frequency would have a stronger or weaker effect according to the level of force? Maybe if you added a plot? – CaroZ Sep 17 '16 at 13:39
• Frequency will have a lower effect if force increases (look at the sign of the betas). – Cristiano Sep 17 '16 at 15:09
• But by the way are both these variables continuous? – CaroZ Sep 19 '16 at 14:28
• Yes, they are. Although, the experiment considers only two frequency. – Cristiano Sep 19 '16 at 14:34