# [FieldTrip] WPLI statistic, permutation like test??

Matteo Demuru suforraxi at gmail.com
Tue Jun 28 14:46:28 CEST 2011

```Hi,

I have a couple of questions about using the WPLI index to assess the phase
on my MEG data.

The experiment consists of recordings during a mental calculation task: I
have 30 sec in which each subject performed continuously an arithmetic
operation.

It seems to me that WPLI index required more than one trial in order to be
computed. Am I right? (Is this necessary in order to reduce volume
conduction problems?)
I could divide my 30 sec in 5 sec-trials to create my trials, but I was
wandering if this could be a misuse of the WPLI, i.e. WPLI is not
appropriate for my experiment.

I am also interested in assessing the significance of WPLI index, I would
like to gauge the significance per se of my WPLI values.
The idea is to calculate the WPLI distribution under the null hypothesis
(not phase coupling) for each pair of channels in this way:

Example to assess the significance of WPLI value for ch1 vs ch2

1) Calculate the WPLI for ch1 and ch2, this would be the observed WPLI
(WPLI_observed)

2) Randomly permute the ch2 time series

3) Calculate the WPLI for ch1 and ch2 (WPLI_i)

4) Repeat step 2 and 3 (for instance 100 times) in order to create the WPLI_i
distribution

5) Calculate the proportion ( # (WPLI_i  > WPLI_observed)  /  # (WPLI_i  ) )
of WPLI_i which are greater than the WPLI_observed, if this  proportion is
< 0.05 I could say that the WPLI_observed represents a significant degree of
phase, otherwise not.

Does it make sense or is it not the right approach?

Let suppose this is a correct approach, I have two other questions:

First, usually when I compute the WPLI value between two channels I obtain a
number of WPLI values  according to the cross-spectrum times (one WPLI for
each sliding window), in the steps above I am assuming to compute the
average WPLI_observed and the average WPLI_i for each step. Does this raise
any problems?

Second, is it a problem using the same random permutations employed to
obtain ch1-ch2 (WPLI_i distribution) to calculate also the ch1-ch3
(WPLI_i distribution).
This is just an implementatiion question. I would like to know if I could
shuffle the time series of other channels in one step (i.e. for ch1
something like data.trial{other_than_ch1,perm}), and finally extract just
the column relative to ch1 from WPLI matrix.

thanks

Matteo
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