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<p class="MsoNormal"><span lang="EN-GB" style="font-size:12.0pt;line-height:115%">Dear FieldTrip users,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-size:12.0pt;line-height:115%">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:
<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-size:12.0pt;line-height:115%">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.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-size:12.0pt;line-height:115%">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.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-size:12.0pt;line-height:115%">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.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-size:12.0pt;line-height:115%">I would greatly appreciate any comments and advice on this matter.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-size:12.0pt;line-height:115%">Thanks for your help,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-size:12.0pt;line-height:115%">Thomas<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-size:10.0pt;line-height:115%"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-size:10.0pt;line-height:115%"><o:p> </o:p></span></p>
<p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt"><span lang="EN-GB" style="font-size:9.0pt;line-height:115%">Thomas Baumgarten, PhD Student<o:p></o:p></span></p>
<p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt"><span lang="EN-GB" style="font-size:9.0pt;line-height:115%">Institute of Clinical Neuroscience and Medical Psychology, Medical Faculty, Heinrich-Heine-University Düsseldorf, Universitätsstraße
1, 40225 Düsseldorf, Germany</span><o:p></o:p></p>
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