[FieldTrip] impact of skewed power distributions on data analysis

Tue Dec 13 00:14:56 CET 2016

Dear Teresa,

The power is indeed not normally distributed over time.
A more robust method is to use the median instead of the mean.

-Simon

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2016-12-12 22:39 GMT+01:00 Teresa Madsen <tmadsen at emory.edu>:

> No, sorry, that's not what I meant, but thanks for giving me the
> opportunity to clarify. Of course everyone is familiar with the 1/f pattern
> across frequencies, but the distribution across time (and according to the
> poster, also across space), also has an extremely skewed, negative
> exponential distribution. I probably confused everyone by trying to show
> too much data in my figure, but each color represents the distribution of
> power values for a single frequency over time, using a histogram and a line
> above with circles at the mean +/- one standard deviation.
>
> My main point was that the mean is not representative of the central
> tendency of such an asymmetrical distribution of power values over time.
> It's even more obvious which is more representative of their actual
> distributions when I plot e^mean(logpower) on the raw plot and
> log(mean(rawpower)) on the log plot, but that made the figure even more
> busy and confusing.
>
> I hope that helps,
> Teresa
>
> On Mon, Dec 12, 2016 at 3:47 PM Nicholas A. Peatfield <
> nick.peatfield at gmail.com> wrote:
>
>> Hi Teresa,
>>
>> I think what you are discussing is the 1/f power scaling of the power
>> spectrum. This is one of the reasons that comparisons are made within
>> a band (i.e. alpha to alpha) and not between bands (i.e. alpha to gamma),
>> as such the assumption is that within bands there should be a relative
>> change against baseline and this is what the statistics are performed on.
>> That is, baseline correction is assumed to be the mean for a specific
>> frequency and not a mean across frequencies.
>>
>>  And this leads to another point that when you are selecting a frequency
>> range to do the non-parametric statistics on you should not do 1-64 Hz but
>> break it up based on the bands.
>>
>> Hope my interpretation of your point is correct. I sent in individually,
>> as I wanted to ensure I followed your point.
>>
>> Cheers,
>>
>> Nick
>>
>>
>> On 12 December 2016 at 08:23, Teresa Madsen <tmadsen at emory.edu> wrote:
>>
>> FieldTrippers,
>>
>> While analyzing my data for the annual Society for Neuroscience meeting,
>> I developed a concern that was quickly validated by another poster (full
>> abstract copied and linked below) focusing on the root of the problem:
>>  neural oscillatory power is not normally distributed across time,
>> frequency, or space.  The specific problem I had encountered was in
>> baseline-correcting my experimental data, where, regardless of
>> cfg.baselinetype, ft_freqbaseline depends on the mean power over time.
>> However, I found that the distribution of raw power over time is so skewed
>> that the mean was not a reasonable approximation of the central tendency of
>> the baseline power, so it made most of my experimental data look like it
>> had decreased power compared to baseline.  The more I think about it,
>> the more I realize that averaging is everywhere in the way we analyze
>> neural oscillations (across time points, frequency bins, electrodes,
>> trials, subjects, etc.), and many of the standard statistics people use
>> also rely on assumptions of normality.
>>
>> The most obvious solution for me was to log transform the data first, as
>> it appears to be fairly log normal, and I always use log-scale
>> visualizations anyway.  Erik Peterson, middle author on the poster, agreed
>> that this would at least "restore (some) symmetry to the error
>> distribution."  I used a natural log transform, sort of arbitrarily to
>> differentiate from the standard decibel transform included in FieldTrip as
>> cfg.baselinetype = 'db'.  The following figures compare the 2
>> distributions across several frequency bands (using power values from a
>> wavelet spectrogram obtained from a baseline LFP recorded in rat prelimbic
>> cortex).  The lines at the top represent the mean +/- one standard
>> deviation for each frequency band, and you can see how those descriptive
>> stats are much more representative of the actual distributions in the log
>> scale.
>>
>>
>> 
>> For my analysis, I also calculated a z-score on the log transformed power
>> to assess how my experimental data compared to the variability of the noise
>> in a long baseline recording from before conditioning, rather than a short
>> pre-trial baseline period, since I find that more informative than any of
>> FieldTrip's built-in baseline types.  I'm happy to share the custom
>> functions I wrote for this if people think it would be a useful addition to
>> FieldTrip.  I can also share more about my analysis and/or a copy of the
>> poster, if anyone wants more detail - I just didn't want to make this email
>> too big.
>>
>> Mostly, I'm just hoping to start some discussion here as to how to
>> address this.  I searched the wiki
>> <http://www.fieldtriptoolbox.org/development/zscores>, listserv
>> <https://mailman.science.ru.nl/pipermail/fieldtrip/2006-December/000773.html>
>>  archives
>> <https://mailman.science.ru.nl/pipermail/fieldtrip/2010-March/002718.html>,
>> and bugzilla <http://bugzilla.fieldtriptoolbox.org/show_bug.cgi?id=1574> for
>> anything related and came up with a few topics surrounding normalization
>> and baseline correction, but only skirting this issue.  It seems important,
>> so I want to find out whether others agree with my approach or already have
>> other ways of avoiding the problem, and whether FieldTrip's code needs to
>> be changed or just documentation added, or what?
>>
>> Thanks for any insights,
>> Teresa
>>
>>
>> 271.03 / LLL17 - Neural oscillatory power is not Gaussian distributed
>> across time
>> <http://www.abstractsonline.com/pp8/#!/4071/presentation/24150>
>> Authors**L. IZHIKEVICH*, E. PETERSON, B. VOYTEK;
>> Cognitive Sci., UCSD, San Diego, CADisclosures *L. Izhikevich:* None. *E.
>> Peterson:* None. *B. Voytek:* None.AbstractNeural oscillations are
>> important in organizing activity across the human brain in healthy
>> cognition, while oscillatory disruptions are linked to numerous disease
>> states. Oscillations are known to vary by frequency and amplitude across
>> time and between different brain regions; however, this variability has
>> never been well characterized. We examined human and animal EEG, LFP, MEG,
>> and ECoG data from over 100 subjects to analyze the distribution of power
>> and frequency across time, space and species. We report that between data
>> types, subjects, frequencies, electrodes, and time, an inverse power law,
>> or negative exponential distribution, is present in all recordings. This is
>> contrary to, and not compatible with, the Gaussian noise assumption made in
>> many digital signal processing techniques. The statistical assumptions
>> underlying common algorithms for power spectral estimation, such as Welch's
>> method, are being violated resulting in non-trivial misestimates of
>> oscillatory power. Different statistical approaches are warranted.
>>
>> --
>> Teresa E. Madsen, PhD
>> Research Technical Specialist:  *in vivo *electrophysiology & data
>> analysis
>> Division of Behavioral Neuroscience and Psychiatric Disorders
>> Yerkes National Primate Research Center
>> Emory University
>> Rainnie Lab, NSB 5233
>> 954 Gatewood Rd. NE
>> Atlanta, GA 30329
>> (770) 296-9119
>> braingirl at gmail.com
>> https://www.linkedin.com/in/temadsen
>>
>>
>> _______________________________________________
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>> fieldtrip at donders.ru.nl
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>>
>>
>>
>>
>> --
>> Nicholas Peatfield, PhD
>>
>>
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