Global Scaling

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Below is a series of postings to the SPM mailing list describing the difference between global noralization and grand mean scaling. This is an important distinction that will have important consequences for your statistics at the first level.



- From Jesper Andersson

Global scaling: Is used to remove global signal drifts/trends across an indidividual time-series (session). It is largely a remnant from the PET days where differences in injected activity could be a large part of the scan-scan variance. For fMRI a) most of the "global" changes are removed by the high-pass filter and b) the "estimator" of "global" intensity that is commonly used can be biased by true activations. For that reason it is typically not recommended.

Grand mean scaling: Simply means putting all time series on a common scale by normalising the mean of all voxels (over space and time)t to 100. Doesn't change first-level stats at all (though its application at first level will change second level results). Should always (I think) be used at first level unless data are somehow "quantitative". For second level analysis it is less clear if it should be applied or not. Its application at the second level doesn't change the 2nd level stats. Neither do I think it helps interpretation. The "grand mean scaling" is applied automatically if "global normalisation" isn't selected. This means that the effects you observe at a second level all have a common scale (as common as it gets with BOLD). The purpose of "grand mean scaling" is to facilitate interpretation of the betas and of any plots that you might do. Say for example you have a scanner where BOLD data are arbitrarily scaled so that "normal" intensity values are in the range 10e-6. This means your betas and the y-axis of any plots will be in the same range, and it would take a bit of experience with that particular data until you "know" what is a "big" beta. If the data are scaled prior to any analysis so that the mean (across voxels and time) voxel intensity is 100, then interpretation is easier and you can think of it as "sort of" % change (N.B. it is _not_ really % change). What is meant by "quantitative" is if your data consist of for example calculated rCBF values (using PET) in which case each voxel value has an absolute value in terms of ml/(min*100ml) (typically around 70-80 in gray matter). Then one would typically not want to do either global normalisation nor grand mean scaling.

Global normalisation at the second level would change results at the second level. If you have two groups and you find that BOLD signal is vastly different in one group compared to the other regardless of type of task, then your data will always be very difficult to interpret. One possible way would be to model each subjects signal with the subjects own HRF (including its height) as assessed by a separate scan with some very basic sensory task (e.g. rev. checkerboard). When then applying that to some task of interest it might be possible to assess if there are differences over an above those due to some overall BOLD response difference. The big problem here would be how to select the set of voxels in the basic scan over which to assess the height of the HRF (would be VERY dependent on which voxels are chosen).

Thresholding at the second level will simpy affect what parts of the brain that are being included in the calculations


- From Karsten Specht
Department of Biological and Medical Psychology , University of Bergen, Norway

"Global scaling" should be skipped on the first level, and skipped definitely on the second level.

The session/subject regressor, assuming that there are no scaling differences within one session, captures the different baselines on the first level.

The scaling on the second level is only useful when analysing other images than con_images (MRI-Perfusion images or PET images, for example). Here, it is necessary, that the global mean is the same across subjects.In case of a 'classical' second level analysis, con-images are already appropriately scaled, i.e. positive values are reflecting a signal increase, negative values a decrease and the value itself represents somewhat like the strength of the effect.


- From Stephen J. Form:

A few years ago it was common for people to do global scaling in SPM fMRI analyses. Nowadays the advice is that, in most situations, it shouldn't be done. SPM does grand mean scaling implicitly. The purpose of grand mean scaling is to attempt to deal with scaling differences, without doing something as strong as global scaling. In grand mean scaling, the mean over all (intracerebral, essentially) voxels in all volumes in the session is computed. Then all voxels in all volumes in that session are scaled by this mean (and perhaps then multiplied by something like 100). This takes care of scaling differences between *sessions*. It doesn't address the issue of scaling differences between volumes within a *session*. The presumption is that those latter differences aren't that high.