[Eeglablist] About ERSP averaging and normalisation

[Marco Buiatti]

Dear Kazuhiro and Scott,

Scott Makeig wrote:

> Kazuhiro Shishida wrote:
>
>> Dear Marco,
>>
>> Marco Buiatti <marco.buiatti at univ-paris5.fr> wrote:
>>
>>  
>>
>>> 2) The non-linearity of the log causes averages over 
>>> electrodes/subjects to be biased: don't you think this can be 
>>> misleading?
>>>   
>>
>>
>> The average of logarithmic value is the radical of products, for 
>> example,
>> when A is a 1 x n vector,
>> mean((log10(A)),2)=log10(prod(A,2)^(1/n)).
>> Of course, it's different from log10(mean(A,2)).
>> So, it is a problem which is physiologically better. I think 
>> intuitively that the former one is better, but also eager to know the 
>> answer about it.
>>
>>  
>>
> If the process creating the 'spectral perturbation' is multiplicative 
> (acting as a gain control), then using log power measures the amount 
> of 'gain change'. If the process is additive, then log power may not 
> be a useful concept - however, plotting linear power changes tends to 
> discount decreases (here modeled as 'subtractions').
>
> Scott Makeig 

This argument answers my first question: eeglab normalises by dividing 
by the mean over the baseline because it assumes a multiplicative model 
of the spectral perturbation. In my second question, I was not 
suggesting to plot linear power changes (I agree that taking the log is 
more informative). I was suggesting to be careful to average the log 
values  when averaging among electrodes/subjects in tftopo.m, because 
the log could introduce a bias. I wonder whether it would be more 
correct to average the power and then, of course, plot the log.

Marco

-- 
Marco Buiatti

Neurophysique et Physiologie du Systeme Moteur - CNRS UMR 8119
UFR biomedicale Les Saints-Peres
45 rue des Saints-Peres 75270 Paris cedex 06
Tel: +33(0)142862146
Fax: +33(0)149279062
http://www.neurophys.biomedicale.univ-paris5.fr/~buiatti/