[FieldTrip] Problems with statistics for circular data

Pierre M├ęgevand pierre.megevand at gmail.com
Wed Jan 15 15:47:30 CET 2014


Dear Thomas,

When the assumptions of the parametric Watson-Williams test aren't met, you
can use non-parametric statistical tests for circular data, such as
Watson's Yr or U2 tests.

The Yr test is implemented in the MATLAB toolbox PhasePACK by Daniel
Rizzuto: cmean_test.m function,
https://github.com/iandol/spikes/tree/master/Various/PhasePACK).

You can find matlab code for the U2 test here:
http://www.mathworks.com/matlabcentral/fileexchange/43543-watsons-u2-statistic-based-permutation-test-for-circular-data.
I programmed this; it runs very slowly, so if anyone is interested in
looking into it I'm sure we could make it much better.

Pierre
--
Pierre M├ęgevand, MD, PhD
Post-doctoral research fellow
Laboratory for Multimodal Human Brain Mapping
Feinstein Institute for Medical Research
Manhasset, NY, USA


On Wed, Jan 15, 2014 at 5:20 AM, <fieldtrip-request at science.ru.nl> wrote:

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>    1. Re: Problems with statistics for circular data (Tobias Staudigl)
>    2. Re: ft_sourcestatistics and sourcegrandaverage    time    series
>       (jan-mathijs schoffelen)
>
>
> ----------------------------------------------------------------------
>
> Message: 1
> Date: Wed, 15 Jan 2014 10:19:04 +0100
> From: Tobias Staudigl <tobias.staudigl at uni-konstanz.de>
> To: FieldTrip discussion list <fieldtrip at science.ru.nl>
> Subject: Re: [FieldTrip] Problems with statistics for circular data
> Message-ID: <52D65288.3070207 at uni-konstanz.de>
> Content-Type: text/plain; charset="iso-8859-1"; Format="flowed"
>
> Dear Thomas,
>
> try using circ_dist.m (in the circ_stats toolbox by Berens).
> This should solve the circular difference issue.
>
> all the best,
> Tobias
>
> Am 15.01.2014 09:35, schrieb Thomas.Baumgarten at med.uni-duesseldorf.de:
> >
> > Dear FieldTrip users,
> >
> > I am working on a set of circular data (phase angles of ongoing
> > oscillations computed via Hilbert transform) and would like to
> > statistically compare two conditions (A,B). For this, I use the
> > circular statistics toolbox for matlab by P. Berens. I worked on this
> > problem from two different angles:
> >
> > 1. First, I tried to directly compare the two conditions via the
> > Watson-Williams two-sample test (function: circ_wwtest).
> > Unfortunately, this didn't work out, since the test requires an
> > average resultant vector length of > 0.45 for n >= 11 entries/
> > subjects, an assumption which is not met by my data.
> >
> > 2. Second, I tried to calculate the angle of difference between the
> > two conditions (angle(A) -- angle(B)) and then used  the one-sample
> > mean angle test (function: circ_mtest) to test if the resulting angle
> > of difference is significantly different from zero. Here, the
> > following problems arise: Since the resulting angles for A and B range
> > from --pi to +pi, there are cases when the subtraction of the two
> > angles results in roughly +2pi or -2pi (e.g. cases where (A = pi) --
> > (B = -pi) = 2pi), resulting in an error from the circ_mtest function.
> > I tried to solve this problem by using a modulus (2pi) operation (i.e.
> > by 'cleaning out' the redundant circumventions while at the same time
> > preserving the angle information), but unfortunately this didn't work
> > out either.
> >
> > The only other option I can think of would be to generate surrogate
> > data (i.e. a matrix with the same dimensions as the matrix with the
> > angles of difference , only filled with zeros) and to apply a
> > cluster-based permutation test (similar to ft_freqstatitics). Although
> > this would take care of my multiple-comparison problem, I am not quite
> > sure if the cluster correction is still valid in this case and if this
> > test would work for circular data.
> >
> > I would greatly appreciate any comments and advice on this matter.
> >
> > Thanks for your help,
> >
> > Thomas
> >
> > Thomas Baumgarten, PhD Student
> >
> > Institute of Clinical Neuroscience and Medical Psychology, Medical
> > Faculty, Heinrich-Heine-University D?sseldorf, Universit?tsstra?e 1,
> > 40225 D?sseldorf, Germany
> >
> >
> >
> > _______________________________________________
> > fieldtrip mailing list
> > fieldtrip at donders.ru.nl
> > http://mailman.science.ru.nl/mailman/listinfo/fieldtrip
>
>
> --
> Dr. Tobias Staudigl
> Fachbereich Psychologie - ZPR
> Postfach ZPR
> 78457 Konstanz
> ZPR, Haus 12
> Tel.: +49 (0)7531 / 88 - 5703
>
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> Message: 2
> Date: Wed, 15 Jan 2014 11:18:53 +0100
> From: jan-mathijs schoffelen <jan.schoffelen at donders.ru.nl>
> To: FieldTrip discussion list <fieldtrip at science.ru.nl>
> Subject: Re: [FieldTrip] ft_sourcestatistics and sourcegrandaverage
>         time    series
> Message-ID: <14425A96-E395-4757-904B-5AFB8FEED3EB at donders.ru.nl>
> Content-Type: text/plain; charset="us-ascii"
>
> Hi Kaelasha,
>
> Sorry for being unclear. You can do something like:
>
> stat = ft_sourcestatistics(cfg, data1, data2, data3, data4, ....), or stat
> = ft_sourcestatistics(cfg, data{:}); where data is a cell-array of
> structures (1 cell for each participant/condition).
>
> Best,
> Jan-Mathijs
>
>
>
>
> On Jan 15, 2014, at 9:14 AM, Kaelasha Tyler wrote:
>
> > Hi Jan-Mathijs,
> >
> > Thanks for this response.
> > I still have a question though.
> > You mentioned that it is not necessary to use ft_sourcegrandaverage to
> perform statistical analysis with source space ERFs across multiple
> participants. However, what you appeared to suggest in your email, does
> appear to still use a grand average, e.g. you wrote:
> >
> > >you can do something like this
> >
> > >cfg = your cfg to ft_sourcestatistics
> > >stat = ft_sourcestatistics(cfg, grandavg{:});
> >
> > Having played around with it a bit more, I am still unclear how to use
> multiple inputs (e.g., multiple subjects source data) when using
> ft_sourcestatistics. I had thought that ft_sourcegrandavarge was a
> necessity.
> > Can you make this a bit clearer?
> >
> > Also, I did go back and use cfg.fixedori='yes' when calling my first
> ft_srouceanalysis and moved also my source.avg.mom data into source.avg.pow
> as you suggested, but this still leaves me with the question above- how to
> use multiple subjects source data in ft_sourcestatistics?
> >
> > Once again, any help from anyone would be much appreciated!
> >
> > Kaelasha
> >
> > From: fieldtrip-bounces at science.ru.nl [fieldtrip-bounces at science.ru.nl]
> on behalf of jan-mathijs schoffelen [jan.schoffelen at donders.ru.nl]
> > Sent: Tuesday, 14 January 2014 5:52 PM
> > To: FieldTrip discussion list
> > Subject: Re: [FieldTrip] ft_sourcestatistics and sourcegrandaverage time
> series
> >
> > Hi Kaelasha,
> >
> > You actually don't need to use ft_sourcegrandaverage if your goal is to
> do statistics. Ft_sourcestatistics in principle knows how to deal with
> multiple inputs.
> > Thus,
> > rather than doing
> >
> > cfg = [];
> > cfg.keepindividual = 'yes';
> > grandavg = ft_sourcegrandaverage(cfg, subjectdata{:});
> >
> > you can do something like this
> >
> > cfg = your cfg to ft_sourcestatistics
> > stat = ft_sourcestatistics(cfg, grandavg{:});
> >
> > Now, the question boils down to 'how to fool ft_sourcestatistics to
> swallow my data?'.
> >
> > The following should more or less work (but requires some manual labour):
> >
> > The time courses at the voxel level are present in source.avg.mom. These
> are most likely 3xN, 3 dipole orientations times N time points. In order to
> reduce this, one can project the orientation along the first pca-axis. This
> can be achieved by a call to ft_sourcedescriptives with
> cfg.projectmom='yes', or by calling ft_sourceanalysis in the first place
> with cfg.fixedori = 'yes'.
> > Then, you could do something like:
> >
> > pow = zeros(size(source.pos,1),length(source.time);
> > pow(source.inside,:) = cat(1,source.avg.mom{source.inside});
> > source.avg.pow = pow;
> >
> > Just to be sure, add a time-axis to the source structure, i.e.
> source.time = tlck.time (tlck being the data structure used to create the
> lcmv-output).
> >
> > I think this should bring you close to doing statistics.
> >
> > Best,
> > Jan-Mathijs
> >
> >
> >
> > On Jan 14, 2014, at 7:19 AM, Kaelasha Tyler wrote:
> >
> >> Hi all,
> >>
> >> Reading through the discussion list, I see others have also had some
> issues with creating grand averaged source space time series (ERFs) and
> subsequent statistical analysis,  but I can't see any solutions....
> >>
> >> Questions:
> >> How can I create time series (ERFs) for grand averaged source space
> data?
> >> And, how can I do cluster analysis on these (yet to be created) grand
> averaged source  space ERFs?
> >>
> >>
> >> I have used ft_SOURCEANALYSIS with method 'lcmv' for individual
> participants to generate source space time series, in data.avg.mom.
> >>
> >> Subsequently I used ft_sourcegrandaverage to combine source space data
> across subjects.
> >>
> >> However my grand averaged source data.avg only contains 'pow' and no
> 'mom'. Eg, no time series for the grand averaged source space data.
> >>
> >> As such, I can not do cluster analysis on grand averaged ERFs in source
> space.
> >>
> >> It appears that ft_sourcestatistics only works with parameters that
> have not more than one value per grid point (e.g. pow, nai etc) and is
> unable to work with ERF time series? Is this true?
> >>
> >> Can any one help with this?
> >>
> >> Much obliged.
> >> Kaelasha
> >>
> >>
> >>
> >>
> >>
> >> _______________________________________________
> >> fieldtrip mailing list
> >> fieldtrip at donders.ru.nl
> >> http://mailman.science.ru.nl/mailman/listinfo/fieldtrip
> >
> > 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
> >
> > http://www.hettaligebrein.nl
> >
> > _______________________________________________
> > fieldtrip mailing list
> > fieldtrip at donders.ru.nl
> > http://mailman.science.ru.nl/mailman/listinfo/fieldtrip
>
> 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
>
> http://www.hettaligebrein.nl
>
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