[FieldTrip] impact of skewed power distributions on data analysis

Teresa Madsen tmadsen at emory.edu
Mon Dec 12 22:39:03 CET 2016

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,

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>
> 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
> _______________________________________________
> fieldtrip mailing list
> fieldtrip at donders.ru.nl
> https://mailman.science.ru.nl/mailman/listinfo/fieldtrip
> --
> Nicholas Peatfield, PhD
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