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

[Eric Maris]

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