Activation vs. baseline

Vladimir Litvak litvak at TECHUNIX.TECHNION.AC.IL
Mon Feb 27 18:14:16 CET 2006

Dear Pascal,

At the last SFN meeting Partha Mitra presented a poster with a method for
dealing with exactly this problem. He told me he would put an implementation
on his website. It would be nice if you could incorporate that into
Fieldtrip. Although it has nothing to do with my original problem it can be
helpful for me in other contexts. The abstract is below.




Abstract View  
H.S.Bokil1*; K.Purpura2; D.Thomson3; P.P.Mitra1  
1. Cold Spring Harbor Laboratory, Cold Spring Harbor, NY, USA 
2. Weill Med. Col. of Cornell Univ., New York, NY, USA 
3. Mathematics, Queens Univ., Kingston, ON, Canada 
The spectrum and the coherency are classical measures of temporal structure
of and association between time series. The multitaper method provides
robust estimates of these quantities for noisy and non-stationary time
series that are characteristic of neurophysiological recordings. This method
has recently been shown to be useful in studying working memory and
selective visual attention. However, these studies have raised the important
technical issue of comparison of spectra or coherences from two samples of
unequal sizes, for example when comparing estimates from different
experimental conditions. This is difficult with existing statistical tests
since the bias in the estimates depends on the sample size. 

Here we propose a set of procedures to resolve this issue. Our procedure for
the coherence is based on the previously described quantity
z=(tanh(c)-tanh(d))/sqrt(1/(2m-2)+1/(2n-2)), where c and d are coherence
estimates from 2m and 2n samples respectively. When the number of samples is
large, then under the null hypothesis of equal population coherence, z is
distributed as N(0,1) for a stationary stochastic process. By applying the
two sample Jackknife procedure to z, we derive expressions for the mean and
variance of z, and declare the coherences to be equal if the Jackknife
estimates are consistent with N(0,1). Interestingly, strong inconsistency
between the Jackknife and the normal estimates is therefore diagnostic for
the presence of non-Gaussian behavior. A similar analysis is also derived
for two sample spectra. Finally, we provide application of these methods to
experimental data.
Support Contributed By: R01 MH62528-03, Cold Spring Harbor Laboratory
Citation:H.S. Bokil, K. Purpura, D. Thomson, P.P. Mitra. COMPARING SPECTRA
Viewer/Itinerary Planner. Washington, DC: Society for Neuroscience, 2005.
2005 Copyright by the Society for Neuroscience all rights reserved.
Permission to republish any abstract or part of any abstract in any form
must be obtained in writing from the SfN office prior to publication 

-----Original Message-----
From: FieldTrip discussion list [mailto:FIELDTRIP at NIC.SURFNET.NL] On Behalf
Of Pascal Fries
Sent: Monday, February 27, 2006 6:57 PM
Subject: Re: [FIELDTRIP] Activation vs. baseline

Hi Tom,

> Pascal Fries wrote:
> > OK. I had been asking, because coherence (and also power) 
> have a bias 
> > that is sample size dependent. For those measures, particularly for 
> > coherence, I would suggest to use equal sample sizes.
> Correct me if I am wrong, but this bias is due to the slow 
> convergence of the covariance; with more samples, the 
> covariance converges more (assuming it converges at all).  
> Furthermore it probably converges 'up', so if you have more 
> samples, you'll see (apparently) more power.

I still haven't fully understood the sample size bias of power.
For coherence, the issue is simple to understand. As you write, it has to do
with the slow convergence towards the true value as the sample increases.
But in the coherence case, values will converge "down" towards the true
value, not 'up'. For one trial, coherence is numerically always one and will
then decrease as you add more trials. In the case of a true coherence of
one, it will not decrease and in the case of a true coherence zero, it will
rapidly decrease.

This is one of the most important things on the agenda for the basic
spectral analysis in FieldTrip: To get a good estimate of the coherence bias
and subtract it. Until this is finalized, the safest approach is to trim
datasets before comparison to equal size.

> I have sometimes dealt with this problem in the past by 
> simply z-scoring the volumes afterwards, thus shifting the 
> means back to zero.  But perhaps there are skewness issues as 
> well?  I've mostly done that when playing around with things 
> like overlapping windows; for example, using an active window 
> of 0 to 300 ms and a control window of 0 to 250 ms, you 
> expect a slightly higher power in the active state because of 
> the increase convergence, but then normalizing that spatially 
> can give you an estimate of active areas for that 250-300 ms 
> window.  There may also be problematic beamformer overlap in 
> this case, though, but that can be dealt with too.  Just a thought.

I agree: If sample sizes are not orders of magnitude different, then a
z-transformation can take care of most of the bias.

Best, Pascal

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