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I could not seem to find a specific answer to my question through searching, so I thought I'd post it.
I am doing an ANOVA and I have a significant three-way interaction, each factor has only 2 levels, though. Is the Tukey HSD command in R software appropriate to tell where the differences are-- or do I need to do a simple-effects analysis?
Thanks everyone.
Your interaction has 1 df so no further tests are needed to know where the difference is. You have found there is a significant difference between two-way interactions. That's really all the three-way interaction is telling you. The easiest way to interpret the interaction is to plot the two-way interactions separately for the two levels of the third variable. You might end up saying something such as "The effect of A was larger at B1 than at B2, and the extent to which that was true was greater at C1 than at C2."
However, since the two-ways differ as a function of the third variable, you might want to test them separately. You woukd do this if you were interested in the two ways for their own sakes. Tests of two ways reveal nothing about the interaction.
