[FieldTrip] 2x3 anova in cluster analysis

[jan-mathijs schoffelen]

Hi Stan et al,

Actually FieldTrip allows in a very straightforward way to plug-in one's favourite statistic. The idea is the following: when specifying cfg.statistic you need to specify a string that under the hood points to a function, e.g. 'indepsamplesT' eventually causes a function to be called, answering to the aptly chosen name: 'statfun_indepsamplesT' which is doing the legwork. As long as the statfun_younameit has properly defined input and output arguments, you can let it do whatever you want. FieldTrip contains a bunch of 'statfuns' in the statfun directory but there's no reason not to implement any yourself (and ideally contribute them to the repository).
Another discussion altogether is the question whether the test statistic of interest is an appropriate one that allows for statistical inference using the permutation framework. Over the past years there have been various threads on this mailing list regarding the possibility to test for interactions using a permutation test. You can look this up in the archive. Strictly speaking this is statistically not possible this way. The permutation-framework tests the null-hypothesis of exchangeability of data across allocated conditions, whereas when one wants to test for an interaction effect tests one tests for a particular linear (parametric) model of the dependent variables explaining variance in the dependent variable. Inferring that exchangeability across conditions is unlikely (i.e. obtaining a small p-value through permutation) does not necessarily lead to the conclusion that there is an actual interaction effect. Though opinions among the statisticians about this seem to vary, there may be a way out: one could either use bootstrapping to obtain confidence intervals for the interaction F under the null-hypothesis. The recipe for this would be to do a cell-specific demeaning of the data to impose the null-hypothesis of no interaction, and then through bootstrap resampling obtain a reference distribution of the interaction F. Alternatively, although I haven't thought this one through for any case other than a 2x2 anova, one could reduce the interaction effect to a two-condition contrast where observations belonging to the 'main diagonal' of the 2x2 conditions design are labeled as condition 1, and the observations belonging to the other diagonal are labeled as condition 2. One could then proceed with using a T-statistic as a descriptive statistic across these two 'conditions' on which inference can be done.

Cheers and a happy Sinterklaas to you all,

Jan-Mathijs


On Dec 5, 2011, at 8:17 PM, Stanley Klein wrote:

> Nico,
> 
> Your question gives me the chance to ask something I've been curious about. It seems to me that one of the nifty things about permutation cluster analysis is that it allows you to do anything that seems reasonable as long you decide on the process ahead of time and don't do any future tweaking other than fixing coding errors. I'm curious whether the Fieldtrip code make it easy to insert new statistics modules.
> 
> I presume your actual question had to do with whether Fieldtrip already has the possibility of doing that 2x3 ANOVA.  I suspect it doesn't have that capability. However, it would be nice if the permutation cluster analysis could be made sufficiently modular that one could make use of all the complicated clustering and permuting and all, but enable the user to substitute their own statistical method.  I haven't actually watched my students doing the nitty-gritty use of Fieldtrip's version of the permutation test (other than knowing that is is very nice and well documented) so I don't know how easy it is to stick in one's own favorite statistic, but I'm hoping it is easy.
> 
> Stan
> 
> 
> On Mon, Dec 5, 2011 at 4:58 AM, Nico Alexander Willi Kremers <nkremers at uni-bonn.de> wrote:
> 
> Hi,
> 
> I followed the discussion about implementing a 2x2 within subjects design into a cluster statistic with much interest. I want to implement a 2x3 repeated measure anova in a cluster analysis using fieldtrip. I think for this type of analysis subracting two conditions from each other and then calculate a ttest is not appropriate. Is there another way of calculating the interaction effect between the two factors and generate clusters for real and permutation data? What specifications must be set and how?
> 
> Thank you very much for your answer,
> 
> Nico
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Jan-Mathijs Schoffelen, MD PhD 

Donders Institute for Brain, Cognition and Behaviour, 
Centre for Cognitive Neuroimaging,
Radboud University Nijmegen, The Netherlands

Max Planck Institute for Psycholinguistics,
Nijmegen, The Netherlands

J.Schoffelen at donders.ru.nl
Telephone: +31-24-3614793

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