# [Eeglablist] Non-parametric statistics regarding pooling trials across subject

Zhongxu Liu lzx72 at hotmail.com
Mon Dec 27 11:36:47 PST 2010

```Dear All,

In a study I am trying to test developmental (i.e., age) effect on ERSPs and
ERPs. Although I have more than 100 children tested, the number of
artifact-free trails for each subject is on average only about 20 and with
large variations (ranging from several to several dozens). I can regress
these ERSP/ERP measures on age while control for trial number, however, with
many subjects having very few trials, the regression analysis may be
influenced by those low-trial (consequently, high noise) data points.
Covariating the trial number may not solve the problem (if not adding new
problems).

After reading a previous discussion among Drs. Delorme, Scott, Rousselete,
and Robert (see below), I am thinking whether I can also use a nonparametric
statistical analysis: One option is to pool all the trials from all the
subjects, then, randomly split the trials into psudo Young and Old trials,
and calculate differences on ERSP and ERP measures. Repeat this e.g., 500
times to get null distribution. Then using true age information to split the
trials again into true Young and Old trials, and calculate the ERSP/ERP
differences again. Finally, I can check whether the real age differences
fall within or outside the 95% confidence interval of the null distribution.

The questions are: 1) Because there are 100 subjects, should the results be
generalized to the whole population from which I sampled? 2). Now with each
ERP/ERSP calculation using about 1000 trials (although the trials are from
different subjects), can I believe that the stability of the data can be
improved and I may have better chance to detect significant age effect? 3).
Will there be a difference (theoretically or in terms of statistical power)
if I randomly choose with replacement the psudo Young and Old trials (i.e.,
bootstrapping the pooled trials) instead of using permutation method?

Based on my limited reading, I did not find relevant literature on this kind
use of non-parametric methods. So I would really appreciate if someone can
give me some suggestions.

Have a good holiday!

Zhongxu

On Wed, Nov 18, 2009 at 6:20 PM, <eeglablist-request at sccn.ucsd.edu> wrote:

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> Today's Topics:
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>   1. Re: statistics in EEGLAB (Robert Brown)
>
>
> ---------- Forwarded message ----------
> From: Robert Brown <bobrobbrown at googlemail.com>
> To: Guillaume Rousselet <g.rousselet at psy.gla.ac.uk>, arno delorme <
> arno at ucsd.edu>
> Date: Wed, 18 Nov 2009 12:39:16 +0200
> Subject: Re: [Eeglablist] statistics in EEGLAB
> thank you very much for your responses,
>
> I'll try to proceed with the strategy proposed by myself and supported by
> Scott and Guillaume (1. do the single trial analysis in a single subject. 2.
> look, if and where there is overlap in the effects).
>
> one question remains (just to be sure to be doing the right thing): is the
> eeglab newtimef function in case of condition comparisons providing me the
> required "single subject single trial" analysis? (that is, if the
> alpha-level output is showing me regions where in case of this subject there
> are significant differences between the conditions as evaluated on basis of
> single trials. I could not be sure of this, because the alpha level is also
> computed for the conditions). if not, then can you please lead me to the
> more appropriate way of doing this in eeglab (I know this is possible in
> fieldtrip, but I've already done all the other analysis and preprocessing in
> eeglab).
>
> thank you very much for your time and for your ideas.
>
> best,
> Bob
>
> 2009/11/17 Guillaume Rousselet <g.rousselet at psy.gla.ac.uk>
>
>> Robert,
>>
>> there is no theoretical reason to limit your statistical analyses to group
>> effects. It can be easily argued that you will have actually more power when
>> you do a comparison across 200 trials, rather than across 10 subjects.
>> Chances that a robust effect will occur by chance in 4 subjects are almost
>> null if you have enough trials and a clean signal. So you could do your
>> stats across trials in each subject, show the data for each subject, and
>> then report something like the number of subjects showing a significant
>> effect at any given time point, electrode, or for a given cluster, ICA...
>>
>> I've been exploring the possibilities of taking into account the variance
>> within observers in the following papers:
>>
>> Rousselet, G. A., Husk, J. S., Bennett, P. J., & Sekuler, A. B. (2008). Time
>> course and robustness of ERP object and face differences. *Journal of
>> Vision, 8*(12), 3, 1-18, http://journalofvision.org/18/12/13/,
>> doi:10.1167/1168.1112.1163.
>> Rousselet, G. A., Pernet, C. R., Bennett, P. J., & Sekuler, A. B. (2008).
>> Parametric study of EEG sensitivity to phase noise during face processing.
>> *BMC Neuroscience, 9:98*,
>> http://www.biomedcentral.com/1471-2202/1479/1498/.
>>
>> Best,
>>
>> GAR
>>
>>
>>
>>
>> On 13 Nov 2009, at 18:48, Scott Makeig wrote:
>>
>> I agree. For example, if there are 3 subjects, then simple binomial
>> probability can give no better a result than p <= 12.5%.  However, in the
>> case that each single-subject effect, across single trials, is significant
>> (e.g., at the p < .001% level), a much stronger inference can be derived
>> using reasonable subject distribution assumptions.
>>
>> Scott
>>
>> On Thu, Nov 12, 2009 at 4:03 AM, Robert Brown <bobrobbrown at googlemail.com
>> > wrote:
>>
>>> Dear Arno and All,
>>>
>>> thank you very much for your enlightening response.
>>>
>>> maybe one idea: let's say that I only have 4 subjects. the statistics
>>> based on "subject means" would be unreliable and I would not get any
>>> results. however, it could be that in case of each single subject there is a
>>> significant difference based on trials in the same time window, which would
>>> actually be a strong evidence for differences between the conditions and
>>> which could be written as "in case of each single subject p < .05
>>> (corrected)". I am sorry if this is not right, but I assume that there could
>>> be instances where the group statistics with 3-4 subjects would not show
>>> anything but the single trial statistics would. (good examples of important
>>> studies with so few subjects would be Tong & Engel, 2001 in Nature with 4
>>> subjects fMRI and Resulaj et al., 2009 in Nature with 3 subjects behavior.).
>>>
>>>
>>> to conclude: maybe the single trial statistics would work, if it a) would
>>> be calculated individually for each subject based on only this subjects
>>> single trials and then b) the (time-frequency) regions would be plotted,
>>> where all the subjects have significant differences based on their single
>>> trial analysis.
>>>
>>> thank you for your attention and good luck,
>>>
>>> Bob
>>>
>>> 2009/11/11 Arnaud Delorme <arno at ucsd.edu>
>>>
>>>> Dear Bob,
>>>>
>>>> thanks for the comments. I think you are using the statmode option
>>>> "trial" from the command line. This option is quite experimental. It was
>>>> implemented a while ago and is probably not forward compatible with more
>>>> recent changes. Also, the "statmode", "trials" option (assuming it was
>>>> working) should only be used to plot a single subjects. The reason is based
>>>> on the type of null hypothesis.
>>>>
>>>> When testing with 'statmode', 'subject' for two conditions, the NULL
>>>> hypothesis is: given the subjects I have recorded and given that these
>>>> subjects are a good representation of the general population of all possible
>>>> subjects, there is no difference between the ERP/spectrum/ERSP/ITC between
>>>> the two experimental conditions in the general subject population. Using
>>>> parametric, permutation, or bootstrap statistics (and assumptions) you may
>>>> either accept or reject this hypothesis at a given confidence level.
>>>>
>>>> When testing with 'statmode', 'trial' on a single subject (still two
>>>> conditions), the NULL hypothesis is : given the trials I have recorded and
>>>> given that these trials are a good representation of all the population of
>>>> trials for this subject, there is no difference between the
>>>> ERP/spectrum/ERSP/ITC between the two experimental conditions for this
>>>> subject. Again, using parametric, permutation, or bootstrap statistics (and
>>>> assumptions) you may either accept or reject this hypothesis at a given
>>>> confidence level.
>>>>
>>>> As you can see the two hypothesis are quite different. One makes an
>>>> inference about the population of subjects and the other one about the
>>>> population of trials.
>>>>
>>>> Now if you pool the trials from different subjects and attempt to
>>>> perform statistics, this is going to be more complex. The new hypothesis
>>>> would then be: given the trials I have recorded from my subjects and given
>>>> that these trials are a good representation of all the population of trials
>>>> from the general population of subjects, there is no difference between the
>>>> ERP/spectrum/ERSP/ITC between the two experimental conditions in the general
>>>> population of subjects. But the hypothesis is relatively biased because I
>>>> personally think that all the trials are *not* a good representation of
>>>> all the population of trials from the general population of subjects. The
>>>> trials are a good representation of all the trials from all the subjects
>>>> being presently recorded but not necessarily of the general subject
>>>> population. Therefore the real NULL hypothesis would be : given the trials I
>>>> have recorded from all of my subjects and given that these trials are a good
>>>> representation of all the population of trials from these subjects, there is
>>>> no difference between the ERP/spectrum/ERSP/ITC between the two experimental
>>>> conditions in the recorded subjects. As you see, rejecting the NULL this is
>>>> relatively limited as we care about the general population of subjects and
>>>> not the recorded subjects.
>>>>
>>>> If anybody has some better ideas (or Matlab function) of how to handle
>>>> the subject/trial problem (because it would be nice to include trials in
>>>> statistical analysis in order to make them more powerful), we will take
>>>> them.
>>>>
>>>> Best,
>>>>
>>>> Arno
>>>>
>>>> ps: we will remove the 'statmode', 'trial' option for now.
>>>> pps: for basic inferential statistics, you may also refer to this book
>>>> chapter http://sccn.ucsd.edu/~arno/mypapers/statistics.pdf<http://sccn.ucsd.edu/%7Earno/mypapers/statistics.pdf>
>>>>
>>>> On Nov 11, 2009, at 12:29 AM, Robert Brown wrote:
>>>>
>>>> Dear Arno & others,
>>>>
>>>> this does not seem to be as simple as Arno suggested (but thanks),
>>>>
>>>> 1. I have precomputed the values of these channels (with "savetrials",
>>>> "on")
>>>> 2. these channels all have data
>>>> 3. I can plot the data of the same channels when I use "statmode",
>>>> "subjects"
>>>> 4. I'm using EEGLAB v7.1.3.13b
>>>> 5. I now tried it with v7.1.7.18b and I still get the log of zero error
>>>> (you guys might be interested that in addition I now get, in case of
>>>> permutations and bootstrap, "??? Error using ==> reshape" in
>>>> statcond>surrogate at 438 and statcond at 301 and with this latest version
>>>> the reshape error even happens with the "statmode", "subjects")
>>>>
>>>> thus any other suggestions of what could be happening with my single
>>>> trial analysis in study would be very much appreciated.
>>>>
>>>> thank you very much and take care,
>>>> Bob
>>>>
>>>> 2009/11/11 Arnaud Delorme <arno at ucsd.edu>
>>>>
>>>>> Dear Bob,
>>>>>
>>>>> I think this might be because you are trying to plot ERSP of a channel
>>>>> that contains only 0. This error was also arising in old versions of EEGLAB
>>>>> when masking for significance.
>>>>>
>>>>> Hope this helps,
>>>>>
>>>>> Arno
>>>>>
>>>>>
>>>>> On Nov 7, 2009, at 11:38 AM, Robert Brown wrote:
>>>>>
>>>>>  Hi guys,
>>>>>>
>>>>>> I've been trying to get the study ersp analysis working on single
>>>>>> trials but I've not succeeded.
>>>>>>
>>>>>> in the function "std_readdata" I get the "Warning: Log of zero."
>>>>>> error, which is on the line ersp{c,g} = 20*log10(abs(ersp{c,g})); meaning
>>>>>> that the absolute value at some point is 0.
>>>>>> (This leads to) further errors:
>>>>>>
>>>>>> ??? Error using ==> set
>>>>>> Bad value for axes property: 'CLim'
>>>>>> Values must be increasing and non-NaN.
>>>>>>
>>>>>> Error in ==> caxis at 80
>>>>>>            set(ax,'CLim',arg);
>>>>>>
>>>>>> Error in ==> tftopo at 714
>>>>>> caxis([g.limits(5:6)]);
>>>>>>
>>>>>> I've tried to fix it but I'm not clever enough. any help would be
>>>>>> appreciated.
>>>>>>
>>>>>> thank you so much,,
>>>>>> Bob <ATT00001.txt>
>>>>>>
>>>>>
>>>>>
>>>>
>>>>
>>>
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>>
>>
>>
>> --
>> Scott Makeig, Research Scientist and Director, Swartz Center for
>> Computational Neuroscience, Institute for Neural Computation, University of
>> California San Diego, La Jolla CA 92093-0961, http://sccn.ucsd.edu/~scott<http://sccn.ucsd.edu/%7Escott>
>>  _______________________________________________
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>>
>>
>>
>> ************************************************************************************
>> *Guillaume A. Rousselet, Ph.D.*
>> *
>> *
>> Lecturer
>>
>> Centre for Cognitive Neuroimaging (CCNi)
>> Department of Psychology
>> Faculty of Information & Mathematical Sciences (FIMS)
>> University of Glasgow
>> 58 Hillhead Street
>> Glasgow, UK
>> G12 8QB
>>
>> The University of Glasgow, charity number SC004401
>>
>> http://web.me.com/rousseg/GARs_website/
>>
>> Email: g.rousselet at psy.gla.ac.uk
>> Fax. +44 (0)141 330 4606
>> Tel. +44 (0)141 330 6652
>> Cell +44 (0)791 779 7833
>>
>> *
>> *
>> *"For reasons I wish I understood, the spectacle of sync strikes a chord
>> in us, somewhere deep in our souls. It's a wonderful and terrifying thing.
>> Unlike many other phenomena, the witnessing of it touches people at a primal
>> level. Maybe we instinctively realize that if we ever find the source of
>> spontaneous order, we will have discovered the secret of the universe.*"
>>
>>
>> Steven Strogatz - *Sync* - 2003
>>
>> ************************************************************************************
>>
>>
>>
>>
>>
>
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