# ANOVA with and without interactions giving different values for main effects

I have measured Copper content in fishing nets. I have 2 independent variables - treatment of the net with 4 levels and type of net with 2 levels. I'm using R to do the ANOVA.

I care about the interaction, so I should do:

mCu = aov(Cu ~ Type * Treatment, data = Ultrasonic)


But why do I get different values for the difference in type if I do:

mCu = aov(Cu ~ Type + Treatment, data = Ultrasonic)


I thought using the asterisk instead of the plus sign would just add the interactions as well, not change the analysis of the variables by themselves. (Although, the values are not very far off.)

• There is a basic confusion here, but I don't see how this merits a downvote. – gung - Reinstate Monica Dec 7 '15 at 18:26

## 1 Answer

The issue is that when you include an interaction term, the meaning of the main effects changes. Specifically, what would be called the "main effects" in an additive model are really just the effects when the other interacting variable is at the reference level in an interaction model. (There is a fairly thorough write-up which concludes by discussing this issue in my answer here: What does “all else equal” mean in multiple regression?; that may help you to understand this topic better.)

• Cheers mate, that helps a lot. The mean difference returned actually stays the same, but the range is slightly bigger without interactions. Would you say the difference doesn't really matter then and I can just go ahead and use the results I get when I run the anova with interactions? – Virolainen Dec 8 '15 at 9:37
• @Virolainen, if you are interested in the interaction, & it is significant, then you should use the interaction model; if the interaction is sufficiently non-significant, you could use the non-interaction model. – gung - Reinstate Monica Dec 8 '15 at 13:19