Hi,
I think the set notation and Venn diagrams are unhelpful here... when
people talk about A>B they mean a contrast with null hypothesis A-B =
0, and a right-tailed (single-tailed) alternative hypothesis. This
might sound like pedantry, but with more complex contrasts, I think it
clarifies things. [1 -1 -1 1] has null hypothesis Al-Ar+Br-Bl = 0,
with right-tailed alternative. Which could be expressed as Al-Ar >
Bl-Br or Al+Br > Ar+Bl, or various alternatives. Now, you can see that
several things could happen to reject the null hypothesis, for
example, Al could be *less* than Ar and Bl less than Br (by a larger
amount). In other words, you are not testing ((Al - Ar) > (Bl - Br)) &
(Bl > Br), where the & is the crucial bit. The contrast vector is used
as a whole, and the result compared with zero, so there is no question
of "ordering" of any "component" contrasts.
You can mask the results of the [1 -1 -1 1] contrast by the sign of a
simpler contrast, for example [0 0 1 -1], to ensure that Bl > Br and
(Al-Ar) > (Bl-Br). SPM has some kind of contrast-masking buttons you
can push; I don't know if there is anything similar in FEAT, but you
could use fslmaths with T or Z images to reproduce the effect, I
think.
I hope that helps,
Ged.
On 24/10/2007, Jose Paulo Santos <[log in to unmask]> wrote:
> Hello,
>
> I'm a bit confused with the problem below.
>
> A graphical visualization could be as in Fig1. But if the question is
> (Al>Ar) > (Bl>Br), the contrast should be:
>
> [ 1 -1 0 0 ] - [ 0 0 1 -1 ] = [ 1 -1 -1 1 ]
>
> which is the same!? How can it be? Graphically (Fig2), the answers are
> similar, but not equal. It seems that the order of the operations matters.
> In this case, at the third level, it should be processed the contrasts
> that are in the parentheses and then, at the fourth level, the overall
> question.
>
> How does FSL computes the contrast [ 1 -1 -1 1 ]? Linearly or by any order
> (Fig3)?
>
> Kind regards,
> Jose Paulo Santos
>
> On Mon, 30 Jul 2007 09:26:07 +0100, Steve Smith <[log in to unmask]>
> wrote:
>
> >Hi - I'm pretty sure you can do this at the third level. If your 3rd
> >level EVs are:
> >
> >>>> Al > bl, Ar > bl, Bl > bl and Br > bl
> >
> >Then do ask
> >
> >>>> (Al>Bl) > (Ar>Br)
> >
> >At the third level you just want the contrast:
> >
> >[ 1 0 -1 0 ] - [ 0 1 0 -1 ] = [ 1 -1 -1 1 ]
> >
> >which is a typical interaction contrast. Note that you may want to
> >use contrast masking to ensure that (e.g.) Al>Bl and Ar>Br (etc) to
> >help the interpretation of the interaction.
> >
> >Cheers, Steve.
> >
> >
> >
> >On 26 Jul 2007, at 18:16, Stephane Jacobs wrote:
> >
> >> Hi Steve,
> >>
> >> Well, I don't think it is possible with the way my analysis has
> >> been run
> >> up to the 3rd level. If I take the example of the interaction
> >> (Al>Ar) >
> >> (Bl-Br), I get both contrasts Al>Ar and Bl>Br only at the output of
> >> the
> >> 3rd level analysis, so I don't see how I could contrast them one
> >> against
> >> another within the same analysis...
> >> Should I set the differential contrasts (e.g. Al>Ar, etc...) as
> >> soon as
> >> the 2nd level, for each subject? Then I guess I could set my
> >> interaction
> >> contrasts at the 3rd level...
> >> Do you see any reason why this should fail at the 4th level?
> >>
> >> Thanks again for your help,
> >>
> >> Stephane
> >>
> >>
> >> Steve Smith wrote:
> >>> Hi - it sounds like you should be finding this interaction as
> >>> additional contrasts at the 3rd level, not via a 4th level analysis -
> >>> does that sound possible?
> >>> Cheers.
> >>>
> >>>
> >>> On 25 Jul 2007, at 23:54, Stephane Jacobs wrote:
> >>>
> >>>> Hello,
> >>>>
> >>>> I'm trying to set up interaction contrasts in a 4th level-
> >>>> analysis. I
> >>>> have 2
> >>>> conditions (A and B) x 2 sides (l and r) design, and I'd like to
> >>>> analyze the
> >>>> interaction between the factors SIDE and CONDITION.
> >>>> The second level analysis is run for each subject separately to
> >>>> model
> >>>> between run variance, and outputs each of the 4 conditions vs.
> >>>> resting
> >>>> baseline (bl): Al > bl, Ar > bl, Bl > bl and Br > bl.
> >>>> The third level analysis models between-subjects variance, and is
> >>>> basically
> >>>> a "quadrupled" T-test, computing paired-comparisons between my 4
> >>>> conditions:
> >>>> Al > Bl, Ar > Br, Al>Ar, Bl > Br, and the reverse contrasts.
> >>>>
> >>>> Now, I want to take these copes from the 3rd level analysis to
> >>>> test for
> >>>> interactions between SIDE and CONDITION. To this end, I set up the
> >>>> following
> >>>> contrasts in my 4th level analysis:
> >>>>
> >>>> (Al>Bl) > (Ar>Br) to test the difference between both sides for
> >>>> (A > B)
> >>>> (Al>Ar) > (Bl>Br) to test the difference between both conditions for
> >>>> (l > r)
> >>>> etc... I have a total of 8 contrasts set, using 8 EVs coming from
> >>>> the
> >>>> 3rd
> >>>> level analysis.
> >>>>
> >>>>
> >>>> I guess (hope!) all this makes sense so far, but FEAT fails
> >>>> running the
> >>>> analysis when doing higher-level stats:
> >>>>
> >>>> An exception has been thrown
> >>>> Singular design. Number of EVs > number of time points. Trace:
> >>>> Gsmanager::ols; Gsmanager::run.
> >>>>
> >>>>
> >>>> I can't figure out why this is happening... I understand it suggests
> >>>> I don't
> >>>> have enough data to run these contrasts, but it surprises me as I
> >>>> have 20
> >>>> subjects in my group, and quite a few trials per condition. This
> >>>> being said,
> >>>> I'm not quite sure of what the number of time points represents for
> >>>> such a
> >>>> high-level analysis...
> >>>>
> >>>> Any help would be most appreciated!
> >>>>
> >>>> Best regards,
> >>>>
> >>>> Stephane
> >>>
> >>>
> >>> ---------------------------------------------------------------------
> >>> ------
> >>>
> >>> Stephen M. Smith, Professor of Biomedical Engineering
> >>> Associate Director, Oxford University FMRIB Centre
> >>>
> >>> FMRIB, JR Hospital, Headington, Oxford OX3 9DU, UK
> >>> +44 (0) 1865 222726 (fax 222717)
> >>> [log in to unmask] http://www.fmrib.ox.ac.uk/~steve
> >>> ---------------------------------------------------------------------
> >>> ------
> >>>
> >>>
> >>>
> >
> >
> >------------------------------------------------------------------------
> >---
> >Stephen M. Smith, Professor of Biomedical Engineering
> >Associate Director, Oxford University FMRIB Centre
> >
> >FMRIB, JR 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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