| 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?
At its simplest, a t statistic is an estimate of a mean (or a mean difference)
divided by the square root of the variance estimate of the mean. The t tests
that SPM99 does assume the same residual variance for all observations,
so in this case, the variance will be estimated from the residuals
corresponding to the control group. The residuals are zero for the
patient images as the model can fit this data exactly.
A quick word of warning... A t test assumes that the residuals are drawn
from a normal distribution. VBM data are not quite normally distributed,
but this makes little difference when comparing one group with another.
However, when comparing an individual subject with a group, it may be
an idea to be a little cautious of the p values. The error on the
estimate of a group mean is likely to be normally distributed because of
the central limit theorem (the average of lots of observations drawn from
distributions that may not be normal tends towards being normally distributed).
The average of an individual observation is the observation itself. If
this is not drawn from a normal distribution, then the difference between
it and the mean of a group is not likely to be normally distributed - possibly
leading to erroneous p values.
Another word of warning... Because the t tests in SPM99 assume the same
variance for all observations, I'm not sure what happens when you compare
a group of patients with a group of controls, as there is often more
variability among a patient group than a control group.
Comments from a proper statistician would be appreciated.
Best regards,
-John
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