Hi Jack,
> >Yes, EVs 1,2,3 are probably all estimable, but it may well be
> >that contrasts between them are not (once noise is taken into account).
> > ....
> >In general you should make "distinguishing judgments" such as you are
> >doing by using contrasts, as you suggest towards the bottom. This gives
> >the most unambiguous test of what you want to know...
>
> But if the contrasts are not estimable, then are any "distinguishing judgements" valid?
Well, you have to be really careful; in particular you have to avoid
saying in effect "A is just over threshold and B is just under threshold
and so they are significantly different from each other". That's why an
explicit contrast is clear. But you don't _have_ to decide in advance that
the contrast isn't at all estimable - if you tri it and it works out
that's fine....(read on)
> WRT my reviewers: Is there anything I can do to quantify my confidence in the EV contrasts?
so if you have run an actual contrast, and it shows something as
significance, then you don't need to do anything else to prove your case.
Regardless of how similar the two EVs are that you are contrasting, if the
contrast shows up as significant, then the maths says that you have a real
effect - it's just that to reach significance you needed a real difference
to be there to overcome the fact that the EVs were similar, and the maths
works out automatically that the variance on this contrast estimator was
always going to be high, and has taken that into account. You can say
something like "the fact that the two EVs feeding into the contrast are
fairly collinear is automatically, explicitly taken into account when
computing the variance of the estimated contrast, so any reported
significant result is valid. For more details see [Keith's chapter in our
FMRI book]"
Cheers.
Stephen M. Smith DPhil
Associate Director, FMRIB and Analysis Research Coordinator
Oxford University Centre for Functional MRI of the Brain
John Radcliffe Hospital, Headington, Oxford OX3 9DU, UK
+44 (0) 1865 222726 (fax 222717)
[log in to unmask] http://www.fmrib.ox.ac.uk/~steve
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