# cluster statistic on one sample

Eric Maris e.maris at DONDERS.RU.NL
Mon Oct 20 16:02:39 CEST 2008

```Dear Fieldtrip-list-readers,

> What about performing a nonparametric test, based on the bootstrap
> distribution of the beta weights under the null-hypothesis?
> This problem sounds similar to one I came across recently (and which
> I still have to write something about on fieldtrip's wiki-page (sorry
> Eric)), which has to do with the testing of the significance of the F-
> value for interaction in a 2x2 repeated measure anova. Also in this
> case, one also wants to test a parametric null-hypothesis, as Eric
> phrased it in his last e-mail. One way to test this (I don't have the
> reference at hand), is to test the observed F-statistic against a
> null-distribution, obtained from bootstrapping your data, which you
> preconditioned as to impose the null-hypothesis (in the case of an
> anova it would be to remove from each of the observations the mean of
> the cell to which the observation belongs). I don't know yet how to
> impose the null-hypothesis in the regression case, but would this
> line of thought be a possibility?
> As to a potential implementation: Robert and I are pretty close to
> have the bootstrapping implemented.

Again, I can only try to clarify some points here. I will not be able to
offer a solution for your problems.

1. Contrary to the permutation test, there is no useful statistical theory
for statistical tests based on the bootstrap distribution. By "useful", I
mean a theory that allows one to specify a scientifically interesting null
hypothesis (such as, "An expected value equal to 0") under which the false
alarm rate of a boostrap-p-value-based test can be controlled.

2. The bootstrap distribution has a nice intuitive appeal, because the
procedure to generate it (sampling with replacement) mimicks the sampling
process behind the sampling distribution (which is the ultimate "thing to
get" if you want to quantify the reliability of some quantity). But that is
not a proof of false alarm rate control!

3. I think the bootstrap distribution can be useful in situations where
parametric statistical tests do not exists, but I know of no rigourous
statistical argument to substantiate this claim.

Greetings,

Eric Maris

>
> Yours,
>
> Jan-Mathijs
>
>
> On Oct 20, 2008, at 11:05 AM, Vladimir Litvak wrote:
>
> > Dear Floris and Eric,
> >
> > Parametric tests at scalp level taking into account spatial
> > relationship between sensors can be done in SPM (with RFT correction).
> > That'll require using some low-level functions to convert
> > coefficients to images but in principle shouldn't be that difficult.
> >
> > Best,
> >
> >>
> >> On Mon, Oct 20, 2008 at 10:17 AM, Eric Maris
> >> <e.maris at donders.ru.nl> wrote:
> >>> Dear Floris,
> >>>
> >>>
> >>>
> >>>> I have a question about statistical analysis on the sensor level.
> >>>> I would like to make use of the cluster size thresholding of the
> >>>> clusterrand routine in Fieldtrip. Unfortunately, in the current
> >>>> wrapper, it seems there is no option for a one-sample T-test?
> >>>> There is
> >>>> an activation-baseline test, and a (in)dependent samples test
> >>>> between
> >>>> two conditions, but what I want to do is simply test whether a 14
> >>>> (subjects) x 275 (channels) matrix is different from zero,
> >>>> taking into
> >>>> account the spatial relations between adjacent sensors. (The data
> >>>> points are regression weights from a multiple-regression
> >>>> analysis, so
> >>>> there's no easy way to split it into two parts.)
> >>>> I assume this should be easy to tweak, but I couldn't come up
> >>>> with any
> >>>> smart ideas how to do it.
> >>>> Anyone any ideas?
> >>>
> >>> I'm afraid that I have to disappoint you, Floris. Your null
> >>> hypothesis is a
> >>> typical parametric null hypothesis; the expected value of some
> >>> (matrix-valued) variable being equal to zero. The null hypothesis
> >>> that is
> >>> tested by a nonparametric permutation test is equality across
> >>> experimental
> >>> conditions of the probability distribution from which the
> >>> (condition-specific) data are drawn. Since you have single
> >>> condition only, I
> >>> see no way of applying the theory behind nonparametric
> >>> permutation testing
> >>> (of the type described by Maris & Oostenveld, 2007) to your data.
> >>>
> >>> To solve your problem we need a brilliant theoretical insight.
> >>>
> >>>
> >>> Greetings,
> >>>
> >>> Eric
> >>>
> >>>
> >>>
> >>>
> >>>
> >>>
> >>>>
> >>>>
> >>>> Floris
> >>>>
> >>>> ----------------------------------
> >>>> 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.
> >>>> http://www.ru.nl/fcdonders/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/
> >>> fcdonders/fieldtrip.
> >>>
> >>>
> >>
> >
> > ----------------------------------
> > The aim of this list is to facilitate the discussion between users
> > of the FieldTrip  toolbox, to share experiences and to discuss new
> > archives/fieldtrip.html and http://www.ru.nl/fcdonders/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.