Thanks for your reply. How can I test the hypothesis that the residuals from the GLM have a normal distribution? Can I for example use a Lilliefors test or a Kolmogorov-Smirnov test? Should the test be applied separately for each timeseries, or once for all the voxels?

A quick test shows that the residuals (for all the voxels) are very close to a normal distribution, but the distribution has very long tails.

/Anders

2010-10-28 19:31, Paul Mazaika skrev:

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The general assumption is that most fMRI data is normally distributed, but I don't know of any study that proves this assumption. The SPMd toolbox includes statistical measures that test for normality of the residual timeseries after all the effects in the data have been modeled (Luo and Nichols, 2003). For many cases, the distribution of the residual timeseries is not significantly different from a normal distribution, thus the normal distribution is a good approximation for the null data.

In some fMRI datasets, the actual data may include transient effects such as subject motion, artifacts from rapid motion, electrical noise transients in the scanner, or the subject took a deep breath and the GLM did not include physiological effects. Thus, it is possible for the non-task data to be not from a stationary normal distribution, and these transients may affect the statistical distributions if they are not modeled properly.

Best wishes,
   Paul


----- Original Message -----
From: "Anders Eklund" <[log in to unmask]>
To: [log in to unmask]
Sent: Thursday, October 28, 2010 8:34:25 AM
Subject: Re: [SPM] Distribution of test statistics

Hi Michael,
but this also assumes that the null data is normally distributed, right? 
Is there any general opinion whether fMRI null data is normally 
distributed or not?

/Anders

Michael Harms skrev 2010-10-28 16:10:
  

HI Anders,
Keep in mind that the distribution of the statistic is under the null
hypothesis of no signal.  If you are examining the distribution (across
voxels) of the t-statistic on actual data from an experimental task, the
distribution may very well not be a t-distribution (e.g., say half your
voxels contain a strong, real response -- then your distribution of t-
values will be skewed positive relative to the t-distribution for null
data of the same dof).

If you input true null data into a processing stream, then by definition
you better get the expected distribution (otherwise, that points to the
existence of a problem/bug in your processing stream).

cheers,
-MH

On Thu, 2010-10-28 at 13:16 +0200, Anders Eklund wrote:
    

Dear SPMers,

I've implemented my own single subject fMRI analysis in Matlab (slice
timing correction, motion compensation, smoothing, detrending, GLM&
t-test) and get activity maps that seem reasonable. I now want to
calculate a threshold that is corrected for multiple comparisons and
have for that purpose used two approaches, Bonferroni correction and
random field theory. As I understand it, both these methods rely on the
fact that the test statistics, under the null hypothesis, follows a
Student's t-distribution (since I calculate a t-test value in each voxel).

For most of my datasets the test statistics seems to approximately
follow a Student's t-distribution with the same degrees of freedom, but
it is often slightly wider at the bottom or slightly skewed. For one
dataset, the test statistics is rather far from the t-distribution.

1) How much work has been done on validating the assumption that the
test statistics follow a certain distribution? Is there any paper where
this is discussed?

2) Is there any specific preprocessing step, that I might have missed,
that ensures that the test statistics follows a certain distribution?

3) Does SPM check the distribution of the test statistics?

Best regards,
Anders Eklund

      

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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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