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

Lin Wang wanglinsisi at GMAIL.COM
Wed Nov 25 09:37:51 CET 2009

```Dear Eric,

Thank you very much for you reply.

I'm clear about the testing of multiple-way interaction now. I suppose the
tests I mentioned in the last email is simple effect test. Am I right?

Thanks again.

Lin

2009/11/24 Eric Maris <e.maris at donders.ru.nl>

>  Dear Lin,
>
>
>
>
>
>
>
> Thanks for your clear answer. I also have a question about the permutation
> testing of the interactions in the mixed factorial design.
>
> Suppose I have three factors, with two levels in each:
> 2Group(boys,girls)*2A(A1,A2)*2B(B1,B2). Factor Group is a between-subject
> factor, while factor A and B are within-subject factors. What I want to test
> is whether factors B influences factor A differently on boys and girls (a
> three-way interaction).
>
> Can I test the interaction between factor B and Group separately in B1 and
> B2 conditions? That is, first split the data into two parts (B1, B2), and
> then for each part test the interaction between factor A and Group by
> subtracting the observations of A1 from A2 and taking it as a new dependent
> variable.
>
> Furthermore, if I have another factor C(C1, C2), and I'm interested in
> whether the combination of B and C influences factor A differently on boys
> and girls. Can I first split the data into four parts according to the
> combination of factor B and C (B1C1, B1C2, B2C1, B2C2) and do the
> interaction between factor A and Group separately for each part?
>
>  I do not think it is necessary to split the data and do separate analyses
> on the different parts.
>
> Reformulating an interacting effect null hypothesis as a main effect null
> hypothesis for a different dependent variable is possible if you have at
> most a single between-subjects variable in your design. Thus, it also works
> in the case you describe, with two within-subjects and one between-subjects
> variable. The dependent variable that must be calculated is the two-way
> interaction effect contrast for the 2-factorial within-subjects design with
> the variables A and B: [A1,B1] + [A2,B2] – [A1,B2] – [A2,B1]. You then
> perform a independent samples T-test on the interaction contrast variable,
> comparing the two levels of your between-subjects variable.
>
> This reformulation is also possible when there are more than two
> within-subjects variables in the design. The only thing that changes is the
> interaction effec contrast.
>
>
>
> Best,
>
> Eric
>
>
>
> dr. Eric Maris
> Donders Institute for Brain, Cognition and Behavior
>
> Center for Cognition and F.C. Donders Center for Cognitive Neuroimaging
>
> Radboud University
> P.O. Box 9104
> 6500 HE Nijmegen
> The Netherlands
> T:+31 24 3612651
> Mobile: 06 39584581
>
> F:+31 24 3616066
> E: e.maris at donders.ru.nl <e.maris at donders.ru.nl>
>
>
>
> MSc Cognitive Neuroscience: www.ru.nl/master/cns/
>
>
>
>
>
>
> Thank you in advance.
>
> Lin
>
>
>  2009/11/24 Eric Maris <e.maris at donders.ru.nl>
>
> Dear Stephan,
>
>
>
>
>
> It is sometimes possible to reformulate an interaction effect null
> hypothesis such that it becomes a main effect null hypothesis (however, for
> a different dependent variable, obtained be calculating the difference
> between conditions). Such a reformulation is possible for a two-factorial
> design in which one independent variable is manipulated within subjects (in
> your case, this is condition), and the other between subjects (in your case,
> this is group). You do this by calculating subject-specific difference
> scores, [condition1 - condition2], and using these as the dependent variable
> in a between-groups comparison. This is possible by means of the standard
> independent-samples T-test, but also by means of a permutation test
> (involving permutation of the difference scores), which allows you to deal
> with the multiple comparison problem.
>
>
>
> For a factorial design that only involves between-subject independent
> variables, such a reformulation is not possible (at least, I am not aware of
> it).
>
>
>
>
>
> Best,
>
>
>
> Eric
>
>
>
>
>
>
>
>
>
> > -----Oorspronkelijk bericht-----
>
> > Van: FieldTrip discussion list [mailto:FIELDTRIP at NIC.SURFNET.NL] Namens
>
> > Stephan Moratti
>
> > Verzonden: dinsdag 24 november 2009 10:20
>
> > Aan: FIELDTRIP at NIC.SURFNET.NL
>
> > Onderwerp: Re: [FIELDTRIP] Question about permutation testing of an
> interaction
>
> > in a two by two design
>
> >
>
> > 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
>
> >
>
> > ----------------------------------
>
> > The aim of this list is to facilitate the discussion between users of the
> FieldTrip
>
> > toolbox, to share experiences and to discuss new ideas for MEG and EEG
> analysis.
>
> > See also http://listserv.surfnet.nl/archives/fieldtrip.html and
>
> > http://www.ru.nl/neuroimaging/fieldtrip.
>
> ----------------------------------
>
> The aim of this list is to facilitate the discussion between users of the
> FieldTrip toolbox, to share experiences and to discuss new ideas for MEG and
> EEG analysis.
>
> http://listserv.surfnet.nl/archives/fieldtrip.html
>
> http://www.ru.nl/fcdonders/fieldtrip/
>
>
>
> ----------------------------------
>
> The aim of this list is to facilitate the discussion between users of the
> FieldTrip toolbox, to share experiences and to discuss new ideas for MEG and
> EEG analysis.
>
> http://listserv.surfnet.nl/archives/fieldtrip.html
>
> http://www.ru.nl/fcdonders/fieldtrip/
>
> ----------------------------------
>
> The aim of this list is to facilitate the discussion between users of the
> FieldTrip toolbox, to share experiences and to discuss new ideas for MEG and
> EEG analysis.
>
> http://listserv.surfnet.nl/archives/fieldtrip.html
>
> http://www.ru.nl/fcdonders/fieldtrip/
>

----------------------------------
The aim of this list is to facilitate the discussion between users of the FieldTrip  toolbox, to share experiences and to discuss new ideas for MEG and EEG analysis. See also http://listserv.surfnet.nl/archives/fieldtrip.html and http://www.ru.nl/neuroimaging/fieldtrip.
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