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

[Lin Wang]

Dear Eric,

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?

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. See also http://listserv.surfnet.nl/archives/fieldtrip.html and http://www.ru.nl/neuroimaging/fieldtrip.
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