Hello,
I've got some questions about those parts of SPM.
First, I know temporal smoothing(TS) has been applied before any other
analysis is performed. This TS, is it in function of the haemodynamic
delay or not ? (And if not, where comes haemodynamic delay then in the
picture?) I found some formulas about it in the SPM book on page 86-88,
but I'm not quite sure about them. And which other smoothings are related
to TS and how (Spatial smoothing, ....). What are exactly the consequences
of these smoothings on the degrees of freedom (something done
automatically by SPM, but I'm eager to know how it happens exactly)? I
know it depends on the number of scans taken from a subject (supposing a
single subject study, one run for clarity), but does it vary when it's a
study dealing with two conditions or when e.g. 4 conditions are studied.
And if multiple runs are being used, is it only the multiple of it or not?
Then I've some questions about those t-test-like t-tests used in SPM. When
e.g. a contrast C, namely A - B, is offered, your t-value for every vovel
v will become:
t(v, C) = (Beta(v,A) - Beta(v,B))/Error(v, C)
with Beta(v,i) the regressioncoefficient for condition i in the GLM and
Error(v, C) the error between the modelled signal and the original signal
(for clarity zero mean supposed), given the contrast C. This error, is
that a squared error, i.e. the square of the difference between the
signal-activity and the modelled activity, summed over all scans for that
voxel ? Or, is it a root squared error (thus the root of previous
formula), the used formula in the SPM book is not quite clear about that.
I suppose last option is the correct one, but I'm not quite sure.
And what about it, if you have three conditions in your contrast C, let's
say A + B - 2D. Is in that case the t-test equal to
t(v, C) = (Beta(v,A) + Beta(v,B) - 2Beta(v,D))/Error(v, C)
???
Another question, again related with the degrees of freedom: how are they
calculated exactly for their use in the transition from t-tests to
Z-scores ? Normally a model (with two conditions), looses 3 degrees of
freedom by means of its mean, and the the two regressioncoefficients. So
when having 120 scans, you got a df of 117, i.e. sqrt(117) must be used as
factor, or are there also other Bonferoni-like influences (the smoothing
parameter s e.g., although I've no idea if it's related to the temporal,
the spatial smoothing or I don't know what other kind of smoothing). And,
does it matter if you used 2, 3 or more conditions in your study to
determine the df ? I suppose so, since you've less scans per condition in
case you've more conditions and vice versa, but I found no evidence for it
in literature.
Many thanx in advance for anyone who can tell me more about it,
Kind regards,
Patrick
Ir. Patrick De Maziere
Research Engineer
Computational Neuroscience
Laboratory of Neurophysiology
K.U.Leuven Faculty of Medicine
Campus Gasthuisberg O & N
Herestraat, 49
B-3000 Leuven
Belgium
Tel : +32 16 34.59.61
Fax : +32 16 34.59.93
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http://simone.neuro.kuleuven.ac.be
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