# Permutaion (of residuals) and factorial designs

Michael Wibral michael.wibral at WEB.DE
Wed Sep 29 15:09:04 CEST 2010

```Dear Eric, dear fieldtrip users,

this might sound like nitpicking but, we all routinely seem to analyse the interaction of a factorial design using permutation testing. The example is this: we have two experimental conditions (that we want to compare) and record task and baseline intervals in each. Clearly this is a 2x2 design (task/base and cond1/cond2 are the respective levels of the two factors). What we all do to deal with this is that we compute residuals - either by subtracting the baseline values or normalizing to them and then do a (restricted) permutation between the conditions on these task-base residuals. We are interested in the interaction between the task/base factor and the cond factor.

Anything wrong here or anything particular about this case that saves us from the fundamental difficulties of interaction testing?

Michael

-----Ursprüngliche Nachricht-----
Von: "Eric Maris" <e.maris at DONDERS.RU.NL>
Gesendet: Sep 29, 2010 11:18:06 AM
An: FIELDTRIP at NIC.SURFNET.NL
Betreff: Re: [FIELDTRIP] Coherence differences and factorial designs

>Dear Suresh,
>
>
>
>>     In a fixed effects context I have been obtaining coherence
>> estimates. I have been reading Maris et al 2007 and the theory there
>> describes how to test between two different conditions
>> I would like to extend the theory in that paper (2.7.1) to k sample
>> (one factor eg 1 x 3 ANOVA) and two-way (e.,g. 2 x 2 designs). I was
>> wondering if anyone had attempted such a thing if it can be done, and
>> in particular how one might go about constructing an apprppriate test
>> statistic and surrogate distribution? Prior implementation in fieldtrip
>> isnt needed its more the theory behind it I am asking about
>
>Statistical comparison of coherence estimates in k samples is discussed by
>Amjad et al (2007) in J. Neurosc. Methods.
>
>In the permutation framework there is no analogue of the factorial ANOVA
>(involving both main and interaction effects) for the simple reason that the
>interaction null hypothesis cannot be tested in the permutation framework.
>There is at least one thread in the Fieldtrip Discussion list that deals
>with this issue. However, it is possible to test multiple conditional null
>hypotheses (main effect of one factor separately for each of the levels of
>another factor) and this comes close to an interaction effect test.
>
>
>Good luck,
>
>Eric Maris
>
>
>
>
>
>
>> Dr Suresh Muthukumaraswamy
>>
>> Suresh Muthukumaraswamy, PhD
>> CUBRIC
>> Cardiff University
>> Park Place
>> Cardiff, CF10 3AT
>> United Kingdom
>> email: sdmuthu at cardiff.ac.uk
>> Phone: +44 (0)29 2087 0354
>> http://www.cf.ac.uk/psych/contactsandpeople/researchstaff/muthukumarasw
>> amy-suresh-dr-overview_new.html
>>
>> ----------------------------------
>> The aim of this list is to facilitate the discussion between users of
>> the FieldTrip  toolbox, to share experiences and to discuss new ideas
>> 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.

----------------------------------
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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