How do I interpret the interaction effect in a two way ANOVA

[josnailai94]

If the interaction effect in the two way ANOVA is significant (based on a sig level = 0.05) and none of my main effects are significant, what can I infer from this?

I suppose I am not understanding the overall picture of the two way ANOVA. You test the significance of your mean response over two main effects and then you test whether there is an interaction between your independent variables. Surely I cannot assess the main effects in isolation of the interaction effect and vice versa?

[gasper]

In theory you can come up with an example where interaction could be assessed and main effects not, but it's very unlikely and there's a ton of other options you should check for before you go down that road.

If your main effects turn out non-significant but interaction does, then check for any signs of non.linear main effects. That could be the reason for main effects lurking in the backgroud. Also check the residuals - there can be problems with heteroscedasticy and perhaps some of the transformations of data would be needed. Both could diminish the main effects and pop out in the interaction instead.

Bye,
Gasper

[jonathon]

Surely I cannot assess the main effects in isolation of the interaction effect and vice versa?

i think you're absolutely correct. there's a great paper exploring why you should not do that here:

http://pcl.missouri.edu/sites/default/files/Rouder.etal_.pbr_.2016.pdf

(but not everyone agrees)

cheers

jonathon