<div dir="ltr"><div class="gmail_default" style="font-size:small">Could someone clarify for me the solution for dealing with circular data. Suppose I simple want to calculate the standard deviation of measuring the phase of something. Since the distribution isn't Gaussian, what does one do other than permutation cluster analysis sort of stuff (but not for calculating standard deviation). </div>
<div class="gmail_default" style="font-size:small">Stan</div></div><div class="gmail_extra"><br><br><div class="gmail_quote">On Wed, Jan 15, 2014 at 10:07 AM, <span dir="ltr"><<a href="mailto:Thomas.Baumgarten@med.uni-duesseldorf.de" target="_blank">Thomas.Baumgarten@med.uni-duesseldorf.de</a>></span> wrote:<br>
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<p class="MsoNormal"><span style="color:#1f497d">Dear Tobias,<u></u><u></u></span></p>
<p class="MsoNormal"><span style="color:#1f497d">Thank you for the hint! Indeed, this makes the calculation of the circular difference much easier and the resulting values stay between -pi and pi. Sorry that I didn’t think of this, since the purpose of the
function is rather obvious.<u></u><u></u></span></p>
<p class="MsoNormal"><span style="color:#1f497d"><u></u> <u></u></span></p>
<p class="MsoNormal"><span style="color:#1f497d">Best regards,<u></u><u></u></span></p>
<p class="MsoNormal"><span style="color:#1f497d">Thomas<u></u><u></u></span></p>
<p class="MsoNormal"><span style="color:#1f497d"><u></u> <u></u></span></p>
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<b><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:windowtext">Von:</span></b><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:windowtext"> <a href="mailto:fieldtrip-bounces@science.ru.nl" target="_blank">fieldtrip-bounces@science.ru.nl</a> [mailto:<a href="mailto:fieldtrip-bounces@science.ru.nl" target="_blank">fieldtrip-bounces@science.ru.nl</a>]
<b>Im Auftrag von </b>Tobias Staudigl<br>
<b>Gesendet:</b> Mittwoch, 15. Januar 2014 10:19<br>
<b>An:</b> FieldTrip discussion list<br>
<b>Betreff:</b> Re: [FieldTrip] Problems with statistics for circular data<u></u><u></u></span></p>
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<p class="MsoNormal">Dear Thomas, <br>
<br>
try using circ_dist.m (in the circ_stats toolbox by Berens). <br>
This should solve the circular difference issue.<br>
<br>
all the best, <br>
Tobias<br>
<br>
Am 15.01.2014 09:35, schrieb <a href="mailto:Thomas.Baumgarten@med.uni-duesseldorf.de" target="_blank">
Thomas.Baumgarten@med.uni-duesseldorf.de</a>:<u></u><u></u></p>
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<p class="MsoNormal"><span lang="EN-GB" style="font-size:12.0pt;line-height:115%">Dear FieldTrip users,</span><u></u><u></u></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:
</span><u></u><u></u></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.</span><u></u><u></u></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.</span><u></u><u></u></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.</span><u></u><u></u></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.</span><u></u><u></u></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-size:12.0pt;line-height:115%">Thanks for your help,</span><u></u><u></u></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-size:12.0pt;line-height:115%">Thomas</span><u></u><u></u></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-size:10.0pt;line-height:115%"> </span><u></u><u></u></p>
<p class="MsoNormal"><span lang="EN-GB" style="font-size:10.0pt;line-height:115%"> </span><u></u><u></u></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</span><u></u><u></u></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><u></u><u></u></p>
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<pre>-- <u></u><u></u></pre>
<pre>Dr. Tobias Staudigl<u></u><u></u></pre>
<pre>Fachbereich Psychologie - ZPR<u></u><u></u></pre>
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