Hi Anders,
your data cannot be Gaussian and have a much longer tail. The longer
tail means that they are not Gaussian. Your result tell me one of the
following
1) your data depart so much from normality that parametric results are
not applicable. The Bonferroni too depends on significance values
computed parametrically.
2) your implementation of the permutation test is wrong, or your
implementation of the Bonferroni correction is wrong.
Best wishes,
Roberto
> Hello, I do not apply any second level analysis since I only work with
> single subject fMRI. I have implemented a random permutation test to
> calculate a threshold, but I get higher thresholds than Bonferroni
> correction and random field theory. The residuals look Gaussian
> distributed but have a much longer tail, does this make sense to you?
>
> /Anders
>
> Roberto Viviani skrev 2010-11-01 14:59:
>>> Good point, I mean that the MRI observations have Rician-distributed
>>> noise. My question however remains, is this considered in SPM or is it
>>> assumed that the noise is Gaussian?
>>
>> There is no single distribution that holds for all MRI data used in
>> practice. Voxel-based morphometry data, for example, are
>> probability values bounded between 0 and 1. Other data are ratios
>> of random variables.
>>
>> There are two distributional issues to consider in general:
>> marginal (the distribution of the data seen voxel by voxel) and
>> joint (viewed multivariately). In the SPM approach, the first
>> affects the marginal distribution of the parametric map, the second
>> the exactness of the correction for multiple comparisons.
>>
>> In general, the marginal distribution may not be the same over the
>> volume. So it isn't very useful to think of it as just one
>> distribution. But anyway the parametric map will marginally tend to
>> normality for large samples, as those commonly found in functional
>> MRI. So for fMRI/EPI, I would not worry much about distributional
>> issues arising from the EPI signal. Besides, 'EPI-specific noise'
>> has a limited influence on the distribution of residuals at the
>> second level, which is where you carry out inference. Instead, the
>> dominant source of variance arises from the subject-to-subject
>> variation of the effect of interest.
>>
>> The sensitivity of the test to violations of distributional
>> assumptions depends on the test statistic. Voxelwise corrections
>> (which use the maximum over the volume as test statistic) are
>> quite sensitive to marginal violations, and much less to joint
>> distributional violations. In contrast, cluster-level corrections
>> (using the maximum cluster size) are very sensitive to violations
>> of the joint distributional assumption.
>>
>> There is a simple way to correct for marginal volations: rank the
>> data voxel by voxel, and carry out a permutation test. The issue of
>> corrections for joint distributional assumptions is a topic of
>> active research.
>>
>> Best wishes,
>> Roberto Viviani
>>
>>
>>>
>>> /Anders
>>>
>>> 2010-10-31 10:19, Gael Varoquaux skrev:
>>>> On Sat, Oct 30, 2010 at 07:45:07PM +0200, Anders Eklund wrote:
>>>>
>>>>> An interesting discussion, do you know if SPM uses the fact that the
>>>>> noise in MRI is Rician distributed and not Gaussian distributed?
>>>>>
>>>> Forgive me for asking a naive question, but is the noise in fMRI really
>>>> Rician-distributed? The MRI-observation noise is Rician-distributed. I
>>>> believe that this comes directly from the measurement process. However,
>>>> with EPI, there are much more processes contributing to 'noise' than
>>>> imaging noise, such as residual movement or vascular and respiratory
>>>> noise.
>>>>
>>>> I am not even sure that the EPI-specific noise (such as
>>>> field-inhomogeneity fluctuations that can clearly be seen in the
>>>> ventricles) are Rician-distributed. If someone on the mailing-list who
>>>> understands the physics behind the EPI noise could enlight me, I'd be
>>>> much obliged.
>>>>
>>>> Gael
>>>>
>>>
>>> --
>>> --
>>> -----------------------------------------------------------------------
>>>
>>> Anders Eklund
>>> Phd student
>>>
>>> Medical Informatics, Department of Biomedical Engineering
>>> CMIV, Center for Medical Image Science and Visualization
>>>
>>> Tel: +46 73 6003790 mail: [log in to unmask]
>>> Fax: +46 13 101902 web: http://www.wanderineconsulting.com/
>>> -----------------------------------------------------------------------
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