Question about permutation testing of an interaction in a two by two design

[Stephan Moratti]

Hi all,

Thanks for the interesing discussion about the interaction with respect to 
permutation. I have been also struggling with this question. As we want to 
test the interaction (and not the main effect condition), I am not sure if 
resampling condition would produce the distribution of our null hypothesis. 
Regarding the interaction, we want to check if the mean values across 
conditions follow the same pattern in two groups (if we consider a group x 
condition interaction). If we make a line plot an interaction would be indicated 
by a line crossing if each line represents a group (ideally). No interaction 
would be represented by parallel lines for each group. So I wonder if by 
resampling the subject values between the groups keeping the condition 
structure intact, would create our null distribution for the interaction. If we 
resample condition, we would destroy the condition structure.

What do you think? I would be happy for any input.

Best,

Stephan

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