# Blog

## Why Robust Statistics?

For my new EEG course in Stuttgart I spend some time to make this gif – I couldn’t find a version online. It shows a simple fact: If you calculate the mean, the breakdown point of 0%. That is, every datapoint counts whether it is an outlier or not.
Trimmed or winsorized means instead calculate the mean based on the inner X % (e.g. inner 80% for trimmed mean of 20%, removing the top and bottom 10% of datapoints) – or in case of winsorizing the mean with the 20% extreme values not removed, but changed to the now new remaining limits). Therefore they have breaking points of X% too – making them robust to outliers.

Fun fact: a 100% trimmed mean is just the median!

As you can see, increasing the amount of outliers has a clear influence on the mean but not the 20% trimmed mean.

One important point: While sometimes outlier removal and robust statistics are very important, and arguable a better default (compared to mean) – you should also always try to understand where the outliers you remove actually come from.

The source code to generate the animation is here:

using Plots
using Random
using StatsBase

anim = @animate  for i ∈ [range(3,20,step=0.5)...,range(20,3,step=-0.5)...]
Random.seed!(1);

x = randn(50);
append!(x,randn(5) .+ i); #add the offset

histogram(x,bins=range(-3,20,step=0.25),ylims=(0,9.),legend=false)

vline!([mean(x)],linewidth=4.)
vline!([mean(trim(x,prop=0.2))],linewidth=4.)
#vline!([mean(winsor(x,prop=0.2))])# same as trimmean in this example

end
gif(anim, "outlier_animation.gif", fps = 4)

## New lab in Stuttgart

I will be starting a new lab on Computational Cognitive Science, next month at University of Stuttgart. I will be working on the connection of EEG and Eye-Tracking, Statistics and methods development. The group is attached to the SimTech and the VIS Stuttgart

## EEG recording chamber

I recently asked on twitter whether people can recommend recording chambers to seat the subject in psychological experiments. I had a tough time googling it, terms that could be helpful in case you are in search for the same thing: Testing chamber, subject booth, audiology.

I got a lot of answers and for the sake of “google-ability” will summarize them here:

• Steve Luck recommends a separated chamber, but highlights importance of air-conditioning due to sweating artefacts
• Aina Puce recommends no chamber, but to sit 2-3m behind the subject and use white noise generators

Regarding actual chambers several commercial vendors were thrown in the ring:

• Studiobricks*
• Whisper Rooms*
• Desone
• Eckel
• IAC Acoustics

* no Farraday cage directly available as far as I know. But check this tweet for a custom solution

I haven’t asked all vendors for a price estimate, but as far as I can tell, with climate control & lighting a ~4m² room costs around 8.000€ – 12.000€ without a Farraday Cage. With a cage I would guesstimate +10.00-15.000€ but I actually don’t really know.

## Comparing Manual and Atlas-based retinotopies; my journey through fmri-surface-land

PS: For this project I moved from EEG to fMRI, and in this post I will sometimes explain terms that might be very basic to fMRI people, but maybe not for EEG people.

I want to investigate cortical area V1. But I don’t want to spend time on retinotopy during my recording session. Thus I looked a bit into automatic methods to estimate it from segmented (segment = split up in WhiteMatter/GrayMatter+extract 3D-surfaces from voxel-MRI and also inflate them) brains. I used the freesurfer/label/lh.V1 labels and the neurophythy/Benson et al tools . The manual retinotopy was performed by Sam Lawrence using MrVista. And here the trouble begins:

The manual retinotopy was available only as a volume (voxel-file, maybe due to my completly lacking mrVista skills. I should look into whether I can extract the mrVista mesh-files somehow), while the other outputs I have as freesurfer vertex values, ready to be plotted against the different surfaces freesurfer calculated (e.g. white matter, pial (gray matter), inflated). Thus I had to map the volume to surface. Sounds easy – something that is straight forward – or so I thought.

After a lot of trial&error and bugging colleagues at the Donders, I settled for the nipype call to mri_vol2surf from freesurfer. But it took me a long time to figure out what the options actually mean. This answer by Doug Greve was helpful (the answer is 12 years old, nobody added it to the help :() (see also this answer):

It should be in the help (reprinted below). Smaller delta is better
but takes longer. With big functional voxels, I would not agonize too
much over making delta real small as you'll just hit the same voxel
multiple times. .25 is probably sufficient.

doug

--projfrac-avg min max delta
--projdist-avg min max delta

Same idea as --projfrac and --projdist, but sample at each of the
points    between min and max at a spacing of delta. The samples are then
averaged    together. The idea here is to average along the normal.

The problem is that you have to map each vertex to a voxel. So in this approach you take the normal vector of the surface (e.g. from white matter surface), check where it hits the gray matter, sample ‘delta’ steps between WM (min) and GM (max), and check which voxels are closest to these steps. The average value of the voxels is then assigned to this vertex.

I will first show a ‘successful subject before I dive into some troubles along the way.

Overall a good match I would say, generally benson & freesurfer have a good alignment (reasonable), the manual retinotopy is larger in most subjects. This might also be due to the projection method (see below)

Initially I tried projection withour smoothing, see the results below. I then changed to a smooth of 5mm kernel with subsequent thresholding (for sure there is probably a smarter way).

It is pretty clear that in this example the fit of manual with automatic tools is not very good. My trouble is now that I don’t know if this is because of actual difference or because of the projection.

Next steps would be to double check everything in voxel land, i.e. project the surface-labels back to voxels and investigate the voxel-by-voxel ROIs.

## EEG/ERP rounding event latencies

22.10.2019 Edit: Thanks Matt Craddock, I understand the source of the problem better. He mentioned that this should not occur if the amplifiers record the triggers as trigger channels (before converting it to events). And mentions that this could happen through downsampling. Indeed after checking in the dataset I used it was downsampled from 1024 to 512Hz. This made many eventlatencies ~ X.50001, which will be uprounded with round and floored with floor. This gives some context to the problem.
Full discussion on twitter

TLDR; EEGlab allows for non-integer event latencies (in units of samples). Eeglab chose floor(latency), while others e.g. unfold & fieldtrip choose round(latency) to round the latency to samples. This leads to differences between toolboxes, in my example of up to 1.5µV (or ~25% ERP magnitude). Importantly, this probably does not introduce bias between conditions

This is an ERP, actually its two ERPs. One is calculated using the “unfold” toolbox and one using eeglab’s pop_epoch function

If you look very closely, you can see that they are not identical, even though they should be. So – whats the difference?

It turns out that EEGlab saves event latencies in samples (e.g. stimulus is starting at sample 213), but also allows non-integer latencies (e.g. stimulus is starting between 212 and 213, to be exact: at sample 212.7). This makes sense, i.e. if your EEG sampling resolution is 100Hz you might know your stimulus onset with higher precision and not in 10ms bins. But in order to get ERPs we have to “cut” the signal at the event onset. EEGlab uses “floor” for this and rounds the stimulus onset from 212.7 to sample 212. Other toolboxes (unfold / fieldtrip) use “round”, thus the event would start at sample 213.

It turns out that in the example you see above, this introduces a difference between the two ERPs of 0.5µV (!) thats around 8% of the magnitude.

This is just a random example I stumbled upon. With lower sampling rates, this effect should increase. Indeed, downsampling to 128 Hz gives us a whopping difference of 1.5µV.

#### Floor vs. round (vs. others?)

The benefit of floor, at least the one I can think of, is that it would never shift the onset of a stimulus in the future. That is, it is causal. Possibly there are other benefits I am not aware of.

The benefit of round is that it more accurately reflects the actual stimulus onset. Possibly there are other benefits I am not aware of

Given that we mostly use acausal filtering anyway, I think the causal benefit is not very strong.

There is yet another alternative: a weighted average between samples. We could “split” the event onset to two samples, i.e. if we want the instantaneous stim-onset response, and stim onset is at sample 12.3, then sample 12 should be weighted 30% and sample 13 by 70%. I have to explore this idea a bit more, but I think its very easy to implement in unfold and test. But this for a new blogpost.

## The big picture

In the fMRI community there are papers from time to time reporting that different analysis tools (or versions) lead to different results. I am not aware of any such paper in the EEG community (if you know one, let me know please!) but I think it would be nice if somebody would do such comparisons.

I currently do not forsee if such an event-latency-rounding difference could possibly introduce bias in condition differences. But I forsee that changing it will be difficult for the EEGlab developers, as “floor” has been around for a very long time in eeglab.

## Code

Note that I did not use simulation here (but could have, it should be straight) but I cannot publicly share the data at this point in time.

load('EEG_subj8_inkl_ufresult.mat')
%%
%EEG = pop_resample(EEG,128);
timelimits = [-.3 .5];
EEG = uf_designmat(EEG,'eventtypes','stimulus','formula','y~1');
%deconv based "round" analysis
EEG = uf_timeexpandDesignmat(EEG,'timelimits',timelimits);
EEG = uf_glmfit(EEG,'channel',63);

%eeglab based "floor" analysis
EEGe = pop_epoch(EEG,{'stimulus'},timelimits);

ufresult = uf_condense(EEGe);
%% ERP plot
figure
plot(ufresult.times,mean(EEGe.data(63,:,:),3)) %floor
hold on
plot(ufresult.times,ufresult.beta(63,:,1)) %round
xlim(timelimits)
xlabel('time [s]')
ylabel('ERP [µV]')
box off
export_fig erp.png -m3 -transparent
%% difference plot
figure
title('Diff "floor"-"round"')
plot(ufresult.times,mean(EEGe.data(63,:,:),3)-ufresult.beta(63,:,1)) %floor-round
xlim(timelimits)
xlabel('time [s]')
ylabel('ERP [µV]')
box off
export_fig diff.png -m3 -transparent


## EEG / ERP Lecture

I just gave my lecture at the Donders Toolkit. Many cool and interesting questions! I wish I had two hours, I had to skip some things I was excited about in favour of solid basics.

Find the slides here as pdf (5 mb) or pptx (23 mb).

In case you are interested in other EEG slides, here are slides on overlap correction (deconvolution) and non-linear modeling (pptx, 8mb), an introduction to linear models (pptx, 50mb), and slides on multiple comparison corrections (pptx, 5mb)

Can’t give a proper license unfortunately, as some slides are based on old Donder Toolkit Slides, handed down from the years. All other authors I stole slides should be acknowledge, hope I did not forget something. Do as you wish with the slides. May the copywrite gods see favourable on our educator souls

## Electrode drift in EEG

I coudn’t find an image of electrode drift for my slides, so here I quickly generated one. The only fancy thing is the usage of datetime to have minutes on the x-axis (I also made this post so I don’t forget this trick ;))

Thanks to Anna Lisa Gert for this dataset

% Load Data
% Load filtered data (takes 35min to filter...)
%%
% Convert time to actual time
timesnew = datetime(EEG.times/1000,'ConvertFrom','epochtime','Epoch','2000-01-01');
% select random channels
chix = [5,63,27];

% Plot the unfiltered data
plot(timesnew,EEG.data(chix,:)')
% Make the plot beautiful
datetick('x','MM','keeplimits','keepticks') % only show minutes
xlabel('time [min]')
ylabel('voltage [µV]')
legend({EEG.chanlocs(chix).labels},'Location','East')
box off
title('EEG Electrode Drift (DC Amplifier, avg ref)')
set(gca,'fontsize', 14) % for a presentation
set(gca, 'FontName', 'HelveticaNeueLT Pro 45 Lt')
%%
% Convert again because data have been resampled
timesnew = datetime(EEG_filt.times/1000,'ConvertFrom','epochtime','Epoch','2000-01-01');

plot(timesnew,EEG_filt.data(chix,:)')

datetick('x','MM','keeplimits','keepticks')
xlabel('time [min]')
ylabel('voltage [µV]')
legend({EEG.chanlocs(chix).labels})
box off
title('EEG Electrode Drift (avg ref, 0.1Hz filter)')
set(gca,'fontsize', 14) % for a presentation
set(gca, 'FontName', 'HelveticaNeueLT Pro 45 Lt')


## A (short) laypersons summary

TLDR; Using our data/paper you can find out how well your eye tracker is doing in measuring your favourite eye movement

This newly published paper is open access and I share first co-author ship with the amazing Katharina Groß! In addition this project was done together with Inga Ibs and Peter König: A new comprehensive eye-tracking test battery concurrently evaluating the Pupil Labs glasses and the EyeLink 1000

We move our eyes about four times per second, which is more often than our heart beats! Many studie show that these eye movements are a window into our minds (e.g. König et al. 2017) and are commonly used for basic research, marketing research and clinical assesments.

Even though eyetrackers are so commonly used and so powerful, they are rarely tested for how well they perform besides the manufacturers. Even more critical, no test battery existed before we set out on this project. Together with Katharina Groß (and Inga Ibs and Peter König) we developed a new eye tracker test battery which included most of the typically studied eye movements.

We chose to test two popular eye trackers concurrently: The Eyelink 1000 and the Pupil Labs glasses. The former is the working horse of eye movement research (release 2005), the latter the open hardware/source innovator (release 2014).

Our study reveals some strengths and some weakenesses for both eye trackers, but also of our newly proposed test battery. The results are numerours, so I will only depict two tasks:

## Take home

• Eye tracking scientists need information about the reliability and performance of their equipment to make informed decisions
• Every eye movement has their own parameters to check for, e.g. pupil dilation has different requirements to an eye tracker than microsaccade research
• Eyelink did not reach the promised accuracy (we really tried, see comments in this link)

That concludes this short laypersons summary. If you have any question feel free to comment here, write me, Katharina Groß, or any of my other co-authors. (paper doi: https://doi.org/10.7717/peerj.7086 )

## Brain Art

I submitted this triptychon to the OHBM brain-art competition 2019. I used mouse myelin stains from the Brain Architecture Project and generated Rohrschach-Like creatures. I quite like how it turned out and I definitely want to do more in the future. I especially found the Allen Brain Atlas’ developmental mouse stains very cool – lots of potential there.

If you are interested in other art pieces related to neuroscience feel free to check out my thesis-art collection – one piece for each student I supervised.

Thanks to Ella Bosch & Anna Gert for latin & design advice!

## Threshold Free Cluster Enhancement explained

#### The multiple comparison problem

In neuroimaging analysis one often is confronted with many electrodes/voxels and many timepoints, and often performs a statistical test on each of these electrode/timepoint combinations. This leads to a massive multiple comparison problem, as the probability to find a false positive is greatly enhanced. In the following example we assume independence of all data points . For instance with only 10 electrodes/voxels and 10 timepoints and an alpha of 0.05, the probability for a false positive is:

$$p(significance^*|H_0) = 1-(1-0.05)^{10*10}=99.4$$

*significance of at least one sample

But electrodes/voxels and timepoints usually are not independent. Contrary, data is rather smooth over electrodes, voxels and time. Therefore, by combining data points close in space (electrodes / voxels) and time using so-called cluster tests, one can try to partially circumvent this problem.

For the IICCSSS Summer School I made some slides explaining multiple comparison correction (link to slides, pptx), including Threshold Free Cluster Enhancement (TFCE). I explained cluster permutation tests in an earlier blog post, which you might want to read before this one.

#### Why TFCE and not cluster permutation tests?

In order to use cluster permutation tests, one typically first calculates some kind of statistics, in our example student t-values for each datapoint over subjects (or trials for single subject analyses). The one has to specify a cluster-threshold which defines the clusters. This threshold might miss broad but “weak” clusters, and focus only on “strong” but peaky clusters.

#### Threshold Free Cluster Enhancement

The intuition of TFCE is that we are going to try out all possible thresholds and see whether a given time-point belongs to a significant cluster under any of our set of cluster-thresholds. Instead of using cluster mass, we will use a weighted average between the cluster extend (e, how broad is the cluster, i.e. how many connected samples) and the cluster height (h, how high is the cluster, i.e. how large is the t-value / the evidence for an effect) according to the formula:

$$TFCE = \int_h e(h)^Eh^Hdh$$

for this blogpost, I will put the weights for the extend E and for the height H to 1 (therefore height ‘counts’ the same as width). The usual defaults are E=0.5 and H=2.

As you can see we use a discrete sum, approximating the integral from above. Another difference between TFCE and cluster permutations, is that you generate a TFCE value for each sample.

For instance a hypothetical t-value of 3 (red square in the above animation) is boosted by belonging to a cluster and might receive the TFCE value of 10. The resulting TFCE values can be thought of as a local scaling according to the “clusterdness” of a sample. Note that local minima and maxima stay at the same spot, this is different to a smoothing operation which could move the location of maxima and minima in time or space.

Because we calculated a TFCE value for each sample, we can also calculate a p-value for each sample. In order to get the p-values, we use the same trick wie used with cluster permutation test: the permutation part. We permute conditions (building the $H_0$), calculate the TFCE values for the permutated set, and take the max(TFCE) over all time points and electrodes/voxels. Our observed TFCE value then is either likely or unlikely given our empirical distribution of max TFCE values (under the $H_0$). But note that the interpretation is not that of a typical p-value at an electrodes/voxel!.

#### Interpretation of significant TFCE

I admit I made the following mistake before, it is a very convenient and easy mistake to make: As an example, let’s observe a significant sample e.g. at 100ms, using the TFCE procedure. This does not mean that the sample at 100ms shows a significant effect. It only means, that there exist at least one cluster-threshold (remember we tested all of them), where this sample belongs to a significant cluster. In other words, samples can be pushed to significance solely by being close to a “truely significant” cluster, without showing evidence by themselves to be significant.

I found this pretty confusing. But in practice it is important: Because we don’t know which samples make a cluster a significant one (all of them? half of them? only a single sample?) we cannot say much about the single sample, only about the cluster.

So, in practice what we do is that we look and report the p-values, but in addition make a descriptive statement on the cluster extend. For instance, you could argue that the t-values that you put in TFCE (or cluster permutation) are very much compatible with an effect from X ms to Y ms. Similar statements are also recommended on the fieldtrip site or in this recent paper by Jona Sassenhagen 2018.

Don’t write: “We found a significant cluster starting from 100ms to 200ms with a median effect of 5µV [3.5, 4.7µV].” or even “Conditions differed significantly from 100ms to 200ms (multiple comparison corrected)”.
Write: “We found a significant difference between conditions. The difference was driven by an effect from 100ms to 200ms with a median effect of 5µV [3.5, 4.7µV] .” or “We found a significant cluster, most compatible with an effect from 100ms to 200ms with a median effect of 5µV [3.5, 4.7µV] “.

Dont write: “At t=125ms the conditions differed significantly (TFCE correction for multiple comparisons) with a median effect of 5µV [3.5, 4.7µV] “
Write: “We found significant difference between conditions (TFCE correction for multiple comparisons). This difference was driven by a cluster starting at 125ms with a median effect of 5µV [3.5, 4.7µV] .”

These messages are much less snappy, sexy, short or easy to understand. The important bit is to signal to the reader that the cluster permutation test does not state significance about a single timepoint or electrode/voxel, but only indicates a significant difference somewhen/re between your conditions.

This problem has been recently discussed on twitter. One proposed alternative is All-Resolution-Inference. There is a barebone R-implementation in the hommel package and I would be interested in translating it to matlab to be readily usable with cluster permutation for EEG data.

Thanks for personal discussions (these are not endorsements, all mistakes in this blogpost are mine!) with Eelke Spaak, Robert Oostenveld, René Scheeringa, Olaf Dimigen & Phillip Alday + twitter interactions with Guillame A Rousselet, Cyril Pernet, Thomas Nichols and Martin Hebart. Thanks to Anna Lisa Gert for critical comments on this blogpost.

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