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

Matthew Nelson nelsonmj at CALTECH.EDU
Fri Nov 20 17:19:48 CET 2009

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

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,


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

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