Hi Karl,
I wanted to make a technical comment on your last email...
> A completely seperate issue, you should be aware of, is the use of
> single subject contrasts with VBM. This has nothing to do with the
> validity of the statistical model or inference but pertains to the
> normality asssumptions about the errors. I recently wrote this in
> repsonse to an enquiry:
>
> "There is an argument that parametric assumtions, regarding the
> distribution of residuals, may be more prone to violation when
> comparing a single subject to a group with VBM. This is because the
> original parition images have a highly non-normal density function (it
> is restricted to the range 0 to 1 and generally has more mass at these
> extremes). Although spatial smoothing renders the distribution
> near-normal by central limit theorum, some non-normality may persist.
> Usually this can be discounted because the residuals are themselves a
> linear compound of the data and again, by central limit theorun
> normality is further assured. This compound is determined by the rows
> of the residual forming matrix.
That residuals are more normal than the true (unobservable) errors
is referred to as supernormality. This is a problem, I think,
not a strength, in that it masks potential departures from your
model. Remember the linear model assumption is not that your
residuals are normal, but that your errors are.
In general, as n increases and the number of parameters
stays fixed, supernormality diminishes. Hence it is
mainly a low-df problem; as the df increase the residuals are
distributed more closely to the true error distribution (and they
more closely approximate an independent sample).
As I see it, the "good-stuff" that the CLT gives is that c'\beta,
your contrast of interest, becomes more Normal with increasing n.
Regards,
-Tom
-- Thomas Nichols -------------------- Department of Biostatistics
http://www.sph.umich.edu/~nichols University of Michigan
[log in to unmask] 1420 Washington Blvd
-------------------------------------- Ann Arbor, MI 48109-2029
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|