> From [log in to unmask] Thu Jan 21 15:50:57 1999
> Date: Thu, 21 Jan 1999 09:47:20 -0600
> X-Accept-Language: en
> References: <[log in to unmask]>
> Subject: Re: SPECT comparison Stats
Dear Kevin,
> I have some follow-up questions regarding the interchange quoted below.
> 1) When you say a threshold of 2, you mean uncorrected Z = 2?
Yes.
> 2) What part of the derivation corrected p value assumes a high initial
> threshold,
The expecations of maxima in SPMs are based on high threshold
approximations (expressions for the Euler characteristic are exact but
at low threhsolds this characteristic may reflect 'holes' in the
activated regions).
> and is there any way a priori to figure out what initial
> threshold is acceptable, or how likely a result is to be a false
> positive if we use a given low initial threshold? If the answer is too
> long or involved perhaps you could point me to part of a published
> paper. I ask because we have data on which I would prefer to use a
> lower initial threshold if possible, because the question is more "what
> is the most inclusive, reasonable set of brain voxels that may be
> involved" rather than "is there any signif. difference between
> conditions"?
The only principled way is to use simulations (c.f. randomization
testing). These have already been performed (e.g. Friston KJ Worsley
KJ Frackowiak RSJ Mazziotta JC & Evans AC. Assessing thesignificance of
focal activations using their spatial extent. Human Brain Mapping
1994;1:214- 220 and Friston KJ Holmes A Poline J-B Price CJ Frith CD.
Detecting activations in PET and fMRI: levels of inference and power.
NeuroImage , 1996;4:223-235). They suggest that the inferences are
robust (i.e. relatively insensitive to violations of the assumptions
behind the test - in this instance high thresholds) for thresholds as
low as 2 (and maybe lower). If you simply want to identify an
excursion set 'that may be involved' I would not worry about corrected
inferences. We use very low thresholds when masking one SPM with
another to allow for some specification of the context in which
inferences (using the masked SPM) are made.
With best wishes - Karl
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