[FieldTrip] impact of skewed power distributions on data analysis

Teresa Madsen tmadsen at emory.edu
Mon Dec 12 17:23:34 CET 2016


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
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,

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
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