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

Guillaume Rousselet g.rousselet at PSY.GLA.AC.UK
Fri Nov 20 18:17:46 CET 2009


based on the attached paper and Wilcox 2005 (Wilcox, R.R.,
Introduction to Robust Estimation and Hypothesis Testing. 2nd Ed. ed.
2005: Academic Press),

the null F distributions for the main effects and the interaction are
obtained by sampling with replacement independently from centred
distributions. This is an extension of the bootstrap percentile-t

I'm not aware of robust ANOVA techniques employing permutation.

On 20 Nov 2009, at 16:19, Matthew Nelson wrote:

> Thanks very much for your response. I will browse through the
> archive here
> to see if I can find anything.
> One source I found elsewhere on the web can be found in this book on
> page
> 126-127:
> If I'm understanding his description properly, this can be tested
> simply by
> using the ANOVA sum of squares test statistic for an interaction while
> permuting amongst all the conditions. I would suppose that an
> interaction
> contrast could be tested similarly using the sum of squares for the
> contrast
> as the test statistic while permuting amongst the combinations of
> conditions
> that factor into the particular contrast.
> But if you don't think that that permutation would provide the
> proper null
> hypothesis for either test (the omnibus interaction or an interaction
> contrast), I'd be curious to know.
> Thanks again very much,
> Matthew
> On Thu, 19 Nov 2009 22:06:04 +0100, Eric Maris
> <e.maris at DONDERS.RU.NL> wrote:
>> 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
>> MSc Cognitive Neuroscience:
> ----------------------------------
> 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
>  and

Guillaume A. Rousselet, Ph.D.


Centre for Cognitive Neuroimaging (CCNi)
Department of Psychology
Faculty of Information & Mathematical Sciences (FIMS)
University of Glasgow
58 Hillhead Street
Glasgow, UK
G12 8QB

The University of Glasgow, charity number SC004401

Email: g.rousselet at
Fax. +44 (0)141 330 4606
Tel. +44 (0)141 330 6652
Cell +44 (0)791 779 7833

"no test based upon a theory of probability can by itself
provide any valuable evidence of the truth or falsehood
of a hypothesis.

But we may look at the purpose of tests from another
viewpoint. Without hoping to know whether each separate
hypothesis is true or false, we may search for
rules to govern our behaviour with regard to them, in
following which we insure that, in the long run of
experience, we shall not often be wrong."

	Neyman J & Pearson E, 1933

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 and
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