# How to interpret results of differences of differences in interactions?

I have a dataset composed of 2 factors of several levels each (i.e. exercise[A-B-C] x muscle [1-2-3-4-5-6]. I'm interested on the effect of the different exercises (A,B,C) on the muscle activation amplitude (i.e. 6 different muscles).

After performing the Analysis of Variance of Aligned Rank Transformed Data I found a significant interaction exercise x muscle. Thus, I tested (post hoc) differences of differences for the interaction term (pairwise comparisons).

I obtained some significant results but I'm struggling with the interpreation. Below an example of the statistical outcome:

A - B : 1 - 3 p = 0.001 ***; A - C : 1 - 3 p = 0.003 **; B - C : 1 - 3 p = 1;

Basically, we can ask, is the difference A - B different when muscle = 1 compared to when muscle = 2? So, that seems ok but what does it mean practically?

Thanks

• Could you post the results of your model & the post-hoc comparisons?
– mkt
Jul 30 '17 at 21:16
• Yes, added above in the original post. The analysis was done using rstudio and the packages were artool [1] and phia. In the original post I have used general codes for factors (i.e. A,B,C, and 1-2-3, etc.), however, actual results report real levels names. [1] depts.washington.edu/madlab/proj/art Jul 30 '17 at 22:55