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

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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?


There is no statistical test for "important" - you have to use your judgement and the literature in your field.

E.g. (not with interactions, but to give the idea). If 1 in 1000 vacuum cleaners that are produced do not suck up stuff and have to be replaced, that is probably not important.

If 1 in 1000 airplanes that are produced crash, killing all aboard, that is very darn 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

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  • $\begingroup$ Thanks! Do you know what examining importance of interaction means in that book? $\endgroup$ – Tim Jul 6 '13 at 19:20
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    $\begingroup$ I assume it means thinking about how big the interaction is and whether it matters. $\endgroup$ – Peter Flom Jul 6 '13 at 23:02

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