statistic on planar gradients
Eric Maris
e.maris at DONDERS.RU.NL
Mon Mar 8 13:18:08 CET 2010
Dear Michael,
> you suggested to,...
>
> Use the following test statistic at the level of the (_dV,_dH) channel
> pairs: calculate the difference between the experimental conditions of
> the lengths of the trial-averaged vector-valued (_dV,_dH)-signals (J-M
> calls this â€œto Pythagorasâ€). You do this for all channels and all
> time points....
>
> I disagree here, but not for mathematical/stastical reason, rather
> because of neurophysiology and the problem discussed in the thread
> before :
> I think of two conditions that differ not in their amplitudes but have
> completely opposing direction of a dipole (in an identical location),
> then statitsics on raw fields will easily find this effect, but the
> length of the trial averaged vector valued signals will be identical
> (the dipole does not jitter across trials in this example, hence trial
> averaging of vector valued signals doesn't help. The dipole just
> inverts it's orientation across conditions). That's what I meant by
> multivariate statistics. Some importnat information gets lost (and must
> get lost) when going to a non-directional and unsigned quantity to
> test.
My apologies for not having read the thread far enough back in time.
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:
1. 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 “complex planar representation”.
2. 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.)
3. Find the permutation distributions of the (channel,time)-pair-specific complex phase differences, and use these to find an appropriate threshold.
4. Proceed in the same way as for other cluster-based permutation tests.
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.
Best,
Eric
>
> But maybe I simply misunderstood your suggestion altogether??
>
> Michael
>
> ----------------------------------
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> for MEG and EEG analysis. See also
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> http://www.ru.nl/neuroimaging/fieldtrip.
----------------------------------
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. See also http://listserv.surfnet.nl/archives/fieldtrip.html and http://www.ru.nl/neuroimaging/fieldtrip.
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