# [Eeglablist] About ERSP averaging and normalisation

Scott Makeig smakeig at ucsd.edu
Tue Nov 9 14:00:52 PST 2004

```Marco -

You raise an important point. In averaging the ERSPs across subjects, I
think we do want to average the log (e.g., dB) values, since we want to
make statements like, "On average, mu activity was reduced by -12 dB
following the button press,'  Taking the log of the average of the
baseline-normalized single-subject time/frequency images (e.g., after
dividing each by the baseline spectrum for the subject) would be biased
toward larger (log) devations and thus less stable, probably, than
taking the mean of the dB ERSPs.

Again, a multiplicative model in which 1x -> 1/4x requires as much
'effort' as 1x -> 4,x, changes are better represented as in terms of
changes in log power. However, as you point out

llog(mean(x)) ~= mean(log(x))    % !!

Scott

Marco Buiatti wrote:

> 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
>>>>
>>>
>>>
>>>
>>> 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
>>>
>>>
>>>
>> 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
>

```