[FieldTrip] tests of uniformity for circular data (intertrial coherence / phase-locking value)

[Eelke Spaak]

Dear Pierre,

As you are probably aware, FieldTrip's cluster-corrected statistics
routines rely on permutation of condition labels. If there are no
condition labels, there is basically nothing to permute. So it is not
straightforward to use the default statistics routines for 1-sample
testing.

I think there are three options. First, you could do a 2-sample test
against artificial data. You could generate a data set of the exact
same dimensions as your real data, but with a phase distribution that
is uniform over trials. Then you can use ft_statfun_diff_itc to tell
you whether your observed data has a significantly difference ITC from
this artificial data. Since you know the latter has zero ITC, this
will in effect be a 1-sample test (analogous to doing a paired-sample
t-test against all zero data). At least, I am quite sure that per
time-frequency-channel point the test should be valid, but I am not
entirely sure the cluster correction still is valid with this
approach.

Second, you could generate surrogate data by destroying the ITC in
your observed data. This would entail something like shifting the time
course in each trial by a random amount (with rollover), then
computing the ITC for all points, finding cluster candidates,
computing each cluster's ITC, and adding this to a reference
distribution. Then you apply the same cluster-candidate-finding
algorithm to your observed data and compare the observed clusters'
pooled ITC to your cluster reference distribution. Note that this
essentially means implementing your own cluster permutation routines,
where not the conditions are permuted but the time courses. This is
not a trivial problem, because the neighbourhood structure across
electrodes is typically not regular (time and frequency are easy
because they form straightforward matrices).

Third, perhaps the most elegant, and certainly the easiest option, is
to look at event-related potentials :) If you filter your raw data in
the frequency band of interest (and thus remove the DC component),
then if there is no phase concentration in the data, the averaged ERP
will be zero. If the ERP is significantly non-zero at a given time
point and electrode, this means that there is phase concentration
across trials in the frequency band you filtered in at that point.
Note that for this approach to work, it is probably wise to
(iteratively) filter in relatively narrow frequency bands (using a FIR
filter). This will also allow you to construct a time-frequency plot.

Hope this helps!

Best,
Eelke



On 25 September 2013 04:37, Pierre Mégevand <pierre.megevand at gmail.com> wrote:
> 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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