Indeed - that all makes sense. I would just add that the
arbitrariness of smoothing extent is one of the problems that we try
to resolve with TBSS (see the paper for details) - by projecting
tract centre FA onto the mean FA skeleton, we avoid the need for
smoothing, and this process also is shown to cause the projected data
to be normally distributed across subjects. However we still
recommend using randomise to get the inference correct as GRF
probably isn't going to be valid on the skeletonised data.
Cheers, Steve.
On 1 Aug 2006, at 11:20, Jesper Andersson wrote:
> Dear Chen,
>
>> thanks replay. Please correct me if I am wrong. Jones's paper
>> discussed
>> about the non-normally distribution residual after applied different
>> smoothing filter on FA multiple subjects' analysis under GLM
>> method. If the
>> residual has non-normally distribution, does it means this
>> statistic method
>> did not fit previously hypothesis ? so the FA analysis should not
>> use GLM
>> method to perform statistic inference but rather use non-
>> parametric method ?
>> Or it still could use GLM method to analysis FA image ?
>
> As I said, I haven't actually read Dereks paper (which I probably
> should), but I'll still try to reply.
>
> As you increase the filter width the intensity in any given voxel
> becomes a mixture of intensities from a larger and larger number of
> voxels. Hence, by virtue of the central limit yada yada the values
> will
> become increasingly normal distributed. Hence, by using a wider filter
> you may pre-condition your data to better adhere to the assumption of
> normal distributed errors.
>
> The other effect of filter width comes from the matched filter
> theorem,
> causing you to become less sensitive to focal activations with small
> spatial extent and more to widespread activations with large spatial
> extent.
>
> As for the use of GLM. Even when your errors are not normal
> distributed
> you can still use the GLM to derive meaningful parameter estimates
> such
> as "mean FA in group 1", even though these may no longer be ML
> estimates. Also, it may still be meaningful to form a t-statistic and
> interpret it in terms of "reliability of difference between group 1
> and
> group 2".
>
> The problem comes if you then try to calculate a p-value for that
> t-statistic y assuming that it is t-distributed, because it is likely
> not to be.
>
> I think it is quite useful for you to conceptually divide your
> analysis
> into "estimation" and "inference" (for lack of better terminology),
> where the first step refers to the estimation of parameters and a
> test-statistic (e.g. t) and the second to the translation
> test-statistic->p-vale. It is (mainly) at the second step that you
> will
> have problems when your data are not normal distributed.
>
> For this reason (and reasons of efficiency when you have low df) I
> would
> suggest using randomisation tests when you have reason to believe that
> you have non-normal data. That way you are not forced to impose a
> lot of
> smoothness (that you may or may not want to have in your data) and you
> know that your test is always valid. The only cost it comes with is a
> little extra processing time.
>
> Most often this means still using the GLM machinery for estimation of
> parameters and test-statistic. It is only the final step (the t->p
> translation) that you replace.
>
> Good luck Jesper
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Stephen M. Smith, Professor of Biomedical Engineering
Associate Director, Oxford University FMRIB Centre
FMRIB, JR Hospital, Headington, Oxford OX3 9DU, UK
+44 (0) 1865 222726 (fax 222717)
[log in to unmask] http://www.fmrib.ox.ac.uk/~steve
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