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| '''[TUTORIAL UNDER DEVELOPMENT: NOT READY FOR PUBLIC USE] ''' ''Authors: Francois Tadel, Elizabeth Bock, Dimitrios Pantazis, Richard Leahy, Sylvain Baillet'' |
''Authors: Francois Tadel, Elizabeth Bock, Dimitrios Pantazis, John Mosher, Richard Leahy, Sylvain Baillet'' |
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| * Files A: Subject-level averages for group #1. * Files B: Subject-level averages for group #2. |
* Files A: Subject-level averages for group #1 (G1). * Files B: Subject-level averages for group #2 (G2). |
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| * Correct effect size: We identify correctly '''where and when''' the conditions are different. | * Correct detection: Identify correctly '''where and when''' the conditions are different. |
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| * Incorrect effect size: Doesn't detect correctly the effects when A and B have opposite signs. * Correct sign: We can identify correctly which condition has a '''stronger response'''. * Power(x) = |x|<<HTML(<SUP>2</SUP>)>>, where |x| represents the modulus of the values: * Absolute value for scalar values (recordings, constrained sources, time-frequency maps) * Norm of the three orientations for unconstrained sources. ==== How many trials to include? ==== * '''Single subject''': Include all the good trials (unless you have a very low number of trials). <<BR>>See the [[http://neuroimage.usc.edu/brainstorm/Tutorials/Averaging#Number_of_trials|averaging tutorial]]. * '''Group analysis''': Use a similar numbers of trials for all the subjects (no need to be strictly equal), reject the subjects for which we have much less good trials. |
* Incorrect detection: Not sensitive to the cases where A and B have opposite signs. * Meaningful sign: We can identify correctly which condition has a '''stronger response'''. * Power(x) = |x|<<HTML(<SUP>2</SUP>)>>, where |x| represents the modulus of the values: <<BR>> - Absolute value for scalar values (recordings, constrained sources, time-frequency) <<BR>> - Norm of the three orientations for unconstrained sources. * '''Multiple comparisons''': FDR is a good choice for correcting p-values for multiple comparisons. ==== Design considerations ==== * Use within-subject designs whenever possible (i.e. collect two conditions A and B for each subject), then contrast data at the subject level before comparing data between subjects. * Such designs are not only statistically optimal, but also ameliorate the between-subject sign ambiguities as contrasts can be constructed within each subject. |
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| ==== How many trials to include? ==== * '''Single subject''': Include all the good trials (unless you have a very low number of trials). <<BR>>See the [[http://neuroimage.usc.edu/brainstorm/Tutorials/Averaging#Number_of_trials|averaging tutorial]]. * '''Group analysis''': Use a similar numbers of trials for all the subjects (no need to be strictly equal), reject the subjects for which you have much less good trials. |
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| * Subject averages: Use all the good trials available. * Group averages: Use similar number of trials for all the subjects (no need to be strictly equal). === Statistics: Single subject === |
=== Statistics: Single subject === * '''A ='''''' B''': Parametric or non-parametric t-test, '''independent''', two-tailed. === Statistics: Group analysis, within subject === |
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| * '''Parametric '''or '''non-parametric''' t-test, '''independent''', two-tailed, FDR-corrected. * Use as many trials as possible for A and B: No need to have an equal number of trials. === Statistics: Group analysis, within subject === * '''A ='''''' B''' * '''First-level statistic''': Average * For each subject, compute the sensor average for conditions A and B. * Use all the good trials available. * '''Second-level statistic''': t-test * '''Parametric''' or '''non-parametric''' t-test, '''paired''', two-tailed, FDR-corrected. * Exclude subjects with number of trials that are much lower than the others. === Statistics: Group analysis, between subjects === * '''A ='''''' B''' * '''First-level statistic''': Average * For each subject, compute the sensor average for conditions A and B. * Use all the good trials available. * '''Second-level statistic''': t-test * '''Parametric''' or '''non-parametric''' t-test, '''independent''', two-tailed, FDR-corrected. * Exclude subjects with number of trials that are much lower than the others. |
* '''First-level statistic''': For each subject, sensor average for conditions A and B. * '''Second-level statistic''': Parametric or non-parametric t-test, '''paired''', two-tailed. === Statistics: Group analysis, between subjects === * '''G1 ='''''' G2''' * '''First-level statistic''': For each subject, sensor average for the conditions to test. * '''Second-level statistic''': Parametric/non-parametric t-test, '''independent''', two-tailed. |
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| * Averaging across acquisition runs: Not advised because the head of the subject may move between runs. * Averaging across subjects: Strongly discouraged because the shape of the heads vary but the sensors are fixed. One sensor does not correspond to the same brain region for different subjects. |
* Average across runs: Not advised because the head of the subject may move between runs. * Average across subjects: Strongly discouraged because the shape of the heads vary but the sensors are fixed. One sensor does not correspond to the same brain region for different subjects. |
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| * Note for Elekta/MaxFilter users: You can align all sessions to a reference session, this will allow direct channel comparisons within-subject. Not recommended across subjects. | * Note for Elekta/MaxFilter users: You can align all acquisition run to a reference run, this will allow direct channel comparisons and averaging across runs. Not recommended across subjects. |
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| * Group averages: Use the same number of trials for all the sessions. === Statistics: Single subject === * '''A ='''''' B''' * '''Parametric '''or '''non-parametric''' t-test, '''independent''', two-tailed, FDR-corrected. * Use as many trials as possible for A and B: No need to have an equal number of trials. |
=== Statistics: Single subject === * '''A ='''''' B''': Parametric or non-parametric t-test, '''independent''', two-tailed. |
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| 1. '''Sensor average''': Compute one sensor-level average''' '''per acquisition session and condition. <<BR>>Use the '''same number of trials''' for all the averages. | 1. '''Sensor average''': Compute one sensor-level average''' '''per acquisition run and per condition. 1. '''Sources''': Estimate sources for each average (constrained, no normalization). 1. '''Source average''': Average the source-level run averages to get one subject average.<<BR>>Compute a weighted average to balance for different numbers of trials across runs. 1. '''Low-pass filter''' your evoked responses (optional). * If you filter the average before normalizing wrt baseline, it will lead to an underestimation of the baseline variance, and therefore to an overestimation of the Z scores computed in the next step, especially if the baseline is too short (typically less than 200 time points). The filter increases the autocorrelation of the time series, and therefore biases the estimation of the signal variance ([[https://en.wikipedia.org/wiki/Unbiased_estimation_of_standard_deviation#Effect_of_autocorrelation_.28serial_correlation.29|Wikipedia]]). * You have to take into account the possible [[Tutorials/ArtifactsFilter|edge effects]] due to the filter. You can either extract a small time window or exclude the beginning of the baseline for the normalization. 1. '''Normalize '''the subject min-norm averages: Z-score wrt baseline (no absolute value).<<BR>>Justification: The amplitude range of current densities may vary between subjects because of anatomical or experimental differences. This normalization helps bringing the different subjects to the same range of values. 1. '''Do not rectify the cortical maps''', but display them as absolute values if needed. === Average: Group analysis === 1. '''Subject averages''': Compute within-subject averages for all the subjects, as described above. 1. '''Rectify''' the cortical maps (process: Pre-process > Absolute value). <<BR>>Justification: Cortical maps have ambiguous signs across subjects: reconstructed sources depend heavily on the orientation of true cortical sources. Given the folding patterns of individual cortical anatomies vary considerably, cortical maps have subject-specific amplitude and sign ambiguities. This is true even if a standard anatomy is used for reconstruction. 1. '''Project '''the individual source maps on a template (only when using the individual brains). <<BR>> For more details, see tutorial: [[Tutorials/CoregisterSubjects|Group analysis: Subject coregistration]]. 1. '''Group average''': Compute grand averages of all the subjects.<<BR>>Do __not__ use a weighted average: all the subjects should have the same weight in this average. 1. '''Smooth '''spatially the source maps (optional).<<BR>>You can smooth after step #3 for computing non-parametric statistics with the subject averages. For a simple group average, it is equivalent to smooth before of after computing the average. === Difference of averages: Within subject === 1. '''Sensor average''': Compute one sensor-level average per acquisition run and condition. |
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| 1. '''Low-pass filter''' your evoked responses (optional). 1. '''Normalize '''the subject min-norm averages: Z-score vs. baseline (no absolute value).<<BR>>Justification: The amplitude range of current densities may vary between subjects because of anatomical or experimental differences. This normalization helps bringing the different subjects to the same range of values. 1. '''Do not rectify the cortical maps''', but display them as absolute values if needed. === Average: Group analysis === 1. '''Subject averages''': Compute within-subject averages for all the subjects, as described above. 1. '''Rectify''' the cortical maps (apply an absolute value). <<BR>>Justification: Cortical maps have ambiguous signs across subjects: reconstructed sources depend heavily on the orientation of true cortical sources. Given the folding patterns of individual cortical anatomies vary considerably, cortical maps have subject-specific amplitude and sign ambiguities. This is true even if a standard anatomy is used for reconstruction. 1. '''Project '''the individual source maps on a template (only when using the individual brains). <<BR>> For more details, see tutorial: [[Tutorials/CoregisterSubjects|Group analysis: Subject coregistration]]. 1. '''Smooth '''spatially the sources.<<BR>>Justification: The effects observed with constrained cortical maps may be artificially very focal, not overlapping very well between subjects. Smoothing the cortical maps may help the activated regions overlap between subjects. 1. '''Group average''': Compute grand averages of all the subjects. === Difference of averages: Within subject === 1. '''Subject averages''': Compute within-subject averages for conditions A and B, as described above. 1. '''Subject difference''': Compute the difference between conditions for each subject (A-B). 1. '''Rectify''' the difference of source maps (apply an absolute value). |
1. '''Subject difference''': Compute the difference between conditions for each subject #i: (A,,i,,-B,,i,,) 1. '''Low-pass filter''' the difference (optional) 1. '''Normalize '''the difference: Z-score wrt baseline (no absolute value): Z(A,,i,,-B,,i,,) 1. '''Rectify''' the difference (apply an absolute value): |Z(A,,i,,-B,,i,,)| |
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| 1. '''Smooth '''spatially the sources. 1. '''Group average''': Compute grand averages of all the subjects: average_subjects(|Ai-Bi|). |
1. '''Group average''': Compute grand averages of all the subjects: avg(|Z(A,,i,,-B,,i,,)|). 1. '''Smooth '''spatially the source maps (optional). |
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| 1. '''Subject averages''': Compute within-subject averages for conditions A and B, as described above. 1. '''Grand averages''': Compute the group-level averages for groups #1 and #2 as described in "Average: Group analysis" 1. '''Difference''': Compute the difference between group-level averages: avg(|A1|)-avg(|A2|) |
1. '''Grand averages''': Compute averages for groups #1 and #2 as in ''Average:Group analysis.'' 1. '''Difference''': Compute the difference between group-level averages: avg(|G,,1,,|)-avg(|G,,2,,|) |
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| 1. '''Sources''': Compute source maps for each trial (constrained, no normalization) 1. '''Statistics''': Compare all the trials of condition A vs all the trials of condition B.<<BR>>Use as many trials as possible for A and B: No need to have an equal number of trials. 1. '''A = B''' * '''Parametric''' or '''non-parametric''' t-test, '''independent''', two-tailed, FDR-corrected. * Indicates when and where there is a significant effect (but not in which direction). 1. '''|A| = |B|''' * '''Non-parametric''' tests only, '''independent''', test absolute values, two-tailed, FDR-corrected. * Indicates which condition corresponds to a stronger brain response (for a known effect). === Statistics: Group analysis, within subject === * '''|A - B| = 0''' : Parametric 1. '''Sources''': Compute source maps for each trial (constrained, no normalization) 1. '''First-level statistic''': Compute a t-statistic for the source maps of all the trials A vs B. * Process2 "Test > Compute t-statistic": no absolute values, independant, equal variance. * Use as many trials as possible for A and B: No need to have an equal number of trials. * With a high number of trials (n>30), t-values follow approximately a N(0,1) distribution. 1. '''Low-pass filter''' your evoked responses (optional). 1. '''Rectify '''the individual t-statistic (we're giving up the sign across subjects). 1. '''Project '''the individual t-statistic on a template (only when using the individual brains). 1. '''Smooth '''spatially the t-statistic maps. 1. '''Second-level statistic''': Compute a one-sampled chi-square test based on the t-statistics. * Process1: "Test > Parametric test against zero": One-sampled Chi-square test * This tests for '''|A-B|'''=0 using a Chi-square test: X = sum(|t<<HTML(<SUB>)>>i<<HTML(</SUB>)>>|^2) ~ Chi2(N<<HTML(<SUB>)>>subj<<HTML(</SUB>)>>) * Indicates when and where there is a significant effect (but not in which direction). * '''|A - B| = 0 ''': Non-parametric 1. '''Rectified differences''': Proceed as described in ''Difference of averages: Between subjects'', but stop before the computation of the grand averages (#6) and compute a test instead.<<BR>>You obtain one |A<<HTML(<SUB>)>>i<<HTML(</SUB>)>>-B<<HTML(<SUB>)>>i<<HTML(</SUB>)>>| value for each subject, test these values against zero. 1. '''Non-parametric''' one-sample test, one-tailed, FDR-corrected. 1. Indicates when and where there is a significant effect (but not in which direction). * '''|A| = |B|''' 1. '''Rectified subject averages''': Proceed as described in ''Average: Group analysis'', but stop before the grand average (#5). You obtain two averages per subject (A<<HTML(<SUB>)>>i<<HTML(</SUB>)>> and B<<HTML(<SUB>)>>i<<HTML(</SUB>)>>). 1. '''Non-parametric''' two-sample test, '''paired''', test absolute values, two-tailed, FDR-corrected. 1. Indicates which condition corresponds to a stronger brain response (for a known effect). === Statistics: Group analysis, between subjects === * '''|A| = |B|''' * '''Subject averages''': Compute within-subject averages for A and B, as described above.<<BR>>You obtain two averages per subject (A<<HTML(<SUB>)>>i<<HTML(</SUB>)>> and B<<HTML(<SUB>)>>i<<HTML(</SUB>)>>). * '''Non-parametric''' two-sample test, '''independent''', test absolute values, two-tailed, FDR. * Indicates which condition corresponds to a stronger brain response (for a known effect). === Design considerations === * Use within-subject designs whenever possible (i.e. collect two conditions A and B for each subject), then contrast data at the subject level before comparing data between subjects. * Such designs are not only statistically optimal, but also ameliorate the between-subject sign ambiguities as contrasts can be constructed within each subject. |
* '''A = B''': Parametric or non-parametric * Compute source maps for each trial (constrained, no normalization). * Parametric or non-parametric two-sample t-test, independent, two-tailed.<<BR>>Identifies correctly '''where and when''' the conditions are different (sign not meaningful). * '''Directionality''': Additional step to know which condition has higher values.<<BR>>Compute the difference of rectified averages: |avg(A,,i,,)|-|avg(B,,i,,)|<<BR>>Combine the significance level (t-test) with the direction (difference): [[http://neuroimage.usc.edu/brainstorm/Tutorials/Statistics#Directionality:_Difference_of_absolute_values|See details]]. * '''|mean(A)| = |mean(B)|''': Non-parametric * Compute source maps for each trial (constrained, no normalization). * Non-parametric independent two-sample "absolute mean test", two-tailed.<<BR>>T = (|mean(A)|-|mean(B)|) / sqrt(|var(A)|/N,,A,, + |var(B)|/N,,B,,) * Interesting alternative that provides at the time a correct estimation of the difference (where and when) and the direction (which condition has higher values). === Statistics: Group analysis, within subject === * '''Power(A-B) = 0''': Parametric * '''First-level statistic''': Rectified difference of normalized averages. <<BR>>Proceed as in ''Difference of averages: Within subjects'', but stop before the group average (after step #8). You obtain one measure '''|A,,i,,-B,,i,,|''' per subject, test these values against zero. * '''Second-level statistic''': Parametric one-sample Chi^2^-test. <<BR>>Power = sum(|A,,i,,-B,,i,,|^2^), i=1..N,,subj,, ~ Chi^2^(N,,subj,,) * Identifies '''where and when''' the conditions are different (sign not meaningful). * Warning: Very sensitive test, with lots of false positive (all the brain can be "significant") * '''|A| = |B|''': Parametric or non-parametric * '''First-level statistic''': Rectified and normalized subject averages. <<BR>>Proceed as in ''Average: Group analysis'' to obtain two averages per subject: A,,i,, and B,,i,,. * '''Second-level statistic''': Parametric or non-parametric two-sample t-test, paired, two-tailed. * This test does not consider the sign difference within a subject, and therefore cannot detect correctly when A and B have opposite signs. Works well and indicates '''which condition has higher values''' when A and B have the same sign within a subject. * '''A = B''': Parametric or non-parametric [anatomy template only] * '''First-level statistic''': Normalized subject averages (not rectified, no projection needed). <<BR>>Proceed as in ''Average: Single subject'' to obtain two averages per subject: A,,i,, and B,,i,,. * '''Second-level statistic''': Parametric or non-parametric two-sample t-test, paired, two-tailed. * Applies only if all the subjects are sharing the same template anatomy. <<BR>>Not recommended when using individual anatomies because of the sign issue between subjects (the signs might be opposed between two subjects, and the projection of non-rectified values to a template might be inaccurate). * '''Power(A) = 0''': Parametric * '''First-level statistic''': Rectified and normalized subject averages. <<BR>>Proceed as in ''Average: Group analysis'' to obtain one average per subject #i: |A,,i,,|. * '''Second-level statistic''': Parametric one-sample Chi^2^-test. <<BR>>PowerA = sum(|A,,i,,|^2^), i=1..N,,subj,, ~ Chi^2^(N,,subj,,). === Statistics: Group analysis, between subjects === * '''|G1| = |G2|''': Non-parametric * '''First-level statistic''': Rectified and normalized subject averages. <<BR>>Proceed as in ''Average: Group analysis'' to obtain one average per subject. * '''Second-level statistic''': Non-parametric two-sample t-test, '''independent''', two-tailed. * '''Power(G1) = Power(G2)''': Parametric * '''First-level statistic''': Rectified and normalized subject averages. <<BR>>Proceed as in ''Average: Group analysis'' to obtain one average per subject: |Ai|. * '''Second-level statistic''': Parametric two-sample power F-test. <<BR>>PowerG1 = sum(A,,i,,^2^), i=1..N,,1,, ~ Chi^2^(N,,1,,)<<BR>>PowerG2 = sum(A,,j,,^2^), j=1..N,,2,, ~ Chi^2^(N,,2,,)<<BR>>F(N,,1,,,N,,2,,) = (PowerG1 / N,,1,,) / (PowerG2 / N,,2,,) |
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| === Average: Single subject [???] === 1. '''Sensor average''': Compute one sensor-level average''' '''per acquisition session and condition. <<BR>>Use the '''same number of trials''' for all the averages. 1. '''Sources''': Estimate sources for each average (unconstrained, no normalization). 1. '''Source average''': Average the source-level session averages to get one subject average. 1. '''Low-pass filter''' your evoked responses (optional). 1. '''Normalize '''the subject min-norm averages: Z-score vs. baseline (no absolute value).<<BR>>'''[???]''' HOW TO NORMALIZE UNCONSTRAINED MAPS WRT BASELINE? === Average: Group analysis [???] === 1. '''Subject averages''': Compute within-subject averages for all the subjects, as described above. 1. '''Flatten''' the cortical map: compute the norm of the three orientations at each grid point. 1. '''Project '''the individual source maps on a template (only when using the individual brains). 1. '''Group average''': Compute grand averages of all the subjects. === Difference of averages: Within subject [???] === 1. '''Subject averages''': Compute within-subject averages for conditions A and B, as described above. 1. '''Subject difference''': Compute the difference between conditions for each subject (A-B). 1. '''Flatten''' the cortical map: compute the norm of the three orientations at each grid point. 1. '''Project '''the individual difference on a template. 1. '''Group average''': Compute grand averages of all the subjects: average_subjects(|Ai-Bi|). === Difference of averages: Between subjects [???] === 1. '''Subject averages''': Compute within-subject averages for conditions A and B, as described above. 1. '''Grand averages''': Compute the group-level averages for groups #1 and #2 as described in "Average: Group analysis" 1. '''Difference''': Compute the difference between group-level averages: avg(|A1|)-avg(|A2|) 1. '''Limitations''': Because we rectify the source maps before computing the difference, we lose the ability to detect the differences between equal values of opposite signs. And we cannot keep the sign because we are averaging across subjects. Therefore, many effects are not detected correctly. === Statistics: Single subject [???] === 1. '''Sources''': Compute source maps for each trial (unconstrained, no normalization) 1. '''Statistics''': Compare all the trials of condition A vs all the trials of condition B.<<BR>>Use as many trials as possible for A and B: No need to have an equal number of trials. 1. '''|A| = |B|''' * '''Non-parametric''' tests only, '''independent''', test norm, two-tailed, FDR-corrected. * Indicates which condition corresponds to a stronger brain response (for a known effect). === Statistics: Group analysis, within subject [???] === * '''|A - B| = 0''' : Parametric 1. '''Sources''': Compute source maps for each trial (unconstrained, no normalization) 1. '''First-level statistic''': Compute a t-statistic for the source maps of all the trials A vs B. * Process2 "Test > Compute t-statistic": no absolute values, independant, equal variance. * Use as many trials as possible for A and B: No need to have an equal number of trials. * With a high number of trials (n>30), t-values follow approximately a N(0,1) distribution. 1. '''Low-pass filter''' your evoked responses (optional). 1. '''Rectify '''the individual t-statistic (we're giving up the sign across subjects). 1. '''Project '''the individual t-statistic on a template (when using ). 1. '''Smooth '''spatially the t-statistic maps. 1. '''Second-level statistic''': Compute a one-sampled Chi-square test based on the t-statistics. * Process1: "Test > Parametric test against zero": One-sampled Chi-square test * This tests for '''|A-B|'''=0 using a Chi-square test: X = sum(|t<<HTML(<SUB>)>>i<<HTML(</SUB>)>>|^2) ~ Chi2(N<<HTML(<SUB>)>>subj<<HTML(</SUB>)>>) * Indicates when and where there is a significant effect (but not in which direction). * '''|A - B| = 0 ''': Non-parametric 1. '''Rectified differences''': Proceed as described in ''Difference of averages: Between subjects'', but stop before the computation of the grand averages (#6) and compute a test instead.<<BR>>You obtain one |A<<HTML(<SUB>)>>i<<HTML(</SUB>)>>-B<<HTML(<SUB>)>>i<<HTML(</SUB>)>>| value for each subject, test these values against zero. 1. '''Non-parametric''' one-sample test, one-tailed, FDR-corrected. 1. Indicates when and where there is a significant effect (but not in which direction). * '''|A| = |B|''' 1. '''Subject averages''': Compute within-subject averages for A and B, as described above.<<BR>>You obtain two averages per subject (A<<HTML(<SUB>)>>i<<HTML(</SUB>)>> and B<<HTML(<SUB>)>>i<<HTML(</SUB>)>>). 1. '''Non-parametric''' two-sample test, '''paired''', test absolute values, two-tailed, FDR-corrected. 1. Indicates which condition corresponds to a stronger brain response (for a known effect). === Statistics: Group analysis, between subjects [???] === * '''|A| = |B|''' * '''Subject averages''': Compute within-subject averages for A and B, as described above.<<BR>>You obtain two averages per subject (A<<HTML(<SUB>)>>i<<HTML(</SUB>)>> and B<<HTML(<SUB>)>>i<<HTML(</SUB>)>>). * '''Non-parametric''' two-sample test, '''independent''', test absolute values, two-tailed, FDR. * Indicates which condition corresponds to a stronger brain response (for a known effect). == Regions of interest (scouts) [???] == |
=== Averages === * Proceed as indicated above for constrained cortical sources. * Just replace the step '''Rectify''' with '''Flatten''' (process: Sources > Unconstrained to flat map). * The operator |A| has to be interpreted as "norm of the three orientations":<<BR>> |A| = sqrt(A,,x,,^2^ + A,,y,,^2^ + A,,z,,^2^) === Statistics: Single subject === * '''|mean(A)| = |mean(B)|''': Non-parametric * Compute source maps for each trial (unconstrained, no normalization). * Non-parametric independent two-sample "absolute mean test", independent, two-tailed.<<BR>>T = (|mean(A)|-|mean(B)|) / sqrt(|var(A)|/N,,A,, + |var(B)|/N,,B,,) * Provides at the time a correct estimation of the difference (where and when) and the direction (which condition has higher values). === Statistics: Group analysis, within subject === * '''Power(A-B) = 0''': Parametric * '''First-level statistic''': Flattened difference of normalized averages. <<BR>>Proceed as in ''Difference of averages: Within subjects'', but stop before the group average (after step #8). You obtain one measure '''|A,,i,,-B,,i,,|''' per subject, test these values against zero. * '''Second-level statistic''': Parametric one-sample Chi^2^-test for unconstrained sources. <<BR>>Power = sum(|A,,i,,-B,,i,,|^2^), i=1..N,,subj,, ~ Chi^2^(3*N,,subj,,) * Identifies '''where and when''' the conditions are different (sign not meaningful). * Warning: Very sensitive test, with lots of false positive (all the brain can be "significant") * '''|A| = |B|''': Parametric or non-parametric * '''First-level statistic''': Flattened and normalized subject averages. <<BR>>Proceed as in ''Average: Group analysis'' to obtain two averages per subject: A,,i,, and B,,i,,. * '''Second-level statistic''': Parametric or non-parametric two-sample t-test, paired, two-tailed. * This test does not consider the sign difference within a subject, and therefore cannot detect correctly when A and B have opposite signs. Works well and indicates '''which condition has higher values''' when A and B have the same sign within a subject. * '''Power(A) = 0''': Parametric * '''First-level statistic''': Flattened and normalized subject averages. <<BR>>Proceed as in ''Average: Group analysis'' to obtain one average per subject #i: |A,,i,,|. * '''Second-level statistic''': Parametric one-sample Chi^2^-test for unconstrained sources. <<BR>>PowerA = sum(|A,,i,,|^2^) = sum(A,,ix,,^2^+A,,iy,,^2^+A,,iz,,^2^), i=1..N,,subj,, ~ Chi^2^(3*N,,subj,,). === Statistics: Group analysis, between subjects === * '''|G1| = |G2|''': Non-parametric * '''First-level statistic''': Flattened and normalized subject averages. <<BR>>Proceed as in ''Average: Group analysis'' to obtain one average per subject. * '''Second-level statistic''': Non-parametric two-sample t-test, '''independent''', two-tailed. * '''Power(G1) = Power(G2)''': Parametric * '''First-level statistic''': Flattened and normalized subject averages. <<BR>>Proceed as in ''Average: Group analysis'' to obtain one average per subject: |Ai|. * '''Second-level statistic''': Parametric two-sample power F-test (unconstrained sources). <<BR>>PowerG1 = sum(A,,ix,,^2^+A,,iy,,^2^+A,,iz,,^2^), i=1..N,,1,, ~ Chi^2^(3*N,,1,,)<<BR>>PowerG2 = sum(A,,jx,,^2^+A,,jy,,^2^+A,,jz,,^2^), j=1..N,,2,, ~ Chi^2^(3*N,,2,,)<<BR>>F = (PowerG1 / N,,1,,) / (PowerG2 / N,,2,,) ~ F(3*N,,1,,,3*N,,2,,) == Regions of interest (scouts) == |
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| * Comparison of scout time series between subjects is tricky because there is no way to avoid sign ambiguity for different subjects. Thus there are no clear recommendations. Rectifying before comparing scout time series between subjects can be a good idea or not depending on different cases. Having a good understanding of the data (multiple inspections across channels/sources/subjects) can offer hints whether rectifying the scout time series is a good idea. Using unconstrained cortical maps to create the scout time series can ameliorate ambiguity concerns. | * Comparison of scout time series between subjects is tricky because there is no way to avoid sign ambiguity for different subjects. Thus there are no clear recommendations. Rectifying before comparing scout time series between subjects can be a good idea or not depending on different cases. * Having a good understanding of the data (multiple inspections across channels/sources/subjects) can offer hints whether rectifying the scout time series is a good idea. Using unconstrained cortical maps to create the scout time series can ameliorate ambiguity concerns. |
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| 1. '''Time-frequency maps''': Compute time-frequency maps for each trial. * Apply the default measure: magnitude for Hilbert transform, power for Morlet wavelets. * Do not normalize the source maps: no Z-score or ERS/ERD. * The values are all strictly positive, there is no sign ambiguity as for recordings or sources. 1. '''Average''' all the time-frequency maps together, for each condition separately. * If you are averaging time-frequency maps computed on sensor-level data, the same limitations apply as for averaging sensor level data (see sections about MEG and EEG recordings above). === Average: Group analysis [???] === |
* '''Single trials''': Compute time-frequency maps for each trial ('''magnitude''', no normalization).<<BR>>It is a more standard analysis to take the square root of power before a t-test. * '''Subject average''': Average the time-frequency maps together, separately for each condition. This can be done automatically when computing the TF decompositions. * The values are all strictly positive, there is no sign ambiguity: you can directly subtract the averages of the two conditions and interpret the sign of the difference. * If you average time-frequency maps computed on sensor-level data, the same limitations apply as for averaging sensor level data (see sections about MEG and EEG recordings above). === Average: Group analysis === |
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| 1. '''Normalize''': '''[???]''' Zscore, ERD/ERS, or FieldTrip?<<BR>>Justification: The amplitude range of current densities may vary between subjects because of anatomical or experimental differences. This normalization helps bringing the different subjects to the same range of values. | 1. '''Normalize''' the subject averages: ERD/ERS or Z-score wrt baseline. |
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| === Difference of averages === 1. '''Group average''': Compute the averages for conditions A and B as in ''Average: Group analysis''. 1. '''Difference''': Compute the difference between group-level averages: avg(A)-avg(B). === Statistics: Single subject [???] === 1. '''Time-frequency maps''': Compute time-frequency maps for each trial. * Apply the default measure: magnitude for Hilbert transform, power for Morlet wavelets. * Do not normalize the source maps: no Z-score or ERS/ERD. * The values are all strictly positive, there is no sign ambiguity as for recordings or sources. 1. '''Statistics''': Compare all the trials of condition A vs all the trials of condition B.<<BR>>Use as many trials as possible for A and B: No need to have an equal number of trials. 1. '''A = B''' '''[???]''' * '''Parametric''' or '''non-parametric''' t-test, '''independent''', two-tailed, FDR-corrected. '''[???]''' * Indicates both where there is a significant effect and what is its direction (no sign ambiguity). === Statistics: Group analysis, within subject [???] === * '''A = B ''''''[???]''' 1. '''Subject averages''': Compute within-subject averages for all subjects, as described above. 1. '''Parametric''' or '''non-parametric''' t-test, '''independent''', two-tailed, FDR-corrected. '''[???]''' 1. Indicates both where there is a significant effect and what is its direction (no sign ambiguity). <<TAG(Advanced)>> == Workflow: Current problems [TODO] == The following inconsistencies are still present in the documentation. We are actively working on these issues and will update this tutorial as soon as we found solutions. * [Group analysis] Unconstrained sources: How to normalize wrt baseline with a Z-score? * Zscore(A): Normalizes each orientation separately, we cannot take the norm of it after. * Zscore(|A|): Gets rid of the signs, forbids the option of a signed test H0:(Norm(A-B)=0) * See also the tutorial: [[http://neuroimage.usc.edu/brainstorm/Tutorials/SourceEstimation#Z-score|Source estimation]] * We need a way to normalize across the three orientations are the same time. * [Single subject] Unconstrained sources: How do compare two conditions with multiple trials? * |A|-|B|: Cannot detect correctly the difference. * |A-B|: Cannot be computed because the trials are not paired. * We need a test for the three orientations at the same time. * [Group analysis] Unconstrained sources:Can we use parametric tests? * Time-frequency maps: * Can we use parametric tests for (A-B=0) ? Does (A-B) ~ normal distribution? * Do we need to normalize the time-frequency maps when testing across subjects? * If yes, how to normalize the time-frequency maps? (Z-score, ERS/ERD, divide by std) == References == * Number of trials: http://www.tandfonline.com/doi/pdf/10.1207/s15326942dn2603_6 |
1. '''Difference of averages''': Simply compute the difference of the group averages. === Statistics: Single subject === * '''A = B''': Parametric or non-parametric * Compute time-frequency maps for each trial ('''magnitude''', no normalization). * Parametric or non-parametric two-sample t-test, independent, two-tailed. === Statistics: Group analysis, within subject === * '''A = B''': Parametric or non-parametric [anatomy template only] * '''First-level statistic''': Normalized subject averages (ERS/ERD or Z-score). <<BR>> Proceed as in ''Average: Group analysis'' to obtain two averages per subject: A,,i,, and B,,i,,. * '''Second-level statistic''': Parametric or non-parametric two-sample t-test, paired, two-tailed. === Statistics: Group analysis, between subjects === * '''G1 = G2''': Non-parametric * '''First-level statistic''': Normalized subject averages (ERS/ERD or Z-score). <<BR>> Proceed as in ''Average: Group analysis'' to obtain one average per subject. * '''Second-level statistic''': Parametric or non-parametric two-sample t-test, independent, two-tailed. |
Tutorial 27: Workflows
Authors: Francois Tadel, Elizabeth Bock, Dimitrios Pantazis, John Mosher, Richard Leahy, Sylvain Baillet
This page provides some general recommendations for your event-related analysis. It is not directly related with the auditory dataset, but provides guidelines you should consider for any MEG/EEG experiment.
We do not provide standard analysis pipelines for resting or steady state recordings yet, but we will add a few examples soon in the section Other analysis scenarios of the tutorials page.
Contents
What is your question?
The most appropriate analysis pipeline for your data depends on the question you are trying to answer. Before defining what are the main steps of your analysis, you should be able to state clearly the question you want to answer with your recordings.
What dimension?
- MEG/EEG recordings
- Cortical sources
- Individual anatomy or template
- Constrained (one value per vertex) or unconstrained (three values per grid point)
- Full cortex or regions of interests
- Frequency or time-frequency maps
What kind of experiment?
Single subject: Contrast two experimental conditions across trials, for one single subject.
- Files A: Single trials for condition A.
- Files B: Single trials for condition B.
Group analysis, within subject: Contrast two conditions A and B measured for each subject.
- Files A: Subject-level averages for condition A (all the subjects).
- Files B: Subject-level averages for condition B (all the subjects).
Group analysis, between subjects: Contrast two groups of subjects for one condition.
- Files A: Subject-level averages for group #1 (G1).
- Files B: Subject-level averages for group #2 (G2).
What level of precision?
- Difference of averages
- Statistically significant differences between conditions or groups
What statistical test?
A = B
Tests the null hypothesis H0:(A=B) against the alternative hypothesis H1:(A≠B)
Correct detection: Identify correctly where and when the conditions are different.
- Ambiguous sign: We cannot say which condition is stronger.
Power(A) = Power(B)
Tests the null hypothesis H0:(Power(A)=Power(B)) against the alternative hypothesis H1:(Power(A)≠Power(B))
- Incorrect detection: Not sensitive to the cases where A and B have opposite signs.
Meaningful sign: We can identify correctly which condition has a stronger response.
Power(x) = |x|2, where |x| represents the modulus of the values:
- Absolute value for scalar values (recordings, constrained sources, time-frequency)
- Norm of the three orientations for unconstrained sources.
Multiple comparisons: FDR is a good choice for correcting p-values for multiple comparisons.
Design considerations
- Use within-subject designs whenever possible (i.e. collect two conditions A and B for each subject), then contrast data at the subject level before comparing data between subjects.
- Such designs are not only statistically optimal, but also ameliorate the between-subject sign ambiguities as contrasts can be constructed within each subject.
Common pre-processing pipeline
Most event-related studies can start with the pipeline we've introduced in these tutorials.
- Import the anatomy of the subject (or use a template for all the subjects).
- Access the recordings:
- Link the continuous recordings to the Brainstorm database.
- Prepare the channel file: co-register sensors and MRI, edit type and name of channels.
- Edit the event markers: fix the delays of the triggers, mark additional events.
- Pre-process the signals:
- Evaluate the quality of the recordings with a power spectral density plot (PSD).
- Apply frequency filters (low-pass, high-pass, notch).
- Identify bad channels and bad segments.
- Correct for artifacts with SSP or ICA.
- Import the recordings in the database: epochs around some markers of interest.
How many trials to include?
Single subject: Include all the good trials (unless you have a very low number of trials).
See the averaging tutorial.Group analysis: Use a similar numbers of trials for all the subjects (no need to be strictly equal), reject the subjects for which you have much less good trials.
EEG recordings
Average
- Average the epochs across acquisition runs: OK.
- Average the epochs across subjects: OK.
- Electrodes are in the same standard positions for all the subjects (e.g. 10-20).
- Never use an absolute value for averaging or contrasting sensor-level data.
Statistics: Single subject
A = B: Parametric or non-parametric t-test, independent, two-tailed.
Statistics: Group analysis, within subject
A = B
First-level statistic: For each subject, sensor average for conditions A and B.
Second-level statistic: Parametric or non-parametric t-test, paired, two-tailed.
Statistics: Group analysis, between subjects
G1 = G2
First-level statistic: For each subject, sensor average for the conditions to test.
Second-level statistic: Parametric/non-parametric t-test, independent, two-tailed.
MEG recordings
Average
- Average the epochs within each acquisition runs: OK.
- Average across runs: Not advised because the head of the subject may move between runs.
- Average across subjects: Strongly discouraged because the shape of the heads vary but the sensors are fixed. One sensor does not correspond to the same brain region for different subjects.
- Tolerance for data exploration: Averaging across runs and subjects can be useful for identifying time points and sensors with interesting effects but should be avoided for formal analysis.
- Note for Elekta/MaxFilter users: You can align all acquisition run to a reference run, this will allow direct channel comparisons and averaging across runs. Not recommended across subjects.
- Never use an absolute value for averaging or contrasting sensor-level data.
Statistics: Single subject
A = B: Parametric or non-parametric t-test, independent, two-tailed.
Statistics: Group analysis
- Not recommended with MEG recordings: do your analysis in source space.
Constrained cortical sources
Average: Single subject
Sensor average: Compute one sensor-level average per acquisition run and per condition.
Sources: Estimate sources for each average (constrained, no normalization).
Source average: Average the source-level run averages to get one subject average.
Compute a weighted average to balance for different numbers of trials across runs.Low-pass filter your evoked responses (optional).
If you filter the average before normalizing wrt baseline, it will lead to an underestimation of the baseline variance, and therefore to an overestimation of the Z scores computed in the next step, especially if the baseline is too short (typically less than 200 time points). The filter increases the autocorrelation of the time series, and therefore biases the estimation of the signal variance (Wikipedia).
You have to take into account the possible edge effects due to the filter. You can either extract a small time window or exclude the beginning of the baseline for the normalization.
Normalize the subject min-norm averages: Z-score wrt baseline (no absolute value).
Justification: The amplitude range of current densities may vary between subjects because of anatomical or experimental differences. This normalization helps bringing the different subjects to the same range of values.Do not rectify the cortical maps, but display them as absolute values if needed.
Average: Group analysis
Subject averages: Compute within-subject averages for all the subjects, as described above.
Rectify the cortical maps (process: Pre-process > Absolute value).
Justification: Cortical maps have ambiguous signs across subjects: reconstructed sources depend heavily on the orientation of true cortical sources. Given the folding patterns of individual cortical anatomies vary considerably, cortical maps have subject-specific amplitude and sign ambiguities. This is true even if a standard anatomy is used for reconstruction.Project the individual source maps on a template (only when using the individual brains).
For more details, see tutorial: Group analysis: Subject coregistration.Group average: Compute grand averages of all the subjects.
Do not use a weighted average: all the subjects should have the same weight in this average.Smooth spatially the source maps (optional).
You can smooth after step #3 for computing non-parametric statistics with the subject averages. For a simple group average, it is equivalent to smooth before of after computing the average.
Difference of averages: Within subject
Sensor average: Compute one sensor-level average per acquisition run and condition.
Sources: Estimate sources for each average (constrained, no normalization).
Source average: Average the source-level session averages to get one subject average.
Subject difference: Compute the difference between conditions for each subject #i: (Ai-Bi)
Low-pass filter the difference (optional)
Normalize the difference: Z-score wrt baseline (no absolute value): Z(Ai-Bi)
Rectify the difference (apply an absolute value): |Z(Ai-Bi)|
Project the individual difference on a template (only when using the individual brains).
Group average: Compute grand averages of all the subjects: avg(|Z(Ai-Bi)|).
Smooth spatially the source maps (optional).
Difference of averages: Between subjects
Grand averages: Compute averages for groups #1 and #2 as in Average:Group analysis.
Difference: Compute the difference between group-level averages: avg(|G1|)-avg(|G2|)
Limitations: Because we rectify the source maps before computing the difference, we lose the ability to detect the differences between equal values of opposite signs. And we cannot keep the sign because we are averaging across subjects. Therefore, many effects are not detected correctly.
Statistics: Single subject
A = B: Parametric or non-parametric
- Compute source maps for each trial (constrained, no normalization).
Parametric or non-parametric two-sample t-test, independent, two-tailed.
Identifies correctly where and when the conditions are different (sign not meaningful).Directionality: Additional step to know which condition has higher values.
Compute the difference of rectified averages: |avg(Ai)|-|avg(Bi)|
Combine the significance level (t-test) with the direction (difference): See details.
|mean(A)| = |mean(B)|: Non-parametric
- Compute source maps for each trial (constrained, no normalization).
Non-parametric independent two-sample "absolute mean test", two-tailed.
T = (|mean(A)|-|mean(B)|) / sqrt(|var(A)|/NA + |var(B)|/NB)- Interesting alternative that provides at the time a correct estimation of the difference (where and when) and the direction (which condition has higher values).
Statistics: Group analysis, within subject
Power(A-B) = 0: Parametric
First-level statistic: Rectified difference of normalized averages.
Proceed as in Difference of averages: Within subjects, but stop before the group average (after step #8). You obtain one measure |Ai-Bi| per subject, test these values against zero.Second-level statistic: Parametric one-sample Chi2-test.
Power = sum(|Ai-Bi|2), i=1..Nsubj ~ Chi2(Nsubj)Identifies where and when the conditions are different (sign not meaningful).
- Warning: Very sensitive test, with lots of false positive (all the brain can be "significant")
|A| = |B|: Parametric or non-parametric
First-level statistic: Rectified and normalized subject averages.
Proceed as in Average: Group analysis to obtain two averages per subject: Ai and Bi.Second-level statistic: Parametric or non-parametric two-sample t-test, paired, two-tailed.
This test does not consider the sign difference within a subject, and therefore cannot detect correctly when A and B have opposite signs. Works well and indicates which condition has higher values when A and B have the same sign within a subject.
A = B: Parametric or non-parametric [anatomy template only]
First-level statistic: Normalized subject averages (not rectified, no projection needed).
Proceed as in Average: Single subject to obtain two averages per subject: Ai and Bi.Second-level statistic: Parametric or non-parametric two-sample t-test, paired, two-tailed.
Applies only if all the subjects are sharing the same template anatomy.
Not recommended when using individual anatomies because of the sign issue between subjects (the signs might be opposed between two subjects, and the projection of non-rectified values to a template might be inaccurate).
Power(A) = 0: Parametric
First-level statistic: Rectified and normalized subject averages.
Proceed as in Average: Group analysis to obtain one average per subject #i: |Ai|.Second-level statistic: Parametric one-sample Chi2-test.
PowerA = sum(|Ai|2), i=1..Nsubj ~ Chi2(Nsubj).
Statistics: Group analysis, between subjects
|G1| = |G2|: Non-parametric
First-level statistic: Rectified and normalized subject averages.
Proceed as in Average: Group analysis to obtain one average per subject.Second-level statistic: Non-parametric two-sample t-test, independent, two-tailed.
Power(G1) = Power(G2): Parametric
First-level statistic: Rectified and normalized subject averages.
Proceed as in Average: Group analysis to obtain one average per subject: |Ai|.Second-level statistic: Parametric two-sample power F-test.
PowerG1 = sum(Ai2), i=1..N1 ~ Chi2(N1)
PowerG2 = sum(Aj2), j=1..N2 ~ Chi2(N2)
F(N1,N2) = (PowerG1 / N1) / (PowerG2 / N2)
Unconstrained cortical sources
Three values for each grid point, corresponding to the three dipoles orientations (X,Y,Z).
We want only one statistic and one p-value per grid point in output.
Averages
- Proceed as indicated above for constrained cortical sources.
Just replace the step Rectify with Flatten (process: Sources > Unconstrained to flat map).
The operator |A| has to be interpreted as "norm of the three orientations":
|A| = sqrt(Ax2 + Ay2 + Az2)
Statistics: Single subject
|mean(A)| = |mean(B)|: Non-parametric
- Compute source maps for each trial (unconstrained, no normalization).
Non-parametric independent two-sample "absolute mean test", independent, two-tailed.
T = (|mean(A)|-|mean(B)|) / sqrt(|var(A)|/NA + |var(B)|/NB)- Provides at the time a correct estimation of the difference (where and when) and the direction (which condition has higher values).
Statistics: Group analysis, within subject
Power(A-B) = 0: Parametric
First-level statistic: Flattened difference of normalized averages.
Proceed as in Difference of averages: Within subjects, but stop before the group average (after step #8). You obtain one measure |Ai-Bi| per subject, test these values against zero.Second-level statistic: Parametric one-sample Chi2-test for unconstrained sources.
Power = sum(|Ai-Bi|2), i=1..Nsubj ~ Chi2(3*Nsubj)Identifies where and when the conditions are different (sign not meaningful).
- Warning: Very sensitive test, with lots of false positive (all the brain can be "significant")
|A| = |B|: Parametric or non-parametric
First-level statistic: Flattened and normalized subject averages.
Proceed as in Average: Group analysis to obtain two averages per subject: Ai and Bi.Second-level statistic: Parametric or non-parametric two-sample t-test, paired, two-tailed.
This test does not consider the sign difference within a subject, and therefore cannot detect correctly when A and B have opposite signs. Works well and indicates which condition has higher values when A and B have the same sign within a subject.
Power(A) = 0: Parametric
First-level statistic: Flattened and normalized subject averages.
Proceed as in Average: Group analysis to obtain one average per subject #i: |Ai|.Second-level statistic: Parametric one-sample Chi2-test for unconstrained sources.
PowerA = sum(|Ai|2) = sum(Aix2+Aiy2+Aiz2), i=1..Nsubj ~ Chi2(3*Nsubj).
Statistics: Group analysis, between subjects
|G1| = |G2|: Non-parametric
First-level statistic: Flattened and normalized subject averages.
Proceed as in Average: Group analysis to obtain one average per subject.Second-level statistic: Non-parametric two-sample t-test, independent, two-tailed.
Power(G1) = Power(G2): Parametric
First-level statistic: Flattened and normalized subject averages.
Proceed as in Average: Group analysis to obtain one average per subject: |Ai|.Second-level statistic: Parametric two-sample power F-test (unconstrained sources).
PowerG1 = sum(Aix2+Aiy2+Aiz2), i=1..N1 ~ Chi2(3*N1)
PowerG2 = sum(Ajx2+Ajy2+Ajz2), j=1..N2 ~ Chi2(3*N2)
F = (PowerG1 / N1) / (PowerG2 / N2) ~ F(3*N1,3*N2)
Regions of interest (scouts)
Statistics: Single subject
- Even within-subject cortical maps have sign ambiguities. MEG has limited spatial resolution and sources in opposing sulcal/gyral areas are reconstructed with inverted signs (constrained orientations only). Averaging activity in cortical regions of interest (scouts) would thus lead to signal cancelation. To avoid this brainstorm uses algorithms to manipulate the sign of individual sources before averaging within a cortical region. Unfortunately, this introduces an amplitude and sign ambiguity in the time course when summarizing scout activity.
As a result, perform any interesting within-subject average/contrast before computing an average scout time series.
- Then consider as constrained or unconstrained source maps.
Statistics: Group analysis, within subject
- Comparison of scout time series between subjects is tricky because there is no way to avoid sign ambiguity for different subjects. Thus there are no clear recommendations. Rectifying before comparing scout time series between subjects can be a good idea or not depending on different cases.
- Having a good understanding of the data (multiple inspections across channels/sources/subjects) can offer hints whether rectifying the scout time series is a good idea. Using unconstrained cortical maps to create the scout time series can ameliorate ambiguity concerns.
Time-frequency maps
Average: Single subject
Single trials: Compute time-frequency maps for each trial (magnitude, no normalization).
It is a more standard analysis to take the square root of power before a t-test.Subject average: Average the time-frequency maps together, separately for each condition. This can be done automatically when computing the TF decompositions.
- The values are all strictly positive, there is no sign ambiguity: you can directly subtract the averages of the two conditions and interpret the sign of the difference.
- If you average time-frequency maps computed on sensor-level data, the same limitations apply as for averaging sensor level data (see sections about MEG and EEG recordings above).
Average: Group analysis
Subject averages: Compute within-subject averages for all the subjects, as described above.
Normalize the subject averages: ERD/ERS or Z-score wrt baseline.
Group average: Compute grand averages of all the subjects.
Difference of averages: Simply compute the difference of the group averages.
Statistics: Single subject
A = B: Parametric or non-parametric
Compute time-frequency maps for each trial (magnitude, no normalization).
- Parametric or non-parametric two-sample t-test, independent, two-tailed.
Statistics: Group analysis, within subject
A = B: Parametric or non-parametric [anatomy template only]
First-level statistic: Normalized subject averages (ERS/ERD or Z-score).
Proceed as in Average: Group analysis to obtain two averages per subject: Ai and Bi.Second-level statistic: Parametric or non-parametric two-sample t-test, paired, two-tailed.
Statistics: Group analysis, between subjects
G1 = G2: Non-parametric
First-level statistic: Normalized subject averages (ERS/ERD or Z-score).
Proceed as in Average: Group analysis to obtain one average per subject.Second-level statistic: Parametric or non-parametric two-sample t-test, independent, two-tailed.