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

[Eric Maris]

Dear Matthew,

I agree with your proposal for an interaction test in a within-sessions
design. (I have called this a within-units-of-observation design in the
Maris & Oostenveld paper.)

I know of no permutation test for an interaction effect in a
between-units-of-observation design. The reason is that I do not see how
such a test can be rephrased as a test of the exchangeability null
hypothesis.

This is a recurrent question on this discussion list. You may be good to
browse through the archive of the discussion list.

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

MSc Cognitive Neuroscience: www.ru.nl/master/cns/

> -----Oorspronkelijk bericht-----
> Van: FieldTrip discussion list [mailto:FIELDTRIP at NIC.SURFNET.NL] Namens
> Matthew Nelson
> Verzonden: donderdag 19 november 2009 16:10
> Aan: FIELDTRIP at NIC.SURFNET.NL
> Onderwerp: [FIELDTRIP] Question about permutation testing of an
interaction in a
> two by two design
>
> After the terrific help I received following the last question, I thought
I
> would post an additional question I am currently pondering.
>
> I'm also interested in comparing the coherence of a pair of signals in a
2x2
> design. I am specifically interested in testing the interaction in this
> design and would like to do so using the cluster-based permutation tests
to
> do so across time and frequency. I'm curious to receive feedback and input
> about the proper way to go about this.
>
> Performing the tests across sessions seems to me to be a bit easier to
> conceive and to write code for. In this case the design would be a
> within-sessions design, as all of the four trial types occur in each
> session. My impression is that the proper test could then be to calculate
> for each session the difference along one factor for each condition of the
> other factor, and then performing a permutation test of that difference
> among the conditions of the other factor with the test statistic merely
> being the mean difference of eth differences. It struck me that a 4-way
> permutation of the four trial types, but this would instead be more
> appropriate if the test statistic I was interested in was an omnibus anova
> test, not to test strictly the interaction which is my interest here.
>
> I am less sure how to perform the test if one wanted to do it within a
> single session where there may be different numbers of trials in each
> condition.
>
> I know this question relates more to permutation tests than to frequency
> analysis. If someone could even just point me towards a good reference
where
> I can learn more about these more detailed aspects of permutation tests, I
> would appreciate it. Thanks.
>
> ----------------------------------
> 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.