[Eeglablist] ERSP graphs in microvolts (not in dB)?

[Thomas Ferree]

Zach and Arno,

I have discussed this with a colleague of mine in statistics, and need to
refinemy previous statements:

1. The theory of spectral estimation states that power is chi-square
distributed.
See, for example, Percival and Walden, Spectral Analysis for Physical
Applications,
1998, section 6.6.  (The right skewedness compared to a Gaussian is
intuitive
for this positive-definite quanitity.)

2. The log spectrum does not have an analytical form for its distribution
(at least
not that we know), but it tends to a Gaussian in the limit.  (In effect,
taking the
log compensates for the right skewedness.)  The moments can be computed
analytically and are given in the paper by Bokil et al. (2007).

Note that both the statements apply to statistical estimates of the power,
e.g., averaged over trials.  As sample estimates, the trial-averaged power
values are themselves statististics, and have the above distributions.

Sorry for the confusion,
Tom.

-- 
Thomas Ferree, PhD
Department of Radiology
UT Southwestern Medical Center

On Wed, Sep 17, 2008 at 11:56 AM, Thomas Ferree <tom.ferree at gmail.com>wrote:

>
> The usual thinking is that the log of the power spectrum estimate (whereestimate
> is computed, e.g., as average over trials) is distributed as chi^2,and
> chi^2 approaches Gaussian for many degrees of freedom.
>
> See this paper (section 2.2) for parametric statistical tests
> of differences
> between power spectra:
>
> Bokil H, Purpura K, Schoffelen J-M, Thomson D, Mitra P (2007).  Comparing
> power spectra and
>
> coherences for groups of unequal size.  Journal of Neuroscience Methods
> 159: 337-345.
>
> We have looked at the distribution of some of our data and have found it
> well
> fit by chi^2, but I suspect the result is data set dependent.
>
> --
> Thomas Ferree, PhD
> Department of Radiology
> UT Southwestern Medical Center
>
>
> ------------------------------------------------------------------------------------------------------------
>
> On Tue, Sep 16, 2008 at 2:15 PM, arno delorme <arno at ucsd.edu> wrote:
>
>> Dear Zach,
>>
>> > Thanks for the info - I think a lot of us have been wondering about
>> > this one ( I actually asked pretty much the same question before
>> > your response but it hasn't showed up in the archive yet).  However,
>> > the trouble that I am still having is that I'm wondering what is the
>> > best way to approach this data for (parametric) statistical
>> > analysis.   That is, the default output is in dB which is on a
>> > logarithmic scale and thus not appropriate for parametric stats.
>>
>> Parametric statistics are applicable whenever the data has a
>> probability distribution which is close to gaussian. I do not know if
>> absolute amplitude has a more gaussian distribution than log power.
>> You should test it.
>>
>> > There is the possibility of nonparametric tests, but my options may
>> > be more limited than those of parametric techniques (plus they seem
>> > to be somewhat frowned upon in some circles).
>>
>> Non-parametric ootstrap or permutation test are the norm for single
>> subject analysis. For multi-subject analysis, there are applicable
>> too. If should test if your data is gaussian to apply a parametric test.
>>
>> Best,
>>
>> Arno
>>
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>
>
>
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