# Dissecting three-way interactions

I'm trying to interpret a significant three-way interaction. Basically, I've used hierarchical regression to analyse my data, and I have come up with a significant three-way interaction.

My DV is continuous. My 3 IVs are continuous, categorical (2 levels), and another categorical (3 levels). My sample size is 194.

I know that I can do up graphs to eyeball the interactions, but I need a statistical method in order to figure out whether or not a slope is significant. I'm aware of Jeremy Dawson's template to figure out significant slope differences, but they only work for 3 continuous variables. Is there a method I can use to do this?

I've also had a read through the UCLA's SPSS guide to interpreting three-way interactions. Would this be the way to go?

I am a little confused by your question, since you say that you have already found a significant 3 way interaction and then say you want to find whether slope differences are significant, but I think you want to see which of the levels are different in terms of their slopes, is that right?

I don't know SPSS, but in SAS you can request particular tests of different hypotheses. In SAS you can do this with EFFECT statements. You can also do this inside a LSMEANS statement.

But I would shy away from these statements; first, they usually have low power (unless all your variables are perfectly measured and perfectly reliable). Second, significance just isn't that significant. Effect size is more important. Third, the graphs say more (especially in interaction interpretation) than any p-value could.

To quote my favorite professor in grad school "When an article is full of significance tests, the authors are p-ing all over the research".

• I think you want to see which of the levels are different in terms of their slopes, is that right? Yep, that was what I mean. I have actually never used SAS before. But I'll see if I can find the SPSS equivalent for those functions you mentioned. Jun 20, 2011 at 14:51
• LSMEANS is SAS lingo for marginal means. onbiostatistics.blogspot.com/2009/04/… Jun 21, 2011 at 0:57