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Hi Sebastian,
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<div class="">I would say that for visualization purposes (and for traditional parametric second-level statistics) you are interested in the variance across your units-of-observation. In this case across subjects. This is indeed what ft_timelockgrandaverage
gives you. If you are into more sophisticated estimates, it smells a bit as if you want to be moving into the direction of mixed-effect models, which are gaining quite a bit of momentum these days. Since I am a bit old-school I have not eaten any cheese from
that (<a href="http://www.dwotd.nl/2008/02/360-daar-heb-ik-geen-kaas-van-gegeten.html" class="">http://www.dwotd.nl/2008/02/360-daar-heb-ik-geen-kaas-van-gegeten.html</a>), so perhaps somebody else wants to chime in here.</div>
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<div class="">Best wishes,</div>
<div class="">Jan-Mathijs</div>
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<div class="">On 26 Sep 2022, at 21:36, Sebastian Neudek via fieldtrip <<a href="mailto:fieldtrip@science.ru.nl" class="">fieldtrip@science.ru.nl</a>> wrote:</div>
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<div class="">Hi all,<br class="">
<br class="">
I am currently writing my master's thesis using FieldTrip and might need a bit of your expertise for a little hurdle I encountered.<br class="">
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First a few words about what I want to do:<br class="">
I have data from a MEG-go/nogo study: There are multiple subjects and multiple trials for each condition. I now want to plot the ERF for each condition averaged across all subjects. But together with the ERF I also want to plot the standard error or variance
or confidence interval or standard deviation. Something like this(Figure 3a):<br class="">
<a href="https://urldefense.com/v3/__https://www.researchgate.net/figure/ERP-results-including-P3-amplitudes-a-Grand-average-and-standard-errors-of-ERP_fig2_327651209__;!!HJOPV4FYYWzcc1jazlU!4AKDCxWgDNOVGlWwimPV3Sc-5suVMj59sPhwC-eHwI7h0FQr10-YxE5fzliZsQft3R0I3s5Swpei12UfNPYgMdNHwshEvUe7t8p0Gw$" class="OWAAutoLink" id="LPlnk347301" previewremoved="true">https://www.researchgate.net/figure/ERP-results-including-P3-amplitudes-a-Grand-average-and-standard-errors-of-ERP_fig2_327651209</a><br class="">
Independent which of these measures I finally use, I need to calculate the variance of the ERF at each timepoint.<br class="">
To do this I first used ft_timelockanalysis to calculate the averages of each subject. ft_timelockanalysis returns not only the average, but also the variance of the ERF. Afterwards I use ft_timelockgrandaverage to calculate the group average of the ERF.<br class="">
<br class="">
And this is where my troubles begin. I get how ft_timelockgrandaverage calulates the new average: It averages over the mean values of the subjects (it also accounts for the degrees of freedom). But for the variance it just calculates the variance of the means.
I thought, it will also account for the variances of each subject.<br class="">
In the extreme case it leads to the following:<br class="">
Imagine you have two subjects and you measure very close averages avg(sub1)=1 and avg(sub2)=1.0001. But their variances are extremly high: var(sub1)=var(sub2)=100. Then the variance calculated by ft_timelockgrandaverage is almost zero, when in reality it should
be something like 100.<br class="">
Maybe this should be noted in ft_timelockgrandaverage, because it can lead to wrong statistics if the user isn't aware of this effect.<br class="">
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Back to my task:</div>
<div class="">This is surely not the variance I want to use for my ERF plots and therefore I searched for a different calculation.<br class="">
I found on wikipedia a formula for so called 'pooled variance' (at the bottom of the page for sample-based statistics):<br class="">
<a href="https://urldefense.com/v3/__https://en.wikipedia.org/wiki/Pooled_variance__;!!HJOPV4FYYWzcc1jazlU!4AKDCxWgDNOVGlWwimPV3Sc-5suVMj59sPhwC-eHwI7h0FQr10-YxE5fzliZsQft3R0I3s5Swpei12UfNPYgMdNHwshEvUeBLHOpZA$" class="OWAAutoLink" id="LPlnk563115" previewremoved="true">https://en.wikipedia.org/wiki/Pooled_variance</a><br class="">
<br class="">
But I am not 100% happy with this pooled variance.<br class="">
First of all the deegrees of freedom is not accounted for. Then there is a different mean calculated than in ft_timelockgrandaverage: The mean is accounting for the number of trials for each subject. I don't know if the different mean is a pro or a con (On
the one hand, means with a higher precisision because of a higher number of trials are weighted higher than means with a lower trial number. On the other hand, each subject on the group should be weighted same).<br class="">
<br class="">
I also found a second formula on stackexchange, which also calculates a variances of variances:<br class="">
<a href="https://urldefense.com/v3/__https://stats.stackexchange.com/questions/300392/calculate-the-variance-from-variances__;!!HJOPV4FYYWzcc1jazlU!4AKDCxWgDNOVGlWwimPV3Sc-5suVMj59sPhwC-eHwI7h0FQr10-YxE5fzliZsQft3R0I3s5Swpei12UfNPYgMdNHwshEvUdcUgTl6A$" class="">https://stats.stackexchange.com/questions/300392/calculate-the-variance-from-variances</a><br class="">
<br class="">
Therefore I am uncertain which formula to use, because as it seems, they differ.<br class="">
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I hope somebody of you is a little more experienced in statistics than I am and can help me out finding the correct or best calculation for this variance. Best case would be if it is already implemented in fieldtrip and I only missed it, but I can also implement
it myself.<span class="Apple-converted-space"> </span><br class="">
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Best,<br class="">
Sebastian<br class="">
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