Dear Jérôme,
> We have a 2-groups PET study (9 Healthy(G1) vs 8 Patients(G2)) with 6
> conditions (N,H,A,B,C,S) and 2 replications by condition.
> N and H are control conditions for the S activation condition
> A is control condition for B and C activation condition.
> we wanted to compare the two groups for the S-N, S-H and C-A
> contrasts.
> We first defined individual contrasts and we then performed second
> level analyses in order to compare the two groups, i.e., S-N(G1) and
> S-N(G2) interaction; S-H(G1) and S-H(G2) interaction; C-A(G1) and
> C-A(G2) interaction. These analyses have very low degrees of freedom
> (15). But, since each individual contrast involved in these analyses
> was obtained from 4 scans (2conditions, 2 replications), the total
> number of scans involved in the analyse is 4 x (9 + 8) = 68.
> Is there mean to correct df with the real number of scans?
No, not really. There is a critical distinction between a fixed effects
(FFX) and random effects (RFX) analysis of your data with respect to the
degrees of freedom and the inference. You described the RFX analysis,
leaving you with degrees of freedom, which is a function of the number
of subjects and the design matrix employed at the 2nd level analysis.
In terms of inference, the difference between a FFX and RFX analysis is
that with a RFX analysis you generalise your inferences to the
population of the subjects/patients. With a FFX analysis, you make
inferences only about your measured data. However, the more general
inference facilitated by a RFX analysis has its price in the lower
degrees of freedom available (given that you have more than 1
scan/subject).
There is a helpful website about RFX analyses put together by Darren
Gitelman, where he compiled some references and many of Andrew's answers
to the SPM-mailbase into a knowledge base about RFX analyses....
http://www.brain.nwu.edu/fmri/spm/ranfx.html
Concerning the degrees of freedom:
In a FFX analysis, you analyze the data only at the 1st level. The
estimated error variance at a voxel is a function of the model and the
actual fit to the data, i.e. you look at the variance over scans. Here
one usually has got high degrees of freedom for a group study, because
the degrees of freedom is 'number of scans' - 'rank of design matrix'.
(PET)
In a RFX analysis, one wants to look at the variance over subjects. You
do this in SPM99 by fitting a model to the weighted parameter estimate
images of the 1st level analysis (contrast images). The error variance
of this 2nd level model is then over subjects, not over scans, because
you have got one image per subject. The degrees of freedom for the
estimate of this error variance is here 'number of subjects' - 'rank of
2nd level design matrix', i.e. the degrees of freedom is lower than in
the 1st level analysis, in your case 15 = 17-2.
Stefan
--
Stefan Kiebel
Functional Imaging Laboratory
Wellcome Dept. of Cognitive Neurology
12 Queen Square
WC1N 3BG London, UK
Tel.: +44-(0)20-7833-7478
FAX : -7813-1420
email: [log in to unmask]
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