Dear Walter & Irena,

At 10:56 11/06/99 -0400, [log in to unmask] wrote:
| Our question concerns creating mean images for subsequent random
| effects analysis. Our study design is as follows:
| 	RUN1: A B A B A B A B
| 	RUN2: C B'C B'C B'C B'
| 	RUN3: A B A B A B A B
| 	RUN4: C B'C B'C B'C B'
| 
| A and C pertain to active conditions and B and B' are the control
| conditions. The order of runs is counter-balanced across subjects.
| Now we would like to create a mean image for each condition.  Now we
| know that we must collapse over the replications in order to create a
| single mean image for each condition.  Our question concerns which
| type of adjustment to use for each mean image (scaling or ANCOVA).  In
| the SPM96 help section on adjusted means Andrew Holmes mentions that
| "...multiple runs *must* use the same GM value, and should scale Grand
| mean *by subject*".  We're not quite sure what he means, and how does
| this apply to us?  Thanks for your help.

Grand mean scaling refers to the scaling of a set of images by a common 
factor such that their grand mean (the mean of the global means) is a 
specified value. It arose with qualitative PET data as a a way to
informally 
put the measured "counts" data into the range of rCBF, exploiting the near 
linearity of the counts->rCBF function for normal ranges of both and a 
tightly controlled input dose.

Clearly with proportional scaling global normalisation, grand mean scaling 
is redundent, since if each image is scaled to have pre-specified global 
mean, the grand mean (mean of the globals) will also be the pre-specified 
value.

Grand mean scaling of an entire data set does not affect the statistical 
results. However, grand mean scaling a subjects data in a single subject 
analysis (such that the subjects grand mean is a set value), may well give 
different results to grand mean scaling that subjects data in the context
of 
a group analysis, where the data are scaled such that grand mean across all

scans on all subjects has the desired value. To avoid this predicament, in 
SPM99, by default, grand mean scaling is applied in a session/subject 
specific manner.

Clearly when preparing contrast images from a first level model for a
second 
level random effects analysis you want the contrast images to be on the
same 
scale. Hence the instruction that the grand mean target value (or 
equivalently ) chosen be the same for all data in the model.

The AdjMean programs and SPM99's PET & fMRI designs will by default do the 
right thing. (Grand mean scaling is hardcoded to 100 in the fMRI interface,

and is always applied in a session specific manner.)

Note that in the second level model, you should not need to do any global 
normalisation or grand mean scaling, since that is taken care of in the 
first level analyses.

Hope this helps,

-andrew


+- Dr Andrew Holmes ------------------ mailto:[log in to unmask] -+
|  ___   __  ___ Robertson Centre for Biostatistics                   |
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