# [FieldTrip] Problems with statistics for circular data

Tobias Staudigl tobias.staudigl at uni-konstanz.de
Wed Jan 15 10:19:04 CET 2014

```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.
>
>
> Thomas
>
> Thomas Baumgarten, PhD Student
>
> Institute of Clinical Neuroscience and Medical Psychology, Medical
> Faculty, Heinrich-Heine-University Düsseldorf, Universitätsstraße 1,
> 40225 Düsseldorf, 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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