# [FieldTrip] Problems with statistics for circular data

Antje Strauss strauss at cbs.mpg.de
Wed Jan 15 16:42:23 CET 2014

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Dear Thomas,

my experience with EEG data is that your resultant vector length will hardly ever exceed 0.45 making the Watson-Williams test unapplicable. But I used a solution suggested by Niko Busch and colleagues in 2009 (J Neuroscience). There, they introduce a measure called "bifurcation index" which you could calculate for each time-frequency bin and then run a fieldtrip style cluster permutation statistic against zero.

Best,
Antje

> 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.
>
>
> 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
>
>
>
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>
>
>
> --
> Dr. Tobias Staudigl
> Fachbereich Psychologie - ZPR
> Postfach ZPR
> 78457 Konstanz
> ZPR, Haus 12
> Tel.: +49 (0)7531 / 88 - 5703
>
>
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--
Antje Strauß, M.A.
Auditory Cognition Research Group
Max Planck Institute for Human Cognitive and Brain Sciences
Stephanstr. 1a - Leipzig, Germany
(p) +49 (0)341 9940 2482
(e) strauss at cbs.mpg.de

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