Rajesh,
> I have got a comment from a reviewer for the resubmission of a paper
> on ROC in MRM in the context of False Positive Rate which includes
> the acronym GRF. Do you have any idea what it might stand for? The
> sentence reads
>
> "If GRF claims to control the False Positive Rate at a certain
> fraction, what rate on average will be achieved?"
GRF = Gaussian Random Field, for GRF theory. (Since the inference is
usually on t or F fields, I acutally prefer RFT for Random Field
Theory). SPM uses RFT to find corrected p-values for voxel intensity,
cluster volume and cluster count (set-level).
I read the reviewer's comment as asking, in an unusal way, what is the
corrected significance of your results. The RFT results produce
p-values that control the familywise error rate, the chance of one or
more false positives anywhere in the search region.
If you used a 0.05 corrected significance threshold, you can respond
to the reviewer that if the experiment were repeated again and again,
in the long run no more than 5% of the time would you have any false
positives. Here the "rate on average" that the reviewer is asking
about is 0.05, but it is over repeated realizations of the experiment
(this is the usual, strict interpretation of p-values).
As for "what rate on average *will* *be* *achieved*?", that's asking
what the actual size of the test (as opposed t its level, which is
0.05). The size and level are equal if the tests are exact. The RFT
tests are approximate, so to really know the size you'd have to run
some simluations. In low df or low smoothness, the RFT tests for
intensity tend to be conservative.
Does this help?
-Tom
-- Thomas Nichols -------------------- Department of Biostatistics
http://www.sph.umich.edu/~nichols University of Michigan
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-------------------------------------- Ann Arbor, MI 48109-2029
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