Dear Howard,

> I am performing a VBM analysis of a patient group. There is one image
> per subject and all images were entered into a single design matrix.
> The control scans were entered as a single condition, but each patient
> was entered into the analysis as their own condition. In addition to
> allowing a comparison of the control group with the patient group, each
> patient can be compared with the control group. The results make
> sense, but I'm not sure how to interepret the t-values and p-values
> that result from this analysis, because the patient 'group' in such an
> analysis is actually only one image, thus the variance in that
> condition can't really be measured.
>
> What, exactly does the program do in this instance, and are the
> resulting t and p-values accurate?


SPM does not allow invalid [in-estimable] designs and so your p values
and t values are perfectly OK. If your patients show a pathological
degree of variability in terms of grey matter density then your design
is the correct one because you are modelling each patient seperately.
Although you are using up degrees of freedom you ensure that
homogeniety of variance is not an issue (there is no error variance
associated with the patients). The inference you are making about each
patient is in relation to the variability among the control subjects
and this is fine.

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.

However, some residual forming matrices (e.g. those comaring one
subject to a large number) put most of the weight on one subject. In
this instance the p values may be inexact. In short p values
associated with single subject vs. group contrasts should be treated
with caution if the data are not smoothed substantially. In our
experience, using null contrasts on emprical data, and using simulated
data, this is not a problem provided the smoothing is at least 4mm
FWHM. However it is difficult to generalize statments about robustness
to all situations and one must ensure a qualifed and informed
interpretion."

I hope this helps - Karl


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