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Subject:

Re: non independent analyses ?

From:

Rik Henson <[log in to unmask]>

Reply-To:

Rik Henson <[log in to unmask]>

Date:

Fri, 21 May 2010 08:39:46 +0000

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> Dear Rik,
> 
> Thank you very much for your detailed and clear response, it helps a
> lot. If you don't mind I have a quick related question which actually
> concerns the use of unbiased statistics in the context of forward
> inferences. Let's say I identified, based on a whole-brain analysis, 2
> regions that respond to opposite contrasts (i.e. A>B in region 1 and B>A
> in region 2). If I want to make the point of a qualitative difference
> between regions 1 & 2, I need to show a common activation/deactivation
> of A or B vs C in both regions 1 & 2 (eg A>C in regions 1 & 2). 

Well, that's what I would argue, yes! (but others might argue that these criteria are too stringent...)


> Now if I correctly understand your previous response, it seems that testing the
> A>C difference in regions 1 & 2 only (by means of an ROI analysis) is
> not correct, and that I should instead use a whole-brain mask of the
> A>C contrast to avoid any statistical bias. Am I correct ?

Well, ideally, your two regions would be identified independently by, eg, anatomy, a prior functional study, or a contrast on the same data that is orthogonal to both the [1 -1 0] contrast on A vs B, AND the [1 0 -1] or [0 1 -1] contrasts on A/B vs C (eg [1/3 1/3 1/3 -1] relative to some fourth baseline condition D). Sorry! I realise this is a tough set of constraints to meet (that I have not yet met myself!), so a qualitative difference as defined in those 2005/2006 papers should perhaps be viewed as an aspiration rather than strict necessity! (in reality, I think evidence is a continuum of weaker to stronger data patterns, rather than black-or-white). Ho hum.

Best wishes
Rik




> Thanks a lot again for your time and help, I really appreciate it.
> Sincerely,
> Elise
> 
> 
> Le 20/05/2010 21:11, Rik Henson a écrit :
> > Elise -
> >
> > In the ideal case where the regressors (columns) of your design
> matrix are orthogonal (e.g, if you have a 2nd-level design with equal
> numbers of subjects in each condition A to C), and the error is i.i.d
> (white), then all that matters is whether your contrast weights are
> orthogonal.
> >
> > If so, then taking your first example, and assuming your conditions
> are ordered [A B C], then you cannot use contrast weights [1 -1 0] to
> select a region from which to extract data (or use for SVC) for a
> second contrast with weights [1 0 -1] without inducing some statistical
> bias (since [1 -1 0]*[1 0 -1]' ~= 0).
> >
> > In your second example, where you split condition A into two halves
> A1 and A2, and use contrast weights [1/2 1/2 0 -1] (ordered [A1 A2 B
> C]) to select a region for subsequent testing of [1 -1 0 0], then the
> contrast weights (and regressors) are orthogonal, but the error may not
> be i.i.d (variance associated with the A1 and A2 estimates is likely to
> be greater). The deviation from i.i.d. is unlikely to be large though.
> >
> > If you have correlated regressors (e.g, in a 1st-level fMRI design),
> then you could use the conjunction option to create orthogonal
> contrasts (contrasts are a function of the contrast weights and the
> design matrix). There may also be (auto)correlation in the error, but
> again this should be small. For a more precise answer, see Karl's
> email:
> >
> > https://www.jiscmail.ac.uk/cgi-
> bin/wa.exe?A2=ind0904&L=SPM&P=R89389&I=-3
> >
> > Best wishes
> > Rik
> >
> > ________________________________________
> > From: SPM (Statistical Parametric Mapping) [[log in to unmask]] on
> behalf of elise metereau [[log in to unmask]]
> > Sent: 20 May 2010 18:59
> > To: [log in to unmask]
> > Subject: [SPM] non independent analyses ?
> >
> > Dear SPM experts,
> >
> > I have made some reading on the issue of non-independent analyses and
> > "double dipping", and now I'm wondering about non independence -and
> thus
> > validity- of the following analyses:
> >
> > 1) Let's say I have an fMRI experiment with 3 conditions A, B and C.
> The
> > contrast A>B gives a significant cluster. Now I want to make sure
> that
> > the contrast A>C is also significant in this region, and to this aim
> I
> > extract the % signal change from the above cluster (separately for
> each
> > particpant and each condition) and compare the A and C conditions
> using
> > a paired t-test. Is such an ROI analysis valid or considered a case
> of
> > non independence ? (I could also use a whole-brain mask, but
> considering
> > I'm focusing on one particular cluster, I'm wondering whether the
> less
> > conservative ROI approach might not be sufficient)
> >
> > 2) Let's say I'm comparing condition A versus a control condition C
> and
> > find a significant cluster. Let's now imagine that condition A can
> > actually be split into 2 categories A1 and A2, and that I want to
> > determine whether activity in the previous cluster is modulated by
> these
> > categories. Similarly, is it valid to compare A1 versus A2 in this
> ROI,
> > or is it a case of non independence ?
> >
> > Any insight will be greatly appreciated.
> > Best,
> >
> > Elise


-------------------------------------------------------
                 Dr Richard Henson
         MRC Cognition & Brain Sciences Unit
                 15 Chaucer Road
                   Cambridge
                  CB2 7EF, UK

           Office: +44 (0)1223 355 294 x522
              Mob: +44 (0)794 1377 345
              Fax: +44 (0)1223 359 062

http://www.mrc-cbu.cam.ac.uk/people/rik.henson/personal
-------------------------------------------------------

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