# How to test if two factors interact and test if their interaction is important?

In a two-way ANOVA, from Kutner's Applied Linear Statistical Models:

What differences are between testing if two factors interact and testing if their interaction is important?

I know that testing if two factors interact is the F test via the ratio between the mean interaction sum of squares and the mean error sum of squares.

I was wondering how to test if their interaction is important?

However, while there is no test of importance, there are tools to help you judge. In particular, I would look at predicted values of the dependent variable at different combinations of the independent variables. There are various ways to plot these to get an idea of what is going on, depending on what software you are using. In R look for effect plots and also see this thread