# [FieldTrip] Spike-Field-PLV z-scoring and comparison between three conditions of unequal sample sizes

Hähnke, Daniel daniel.haehnke at tum.de
Mon Nov 7 14:49:35 CET 2016

```Dear FT community,

I’m currently working on spike and LFP data from a behavioural experiment that contained three different stimulus conditions. The conditions were unequally distributed across trials: condition A was in 60 % of trials and conditions B and C each in 20 % of trials.

I want to compare the spike-field PLV between the conditions using a z-scoring approach similar to Buschman et al. 2012, Neuron (http://download.cell.com/neuron/pdf/PIIS0896627312008823.pdf). In that paper they shuffle the trial associations between spike trials and LFP trials to generate a null distribution from which they compute the z-score.

Since I have unequal number of trials across conditions, I also need to equalise the number of spikes across conditions. There are two methods I used to try to accomplish this.

Method 1:
1. Within each condition, shuffle the trial association between spike trials and LFP trials (this is for the null distribution). Do this e.g. 100 times. Compute STS.
2. From each trial shuffle (see 1.) use a random subset of spike phases (matched to the condition with the lowest number of spikes) to compute the PLV. Do this random subsampling e.g. 1000 times.
3. For each trial shuffle  (see 1.) average across subsamples (see 2.).
4. Compute z-score from the trial shuffles' subsampling-average (see 3.), by computing mean and SD across the trial shuffles’ subsampling averages.

Method 2:
1. Within each condition, use a random subset of trials (matched to condition with lowest number of trials). Do this e.g. 1000 times.
2. For each subsample (see 1.)  shuffle the trial associations between spike trials and LFP trials. Do this e.g. 100 times. Compute STS and PLV.
3. For each trial-subset (see 1.) compute z-score by using SD and mean across trial shuffles (see 2.).

Now I see that for method 1, there is a lower SD for condition A, which is why I get higher z-scores. Using method 2 I get unlikely low z-scores.

Despite the differences in the steps, there are also the following differences in the two methods.
In method 1 I shuffled the spike trains so that they can also be referred to an LFP trial that didn’t have any spikes (i.e. I didn’t limit LFP trials to only trials in which the units were recorded). This of course gives condition A a much bigger “shuffling pool” than the other two conditions. In method 2 I only shuffled within the LFP trials that actually also had spikes.
Another difference is that in method 2, the spike numbers are only very similar but not equal, since I only equalised the trial numbers.

Is there another approach to accomplish what I am looking for? Basically, I want to reduce PLV bias by equalising the spike numbers and I also want to normalise the PLV.
I could imagine that limiting the “shuffling pool” in method 1 would maybe equalise the conditions better, but I’m not sure whether the general approach is statistically sound.

It would be great if someone could comment on the methods above and/or propose another method (e.g. would bootstrapping be alright for the generation of the null distribution?).

Best wishes,

Daniel
--
Daniel Hähnke
PhD student

Technische Universität München
Institute of Neuroscience
Translational NeuroCognition Laboratory
Biedersteiner Straße 29, Bau 601
80802 Munich
Germany

Email: daniel.haehnke at tum.de
Phone: +49 89 4140 3356

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