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<p class=MsoPlainText>Dear Michael,<o:p></o:p></p>
<p class=MsoPlainText><o:p> </o:p></p>
<p class=MsoPlainText><o:p> </o:p></p>
<p class=MsoPlainText>> you suggested to,...</p>
<p class=MsoPlainText>> </p>
<p class=MsoPlainText>> Use the following test statistic at the level of the
(_dV,_dH) channel</p>
<p class=MsoPlainText>> pairs: calculate the difference between the
experimental conditions of</p>
<p class=MsoPlainText>> the lengths of the trial-averaged vector-valued
(_dV,_dH)-signals (J-M</p>
<p class=MsoPlainText>> calls this âto Pythagorasâ). You do this for all
channels and all</p>
<p class=MsoPlainText>> time points....</p>
<p class=MsoPlainText>> </p>
<p class=MsoPlainText>> I disagree here, but not for mathematical/stastical
reason, rather</p>
<p class=MsoPlainText>> because of neurophysiology and the problem discussed
in the thread</p>
<p class=MsoPlainText>> before :</p>
<p class=MsoPlainText>> I think of two conditions that differ not in their
amplitudes but have</p>
<p class=MsoPlainText>> completely opposing direction of a dipole (in an
identical location),</p>
<p class=MsoPlainText>> then statitsics on raw fields will easily find this
effect, but the</p>
<p class=MsoPlainText>> length of the trial averaged vector valued signals
will be identical</p>
<p class=MsoPlainText>> (the dipole does not jitter across trials in this
example, hence trial</p>
<p class=MsoPlainText>> averaging of vector valued signals doesn't help. The
dipole just</p>
<p class=MsoPlainText>> inverts it's orientation across conditions). That's
what I meant by</p>
<p class=MsoPlainText>> multivariate statistics. Some importnat information
gets lost (and must</p>
<p class=MsoPlainText>> get lost) when going to a non-directional and
unsigned quantity to</p>
<p class=MsoPlainText>> test.</p>
<p class=MsoPlainText><o:p> </o:p></p>
<p class=MsoPlainText><span lang=EN-US>My apologies for not having read the
thread far enough back in time.<o:p></o:p></span></p>
<p class=MsoPlainText><span lang=EN-US><o:p> </o:p></span></p>
<p class=MsoPlainText><span lang=EN-US>If you want to identify shifts in dipole
orientation produced by your independent variable, then my proposal doesn´t
work. However, here is an alternative (channel,time)-pair-specific test
statistic that will do the job:<o:p></o:p></span></p>
<p class=MsoPlainText style='margin-left:72.0pt;text-indent:-18.0pt;mso-list:
l0 level1 lfo2'><![if !supportLists]><span lang=EN-US><span style='mso-list:
Ignore'>1.<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
lang=EN-US>Represent the (dV,dH)-pair of planar gradient evoked responses as a
single complex number with dH being the real part and dV the imaginary part.
Call this the </span>“<span lang=EN-US>complex planar representation”.<o:p></o:p></span></p>
<p class=MsoPlainText style='margin-left:72.0pt;text-indent:-18.0pt;mso-list:
l0 level1 lfo2'><![if !supportLists]><span lang=EN-US><span style='mso-list:
Ignore'>2.<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
lang=EN-US>From the complex planar representations of the two experimental
conditions, calculate the complex phase difference between the two. (It may
turn out that you get a more sensitive test if this between-condition complex phase
difference is weighted by the amplitudes of the complex planars in the two
conditions. However this is not central for the main idea.)<o:p></o:p></span></p>
<p class=MsoPlainText style='margin-left:72.0pt;text-indent:-18.0pt;mso-list:
l0 level1 lfo2'><![if !supportLists]><span lang=EN-US><span style='mso-list:
Ignore'>3.<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
lang=EN-US>Find the permutation distributions of the (channel,time)-pair-specific
complex phase differences, and use these to find an appropriate threshold.<o:p></o:p></span></p>
<p class=MsoPlainText style='margin-left:72.0pt;text-indent:-18.0pt;mso-list:
l0 level1 lfo2'><![if !supportLists]><span lang=EN-US><span style='mso-list:
Ignore'>4.<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
lang=EN-US>Proceed in the same way as for other cluster-based permutation
tests.<o:p></o:p></span></p>
<p class=MsoPlainText><span lang=EN-US><o:p> </o:p></span></p>
<p class=MsoPlainText><span lang=EN-US>The main difference between this test,
and the previous one that I proposed, is that in step 2 we calculate the phase
difference instead of the magnitude difference.<o:p></o:p></span></p>
<p class=MsoPlainText><span lang=EN-US><o:p> </o:p></span></p>
<p class=MsoPlainText><span lang=EN-US><o:p> </o:p></span></p>
<p class=MsoPlainText><span lang=EN-US>Best,<o:p></o:p></span></p>
<p class=MsoPlainText><span lang=EN-US><o:p> </o:p></span></p>
<p class=MsoPlainText><span lang=EN-US><o:p> </o:p></span></p>
<p class=MsoPlainText><span lang=EN-US>Eric <o:p></o:p></span></p>
<p class=MsoPlainText><span lang=EN-US><o:p> </o:p></span></p>
<p class=MsoNormal><o:p> </o:p></p>
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
<p class=MsoPlainText><span lang=EN-US><o:p> </o:p></span></p>
<p class=MsoPlainText><span lang=EN-US><o:p> </o:p></span></p>
<p class=MsoPlainText><span lang=EN-US><o:p> </o:p></span></p>
<p class=MsoPlainText><span lang=EN-US><o:p> </o:p></span></p>
<p class=MsoPlainText><span lang=EN-US><o:p> </o:p></span></p>
<p class=MsoPlainText><span lang=EN-US>> <o:p></o:p></span></p>
<p class=MsoPlainText><span lang=EN-US>> But maybe I simply misunderstood
your suggestion altogether??<o:p></o:p></span></p>
<p class=MsoPlainText><span lang=EN-US>> <o:p></o:p></span></p>
<p class=MsoPlainText><span lang=EN-US>> Michael<o:p></o:p></span></p>
<p class=MsoPlainText><span lang=EN-US>> <o:p></o:p></span></p>
<p class=MsoPlainText><span lang=EN-US>> ------------</span>----------------------</p>
<p class=MsoPlainText>> The aim of this list is to facilitate the discussion
between users of</p>
<p class=MsoPlainText>> the FieldTrip toolbox, to share experiences and to
discuss new ideas</p>
<p class=MsoPlainText>> for MEG and EEG analysis. See also</p>
<p class=MsoPlainText>> http://listserv.surfnet.nl/archives/fieldtrip.html
and</p>
<p class=MsoPlainText>> http://www.ru.nl/neuroimaging/fieldtrip.</p>
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<p>----------------------------------</p>
<p>The aim of this list is to facilitate the discussion between users of the FieldTrip toolbox, to share experiences and to discuss new ideas for MEG and EEG analysis.</p>
<p> http://listserv.surfnet.nl/archives/fieldtrip.html</p>
<p> http://www.ru.nl/fcdonders/fieldtrip/</p>