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

Guillaume Rousselet g.rousselet at PSY.GLA.AC.UK
Tue Nov 24 11:18:02 CET 2009

Dear Stephan,

to build an appropriate null distribution, the resampling procedure
must stick to the structure of your experimental design. In the case
of a group x condition (repeated measure) interaction, the groups are
independent but the conditions are not. To take that constraint into
account, I think you need to resample from each group independently.
However, for each group, because of the paired nature of the design,
when you sample 1 subject, you have to sample both conditions from
that subject (and all the time points and sensors), i.e. you sample
subjects with replacement independently from each group, but keeping
paired data points together.
The strategy described here relies on a sampling with replacement
under H0. In that case H0 is created by centering the data
a true null hypothesis and through resampling you can derive a table
of F values for the interaction under H0.

Hope this help,

GAR

On 24 Nov 2009, at 09:19, Stephan Moratti wrote:

> 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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************************************************************************************
Guillaume A. Rousselet, Ph.D.

Lecturer

Centre for Cognitive Neuroimaging (CCNi)
Department of Psychology
Faculty of Information & Mathematical Sciences (FIMS)
University of Glasgow
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Email: g.rousselet at psy.gla.ac.uk
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