Hi Joe,
This seems to have gone unanswered for a few weeks... Hopefully you've
had an off-list reply from an expert, such as Satoru Hayasaka, who
previously gave me this very helpful explanation (off-list, but I hope
Satoru won't mind being quoted) when I asked a related question about
FWE correction of non-stationary-smoothness VBM data:
"voxel FWE p-values are calculated from the distribution of the
maximum of the underlying statistic image (T-image, F-image, etc).
If you know the total number of resels (=volume/FWHM) in the image,
you can derive the distribution of the maximum fairly easily from
RFT. Even if the smoothness is not uniform within the image, the
distribution of the maximum should remain the same."
So there shouldn't be a bias towards significance, as you fear.
However, my take on this is that while FWE should be controlled, the
sensitivity may be different in differently smooth areas (hopefully
others might enter the debate here), for example, I think smoother
areas could be corrected unduly harshly due to the presence of some
rougher areas which require the more stringent (max-based) correction.
Generally though, the feeling in the community seems to me to be
that as long as *specificity* is controlled, some loss (or spatial
variability, as I believe might occur here) in *sensitivity* is
acceptable.
I'm really not an expert on this though, so it would be interesting to
hear other (hopefully on-list!) views on this.
Incidentally, I think a very closely related issue can occur even with
non-parametric statistics. Nichols & Holmes
http://dx.doi.org/10.1002/hbm.1058
discuss the problem of non-stationary variance in FWE-corrected
permutation tests of different potential statistics. I think to a
lesser extent, a similar problem could occur with non-stationary
variance t-statistics, and/or non-stationary smoothness. But I might
be missing something... Anyway, quoting from Nichols & Holmes:
"There are, however, additional considerations when
using the non-parametric approach with a maximal
statistic to account for multiple comparisons. For the
single threshold test to be equally sensitive at all
voxels, the (null) sampling distribution of the chosen
statistic should be similar across voxels. For instance,
the simple mean difference statistic used in the single
voxel example could be considered as a voxel statistic,
but areas where the mean difference is highly variable
will dominate the permutation distribution for the maximal
statistic. The test will still be valid, but will be less
sensitive at those voxels with lower variability."
I hope that's interesting,
Ged.
Joseph Dien wrote:
> In working on generating the ctf files for our data, it occurred to me
> that the process of projecting the 3D coordinates onto the 2D plane can
> result in the electrodes not being evenly distributed even if they were
> originally evenly spaced on the head. It seems to me that this could
> affect the Gaussian statistics in that the error variance will not be
> spatially homogenous (the smoothness will vary locally over the 2D
> plane). If I understand how this works correctly, this means that the
> smoothness of the periphery (where the electrodes tend to be more widely
> spaced on the 2D plane) would generally be underestimated, resulting in
> a bias towards significance. Could this also play a part in this
> observation? Relying on voxelwise statistics, as Stefan suggests, would
> address this issue of course. I'm not sure how the multiple comparison
> corrections would work though. Since they rely on estimating the
> resels, doesn't that mean they would be affected too? If my reasoning
> is correct, would the 3D analyses be affected in some manner too? They
> wouldn't have the problem with the projection to a 2D plane but would
> proximity to sensors affect the local smoothness?
>
> Cheers!
>
> Joe
>
>
> On Jun 22, 2006, at 5:27 AM, Stefan Kiebel wrote:
>
>> Dear Yael,
>>
>> the Gaussian random field theory cannot have an influence on such a
>> potential bias for the edges. You can see that by observing that the
>> statistical maps (statistical values -> uncorrected p-values) already
>> show your observed 'edge' pattern.
>>
>> In your images, the most significant effects are located at the
>> sensors. This means that any analysis (e.g. conventional ANOVA of
>> channel data) would find exactly the same results as you do, because
>> SPM takes care to leave the channel data unchanged (by locating data
>> from a single channel in a single voxel without mixing it with data
>> from other channels). In other words, to exclude any potential
>> artefacts due to interpolation between channels, you could choose to
>> only report statistical values/p-values within voxels, that contain
>> channel data (indicated by the green crosses). These maxima are
>> corrected for multiple comparisons (which is a difference to more
>> conventional analyses in the ERP community).
>>
>> If there is an edge bias, it might have to do with the way
>> intersubject-variability expresses itself in EEG.
>>
>> A powerful way to analyse EEG/MEG data would be do first source
>> reconstruct your images. This allows you to make inferences about
>> sources in the brain.
>>
>> Hope this helps,
>>
>> Stefan
>>> Dear Stefan,
>>>
>>> I postoed this message to the SPM-list but no one has answered..I
>>> hoped you can
>>> help..
>>>
>>> We have been evaluating some EEG results using SPM. In many cases we
>>> noticed the significant effects SPM found was located on the edges(the
>>> boundaries of the head map) of our F-map. We added two images as an
>>> example.
>>> Is there something in the Random Field correction that might bias the
>>> results to prefer the edges of the map?
>>>
>>> Thanks,
>>> Yael.
>>>
>>>
>>>
>>> ----------------------------------------------------------------
>>> This message was sent using IMP, the Internet Messaging Program.
>>>
>>> ------------------------------------------------------------------------
>>>
>>
>>
>> --Dr. Stefan Kiebel Wellcome Dept of Imaging Neuroscience Institute of
>> Neurology, UCL 12 Queen Square London WC1N 3BG
>> Phone: (+44) 20 7833 7478 Fax: (+44) 20 7813 1420
>
> --------------------------------------------------------------------------------
>
>
> Joseph Dien
> Assistant Professor of Psychology
> Department of Psychology
> 419 Fraser Hall
> 1415 Jayhawk Blvd
> University of Kansas
> Lawrence, KS 66045-7556
> E-mail: [log in to unmask]
> Office: 785-864-9822 (note: no voicemail)
> Fax: 785-864-5696
> http://people.ku.edu/~jdien/Dien.html
>
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