# 3-way repeated mesures ANOVA

I conducted reaction-time experiment with three factors - set size (4, 16, 64), presense of the target (present, absent) and the third factor with two levels (C, F).

After that I ran a repeated measures ANOVA in R:

m2 <- aov(time ~ pres*fact*size + Error(1/subj), data = data)


fact and pres are factorized. The result is that all main effects and all interactions (including 3-way) are significant.

I have no idea how to interpret 3-way interaction in this case, can I somehow exclude it from the model? And did I even specify an ANOVA correctly?

• It may indicate time to be dependent on all three predictors and there is significant interaction between three predictors.
– rnso
Commented Dec 5, 2014 at 1:45

Although this is five years late, I will post as an FYI for anyone else who happens to stumble upon this thread. The first part of the model is properly specified, i.e.

time ~ pres*fact*size


However, the error term is incorrectly specified. Note that in repeated measures ANOVA, "the error term for any within-subject effect is the interaction of that effect with subjects [or whatever entity that is repeatedly measured] (Keppel, G., & Wickens, T. D., 2004, p. 40)."

For this particular example, if using R's aov() function, the error term would be specified as such:

Error(subj/(pres*fact*size))


So in all, we have:

m2 <- aov(time ~ pres*fact*size + Error(subj/(pres*fact*size)), data = data)


WRT the interpretation of a three-way interaction: The implication is that a two-way interaction varied over the levels of a third factor. In other words, there was a two-way interaction that was only manifest at a specific level or levels of a third factor. To get to the heart of the matter, you would need to follow up your omnibus ANOVA with interaction contrasts. To determine what interaction contrasts you should test, it would be helpful to plot your data using a line graph. As it stands, there is not enough information available in your post to provide further guidance.

Edit Perhaps it goes without saying, but this is in the case that you obtain such a result with the model properly specified.