[FieldTrip] tests of uniformity for circular data (intertrial coherence / phase-locking value)
Pierre Mégevand
pierre.megevand at gmail.com
Wed Sep 25 04:37:50 CEST 2013
Dear Fieldtrip users,
I have a question regarding tests of uniformity for circular data.
In essence, I am looking for a one-sample permutation test of the null
hypothesis that there is no phase concentration at a given electrode and
timepoint, that controls for the repetition of testing over electrodes and
timepoints (family-wise type I error rate).
I am working with intracranial EEG data. If I want to assess which brain
regions respond to an external stimulus, a possible approach is to extract
the high-gamma power for each electrode at each trial following stimulus
presentation, normalize it against a suitable baseline (e.g. before
stimulus presentation), and then compute a one-sample permutation test
based on the tmax statistic. The null hypothesis assessed by this test is
that there is no change in high-gamma power following stimulus
presentation. Such an approach provides strong control for the family-wise
type I error rate (otherwise, the repetition of statistical testing at each
electrode and timeframe would give rise to an unacceptably high risk of
falsely rejecting the null hypothesis) (Groppe et al., Psychophysiology
2011).
Now, I am wondering whether something similar exists for phase
concentration. In my experiment, there is a cue that signals imminent
stimulus presentation (the cue is non-informative as to which condition the
stimulus actually belongs to), and I am looking for signs that phase
concentration (reflected by an increase in the intertrial coherence or
phase-locking value) happened at some electrodes following the cue and
before the actual stimulus was presented. If I have a strong prior
hypothesis on the timing of the effect of the cue (as well as the frequency
band that will undergo phase reset or concentration, and the electrode
location), I can select a timepoint and electrode and use the Rayleigh test
or the omnibus test for circular data (see e.g. Fisher, Statistical
Analysis of Circular Data, 1993; a MATLAB toolbox implementing some of
these tests has been developed:
http://www.mathworks.com/matlabcentral/fileexchange/10676-circular-statistics-toolbox-directional-statistics).
These tests assess the null hypothesis that a sample of circular data (such
as phase angles of brain oscillations) come from a circular uniform
distribution (the alternative hypothesis differs somewhat between these
tests).
But, what if I don't have such a strong a priori hypothesis? Is there a way
for me to compute the intertrial coherence at each timepoint and each
electrode (similar to the high-gamma power), and then perform some sort of
statistical test against a null hypothesis of uniformity, all the while
correcting for multiple comparisons?
Specifically, bearing in mind the one-sample tmax statistic-based
permutation test for changes in high-gamma power mentioned above: is there
a way to design a permutation test for circular data that assesses the null
hypothesis that the data do come from a circular uniform distribution?
I am aware that Fieldtrip includes an option to assess differences in
intertrial coherence across experimental conditions (a 2-sample test), but
here I am specifically looking for a 1-sample test.
Thank you for your thoughts, comments and advice!
Pierre
--
Pierre Mégevand, MD, PhD
Post-doctoral research fellow
Laboratory for Multimodal Human Brain Mapping
Feinstein Institute for Medical Research
Manhasset, NY, USA
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