# Comparing conditions **URL:** \ **Category:** Mailing List Archive (read-only)\ **Tags:** list-archive\ **Created:** [September 29, 2008, 10:28am UTC](https://mne.discourse.group/t/comparing-conditions/64 "2008-09-29T10:28:24Z")\ **Posts on this page:** 14\ **Page:** 1
**Author:** ![system](https://global.discourse-cdn.com/free1/uploads/mne/original/1X/85cc6bd2b69cb698a166dc6d880fb550510d0144.jpeg) [@system](https://mne.discourse.group/u/system)\ **Post date:** [September 29, 2008, 10:28am UTC](https://mne.discourse.group/t/comparing-conditions/64/1 "2008-09-29T10:28:24Z")
Hi there, I have a question regarding how best to statistically compare two conditions. So far I have only being comparing between 2 conditions using ROIs and comparing current estimates over time. However, I'd also like to see the difference between two conditions across the whole brain. I was wondering what the best approach to this was (Ideally ending up with a dSPM map of condition1 - conditon2). Any help on this would be appreciated Thanks, Alex Clarke ---
**Author:** ![system](https://global.discourse-cdn.com/free1/uploads/mne/original/1X/85cc6bd2b69cb698a166dc6d880fb550510d0144.jpeg) [@system](https://mne.discourse.group/u/system)\ **Post date:** [September 29, 2008, 2:45pm UTC](https://mne.discourse.group/t/comparing-conditions/64/2 "2008-09-29T14:45:05Z")
Why not first subtract one average response from the other and then localize? ---
**Author:** ![system](https://global.discourse-cdn.com/free1/uploads/mne/original/1X/85cc6bd2b69cb698a166dc6d880fb550510d0144.jpeg) [@system](https://mne.discourse.group/u/system)\ **Post date:** [September 29, 2008, 3:19pm UTC](https://mne.discourse.group/t/comparing-conditions/64/3 "2008-09-29T15:19:07Z")
Because you are distorting the dipolar topographies when you do a subtraction at the sensor level. The resulting data is likely contain field patterns which do not relate to the leadfields of the actual sources that gave rise to the data. Thus, any source reconstruction which relies on lead field models, i.e. minimum norm, will give spurious results. -Padraig Yury Petrov wrote: ---
**Author:** ![system](https://global.discourse-cdn.com/free1/uploads/mne/original/1X/85cc6bd2b69cb698a166dc6d880fb550510d0144.jpeg) [@system](https://mne.discourse.group/u/system)\ **Post date:** [September 29, 2008, 3:33pm UTC](https://mne.discourse.group/t/comparing-conditions/64/4 "2008-09-29T15:33:20Z")
I didn't understand Padraig's arguments. Minimum norm is a linear method. This means that the same as for the forward matrix the inverse matrix is calculated irrespective of the actual signals measured, except for the noise covariance term. So if you add the noise covariance matrices for the two conditions and feed the resulting "difference" covariance matrix to the inverse routine, it will only change the signal to noise ratios in the trivial way. But the matrix will remain essentially the same, and the topography of the solution should not be "distorted". ---
**Author:** ![system](https://global.discourse-cdn.com/free1/uploads/mne/original/1X/85cc6bd2b69cb698a166dc6d880fb550510d0144.jpeg) [@system](https://mne.discourse.group/u/system)\ **Post date:** [September 29, 2008, 4:02pm UTC](https://mne.discourse.group/t/comparing-conditions/64/5 "2008-09-29T16:02:48Z")
Not necessarily - the sensors pick up signals from multiple generators following the superposition principle. This basically is the sum of the products leadfield L\_ij times dipole moment p\_j plus noise forming the magnetic induction B\_i at sensor i B\_i = L\_ij \*p\_j + n If you subtract two field B1 and B2 and they share a common generator - this one is excluded in sensor space. In theory this works perfectly well in absence of noise. Practically speaking this concept works pretty good for certain EEG components like the ERN which is the difference between incorrect and correct responses. "Distortions" usually come from the noise term and generators not being active in both conditions, or differently active in both conditions. Additionally you have source model related distortions e.g. regularisation. So it depends mostly on your signal to noise ratio if it is wise to subtract fields in sensor space or not. It also depends on how accurate you can position the MEG helmet in headframe coordinates across conditions, subjects, ... If that can not be done reliably don't even think about subtraction in sensor space. You just add additional variance to your data. -Christian > Because you are distorting the dipolar topographies when you do a > subtraction at the sensor level. The resulting data is likely > contain field patterns which do not relate to the leadfields of the > actual sources that gave rise to the data. Thus, any source > reconstruction which relies on lead field models, i.e. minimum > norm, will give spurious results. > > -Padraig > > Yury Petrov wrote: > > > Why not first subtract one average response from the other and > > then localize? > > > > > Hi there, > > > > > > I have a question regarding how best to statistically compare > > > two conditions. So far I have only being comparing between 2 > > > conditions using ROIs and comparing current estimates over time. > > > However, I'd also like to see the difference between two > > > conditions across the whole brain. I was wondering what the best > > > approach to this was (Ideally ending up with a dSPM map of > > > condition1 - conditon2). > > > > > > Any help on this would be appreciated > > > > > > Thanks, > > > > > > Alex Clarke > > > \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ > > > Mne\_analysis mailing list > > > Mne\_analysis at nmr.mgh.harvard.edu > > > [Mne\_analysis Info Page](https://mail.nmr.mgh.harvard.edu/mailman/listinfo/mne_analysis) > > > > \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ > > Mne\_analysis mailing list > > Mne\_analysis at nmr.mgh.harvard.edu > > [Mne\_analysis Info Page](https://mail.nmr.mgh.harvard.edu/mailman/listinfo/mne_analysis) > > -- > P?draig Kitterick > Graduate Student > Department of Psychology > University of York > Heslington > York YO10 5DD > UK > > Tel: +44 (0) 1904 43 2883 > Email: p.kitterick at psych.york.ac.uk > > \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ > Mne\_analysis mailing list > Mne\_analysis at nmr.mgh.harvard.edu > [Mne\_analysis Info Page](https://mail.nmr.mgh.harvard.edu/mailman/listinfo/mne_analysis) Christian Wienbruch University of Konstanz Clinical Psychology Fach D27 78457 Konstanz Christian.Wienbruch at uni-konstanz.de -------------- next part -------------- An HTML attachment was scrubbed... URL: [http://mail.nmr.mgh.harvard.edu/pipermail/mne\_analysis/attachments/20080929/5985a7a3/attachment.html](http://mail.nmr.mgh.harvard.edu/pipermail/mne_analysis/attachments/20080929/5985a7a3/attachment.html) ---
**Author:** ![system](https://global.discourse-cdn.com/free1/uploads/mne/original/1X/85cc6bd2b69cb698a166dc6d880fb550510d0144.jpeg) [@system](https://mne.discourse.group/u/system)\ **Post date:** [September 29, 2008, 4:09pm UTC](https://mne.discourse.group/t/comparing-conditions/64/6 "2008-09-29T16:09:56Z")
If one cannot assume similar source configurations in the two conditions to be compared, presuming that any noise is constant and equivalent, is it safe to say that subtraction would result in distorted data ('distorted' not the best choice of words but my vocabulary has failed me today!), or at least data which would be difficult to interpret? Thanks, P. Christian Wienbruch wrote: ---
**Author:** ![system](https://global.discourse-cdn.com/free1/uploads/mne/original/1X/85cc6bd2b69cb698a166dc6d880fb550510d0144.jpeg) [@system](https://mne.discourse.group/u/system)\ **Post date:** [September 29, 2008, 4:52pm UTC](https://mne.discourse.group/t/comparing-conditions/64/7 "2008-09-29T16:52:00Z")
Well you are right - that's what we see all the time. Even if you do subtraction of incorrect and correct response to get the ERN - which works well for a subset of EEG sensors in fronto-central locations - in other regions not involved in the error processing you get patterns difficult to interpret. But condition comparisons or subtractions in source space must not necessarily be more accurate - in case of minimum norm you "smear" the currents following a mathematical minimization criterion - "the minimum norm". Who says that the brain does work that way in a particular task - minimizing the current. So it is difficult to say what works best in terms of "best physiological model". At that point - I usually don't care that much about the "most accurate source localization" any more and look what is the best measure to differentiate (e.g. conditions, groups) - once you've ruled out all the trivial effects you've got a good chance to see correlates of physiological differences. And if you can replicate that I would call it "a reliable, valuable correlate", which does not necessarily mean "true generator". It is rather a reasonable solution from the infinite amount of inverse solutions, which is probably all what we can expect in psychophysiology anyway. Christian > If one cannot assume similar source configurations in the two > conditions to be compared, presuming that any noise is constant and > equivalent, is it safe to say that subtraction would result in > distorted data ('distorted' not the best choice of words but my > vocabulary has failed me today!), or at least data which would be > difficult to interpret? > > Thanks, > > P. > > Christian Wienbruch wrote: > > > Not necessarily - the sensors pick up signals from multiple > > generators following the superposition principle. This basically > > is the sum of the products leadfield L\_ij times dipole moment p\_j > > plus noise forming the magnetic induction B\_i at sensor i > > > > B\_i = L\_ij \*p\_j + n > > > > If you subtract two field B1 and B2 and they share a common > > generator - this one is excluded in sensor space. In theory this > > works perfectly well in absence of noise. > > Practically speaking this concept works pretty good for certain > > EEG components like the ERN which is the difference between > > incorrect and correct responses. > > > > "Distortions" usually come from the noise term and generators not > > being active in both conditions, or differently active in both > > conditions. Additionally you have source model related distortions > > e.g. regularisation. > > So it depends mostly on your signal to noise ratio if it is wise > > to subtract fields in sensor space or not. > > > > It also depends on how accurate you can position the MEG helmet in > > headframe coordinates across conditions, subjects, ... > > If that can not be done reliably don't even think about > > subtraction in sensor space. You just add additional variance to > > your data. > > > > -Christian > > > > > Because you are distorting the dipolar topographies when you do a > > > subtraction at the sensor level. The resulting data is likely > > > contain field patterns which do not relate to the leadfields of > > > the actual sources that gave rise to the data. Thus, any source > > > reconstruction which relies on lead field models, i.e. minimum > > > norm, will give spurious results. > > > > > > -Padraig > > > > > > Yury Petrov wrote: > > > > > > > Why not first subtract one average response from the other and > > > > then localize? > > > > > > > > > Hi there, > > > > > > > > > > I have a question regarding how best to statistically compare > > > > > two conditions. So far I have only being comparing between 2 > > > > > conditions using ROIs and comparing current estimates over > > > > > time. However, I'd also like to see the difference between two > > > > > conditions across the whole brain. I was wondering what the > > > > > best approach to this was (Ideally ending up with a dSPM map > > > > > of condition1 - conditon2). > > > > > > > > > > Any help on this would be appreciated > > > > > > > > > > Thanks, > > > > > > > > > > Alex Clarke > > > > > \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ > > > > > Mne\_analysis mailing list > > > > > Mne\_analysis at nmr.mgh.harvard.edu > > > > > \ > > > > > [Mne\_analysis Info Page](https://mail.nmr.mgh.harvard.edu/mailman/listinfo/mne_analysis) > > > > > > > > \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ > > > > Mne\_analysis mailing list > > > > Mne\_analysis at nmr.mgh.harvard.edu > > > > \ > > > > [Mne\_analysis Info Page](https://mail.nmr.mgh.harvard.edu/mailman/listinfo/mne_analysis) > > > > > > -- > > > P?draig Kitterick > > > Graduate Student > > > Department of Psychology > > > University of York > > > Heslington > > > York YO10 5DD > > > UK > > > > > > Tel: +44 (0) 1904 43 2883 > > > Email: p.kitterick at psych.york.ac.uk > > > \ > > > > > > \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ > > > Mne\_analysis mailing list > > > Mne\_analysis at nmr.mgh.harvard.edu > > > \ > > > [Mne\_analysis Info Page](https://mail.nmr.mgh.harvard.edu/mailman/listinfo/mne_analysis) > > > > Christian Wienbruch > > > > University of Konstanz > > Clinical Psychology > > Fach D27 > > 78457 Konstanz > > > > Christian.Wienbruch at uni-konstanz.de > > \ > > -- > P?draig Kitterick > Graduate Student > Department of Psychology > University of York > Heslington > York YO10 5DD > UK > > Tel: +44 (0) 1904 43 2883 > Email: p.kitterick at psych.york.ac.uk Christian Wienbruch University of Konstanz Clinical Psychology Fach D27 78457 Konstanz Christian.Wienbruch at uni-konstanz.de -------------- next part -------------- An HTML attachment was scrubbed... URL: [http://mail.nmr.mgh.harvard.edu/pipermail/mne\_analysis/attachments/20080929/efb7a4c8/attachment.html](http://mail.nmr.mgh.harvard.edu/pipermail/mne_analysis/attachments/20080929/efb7a4c8/attachment.html) ---
**Author:** ![system](https://global.discourse-cdn.com/free1/uploads/mne/original/1X/85cc6bd2b69cb698a166dc6d880fb550510d0144.jpeg) [@system](https://mne.discourse.group/u/system)\ **Post date:** [September 29, 2008, 4:56pm UTC](https://mne.discourse.group/t/comparing-conditions/64/8 "2008-09-29T16:56:50Z")
Thanks Christian. This is really helpful. It is so challenging to fully understand the limitations of what one is comparing, and how all of the analysis steps up to that point have contributed to any effects that one finds... But it wouldn't be as much fun if it was easy 😉 -Padraig Christian Wienbruch wrote: ---
**Author:** ![system](https://global.discourse-cdn.com/free1/uploads/mne/original/1X/85cc6bd2b69cb698a166dc6d880fb550510d0144.jpeg) [@system](https://mne.discourse.group/u/system)\ **Post date:** [September 29, 2008, 5:10pm UTC](https://mne.discourse.group/t/comparing-conditions/64/9 "2008-09-29T17:10:55Z")
You can ignore my comment. I was mistakenly thinking of non-linear dipole fits. The solution for the difference data should be identical to the difference between the solutions for the individual conditions as long as the same regularisation parameter and noise covariance matrices are used for both conditions so that the inverse operator is identical in all cases. -P Yury Petrov wrote: ---
**Author:** ![system](https://global.discourse-cdn.com/free1/uploads/mne/original/1X/85cc6bd2b69cb698a166dc6d880fb550510d0144.jpeg) [@system](https://mne.discourse.group/u/system)\ **Post date:** [October 2, 2008, 3:49pm UTC](https://mne.discourse.group/t/comparing-conditions/64/10 "2008-10-02T15:49:47Z")
Hi Alex For what it is worth, I thought about these kinds of questions some time ago and presented a talk that was supposed to open up further discussion and debate. The PDF of that talk is here: [http://www.nmr.mgh.harvard.edu/~daniel/links/presentation/stats\_on\_roi.pdf](http://www.nmr.mgh.harvard.edu/~daniel/links/presentation/stats_on_roi.pdf) It includes some basics on the mathematics and assumptions inherent in them. Then the talk veers into the speculative with some thoughts on newer possible methods for comparing conditions when you have multiple subjects and multiple conditions. I am still interested in developing these questions further, so let me know if these ideas are helpful. Daniel ---
**Author:** ![system](https://global.discourse-cdn.com/free1/uploads/mne/original/1X/85cc6bd2b69cb698a166dc6d880fb550510d0144.jpeg) [@system](https://mne.discourse.group/u/system)\ **Post date:** [October 2, 2008, 5:20pm UTC](https://mne.discourse.group/t/comparing-conditions/64/11 "2008-10-02T17:20:03Z")
Daniel, first of all, thanks for the great MNE review. Some typos that I noticed: page 30: remove Gaussian source distributions page 33: theorm -\> theorem I find the MNE derivation based on Bayesian max-likelihood method (e.g. in the Inverse Problem Theory book below) both simpler and more satisfactory. In particular, it makes the nature of the MNE assumptions much more explicit. [http://www.ipgp.jussieu.fr/~tarantola/Files/Professional/Books/index.html](http://www.ipgp.jussieu.fr/~tarantola/Files/Professional/Books/index.html) I don't see what's 'not cool' with subtracting dSPMs for two conditions. dSPM is, essentially, a singnal-to-noise ratio. Assuming that your noise was the same in both conditions (i.e. the same noise covariance matrix) we just subtract signals, right? ---
**Author:** ![system](https://global.discourse-cdn.com/free1/uploads/mne/original/1X/85cc6bd2b69cb698a166dc6d880fb550510d0144.jpeg) [@system](https://mne.discourse.group/u/system)\ **Post date:** [October 6, 2008, 12:59pm UTC](https://mne.discourse.group/t/comparing-conditions/64/12 "2008-10-06T12:59:11Z")
Yury Thank you for your comments. That textbook you mentioned looks very good. Thank you for the link. On the subject of subtracting F statistics, the more I think about it, the more I wonder if it was premature for me to issue that blanket statement that such a technique does not make statistical sense. Perhaps Yury, you are right and we are simply looking at the difference in SNR for some cases. The things that worry me still are: - if a dipole were to rotate in a fixed position with a fixed amplitude, what would that do in the subtraction case? - when subtracting these F statistics, no account is made for temporal relationships. So if I take the subtraction of two different time points from the same source with a sinusoidal signal that are out of phase by 180 degrees, wouldn't this seem like one time point is more "significant" than the other, when in fact you are looking at different phases of the same thing? - If the noise is not the same (i.e. when comparing two different sources), what is the meaning of the subtraction? Does it relate to significance of effect, or merely SNR due to anatomy/physics? Maybe I am just too new to the field and am asking questions that have been well picked over already. Anyone who can see where I went astray, please feel free to chime in and straighten me out. Daniel ---
**Author:** ![system](https://global.discourse-cdn.com/free1/uploads/mne/original/1X/85cc6bd2b69cb698a166dc6d880fb550510d0144.jpeg) [@system](https://mne.discourse.group/u/system)\ **Post date:** [October 6, 2008, 3:23pm UTC](https://mne.discourse.group/t/comparing-conditions/64/13 "2008-10-06T15:23:16Z")
> - if a dipole were to rotate in a fixed position with a fixed > amplitude, what would that do in the subtraction case? Daniel, you are right, this difference will be lost. But to me it seems more reasonable to subtract electrode signals for the two conditions first, then localize and do the F statistics on the difference signal. So, for example, if a given dipole just changed its orientation from inward in cond 1 to outward in cond 2, and you subtract averaged potentials for cond 1 from cond 2, then the difference will be localized as twice the outward current at the dipole location. > - when subtracting these F statistics, no account is made for > temporal relationships. So if I take the subtraction of two > different time points from the same source with a sinusoidal signal > that are out of phase by 180 degrees, wouldn't this seem like one > time point is more "significant" than the other, when in fact you > are looking at different phases of the same thing? Are you talking about comparing steady-state recordings in frequency/ phase domain? For regular ERPs the F statistics is calculated for each timepoint in the recording, right? Of course, my assumption is that one subtracts the conditions for the same timepoints. > - If the noise is not the same (i.e. when comparing two different > sources), what is the meaning of the subtraction? Does it relate to > significance of effect, or merely SNR due to anatomy/physics? You are right. However, most experiments are done by running interleaved conditions, each condition for 10 - 20 trials within the same run of 15 - 60 minutes long. So the noise covariance should be the same for all conditions. Also, in my (little) experience, the difference in noise covariance matrices between different EEG experiments is not that significant, given that you are using the same head and the same net. It is probably even less significant for MEG, where the electrode and magnetometer locations are fixed on the helmet, and the environmental noise is, generally, better controlled. It is important, of course, to multiply the noise covariance matrix by 2 (or really add the two covariance matrices) when doing F statistics on difference signals. Yury ---
**Author:** ![system](https://global.discourse-cdn.com/free1/uploads/mne/original/1X/85cc6bd2b69cb698a166dc6d880fb550510d0144.jpeg) [@system](https://mne.discourse.group/u/system)\ **Post date:** [November 21, 2008, 11:23pm UTC](https://mne.discourse.group/t/comparing-conditions/64/14 "2008-11-21T23:23:13Z")
Dear Daniel, I was rereading your excellent dSPM intro, and have the following degrees of freedom (DoF) question: what is the right number of DoF for the noise in the F denominator? You say the number of the "baseline" timepoints x 3. Where does this number of baseline timepoints come from? Shouldn't it be just 3 (just as for the numerator), because we add three variances? Also, if it was really not 3, then the correct F value wouldn't be simply F = signal^2/noise^2 but F = signal^2 / 3 / noise^2 / DoF\_noise, i.e. the numerator and denominator would have to be normalized by their respective DoFs, right? Thanks, Yury