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When is the main effect of an interaction not significant?
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.
How to interpret the interaction effect in statistics?
The p-values in the output below tell us that the interaction effect (Food*Condiment) is statistically significant. Consequently, we know that the satisfaction you derive from the condiment depends on the type of food. But, how do we interpret the interaction effect and truly understand what the data are saying?
Can you interpret an interaction that makes theoretical sense?
You can definitely interpret it. If the interaction makes theoretical sense then there is no reason not to leave it in, unless concerns for statistical efficiency for some reason override concerns about misspecification and allowing your theory and your model to diverge.
Is the difference between B1 and A2 significant?
In most data sets, this difference would not be significant. But there clearly is an interaction. The difference in the B1 means is clearly different at A1 than it is at A2 (one difference is positive, the other negative). So yes, you would would interpret this interaction and it is giving you meaningful information.
When are there more than two non-significant effects?
If there are more than two non-significant effects that are irrelevant to your main hypotheses (e.g. you predicted an interaction among three factors, but did not predict any main effects or 2-way interactions), you can summarise them as in the example below go to the table in the paper I gave you.
When to report all significant effects and predicted effects?
Report all significant effects and all predicted effects, even if not significant. If there are more than two non-significant effects that are irrelevant to your main hypotheses (e.g. you predicted an interaction among three factors, but did not predict any main effects or 2-way interactions), you can summarise them as in the example below
Do you include interaction effects in linear models?
As a result, interpreting interaction effects in linear models is difficult. If you have a theory that predicts an interaction effect, you should include it even when insignificant. You may want to ignore main effects if your theory excludes those, but you will find that difficult]