Thanks Eric, that helps, I think I am beginning to
understand!

So now my understanding is that the contrast weights
are making weighted sums of the means of the observed
values within task, rather than the sums of the
observed values within task.  This implies that,
behind the scenes, SPM is taking Raj's original design
matrix:

TaskA TaskB Rest
  1    0     0
  1    0     0
  1    0     0
  0    0     1
  0    0     1
  0    0     1
  0    0     1
  0    1     0
  0    1     0


and rescaling each column like this:

TaskA TaskB Rest
 1/3   0     0
 1/3   0     0
 1/3   0     0
  0    0    1/4
  0    0    1/4
  0    0    1/4
  0    0    1/4
  0   1/2    0
  0   1/2    0


The resulting regression coefficients would then be
the means of the observed values within task, rather
than the sums.


Is this correct?

Thanks!

George


--- Eric Zarahn <[log in to unmask]> wrote:

> Remember that contrasts are linear combinations of
> parameter estimates, not
> linear combinations of the columns of the design
> matrix. As the expected
> value of a parameter estimate does not depend on the
> number of trials (or
> more generally, the number of observations or data
> associated with a given
> effect), the choice of contrast weights do not
> depend on the number of
> trials (well, that is not quite true, as there are
> usually an infinite set
> of contrast weights that all have the same expected
> value, and one wants to
> select the most efficient contrast from this class,
> but the correct choice
> is trivial in Raj's example). George's suggested
> contrasts have a different
> expected value from Raj's, but Raj's expected values
> are the correct ones,
> i.e., they compare the mean effects in the desired
> way. For example the
> contrast weight vector [ 0 1/2 -1/4 ] corresponds to
> a contrast of .5*(Task
> B mean) - .25*(Rest mean), which is not desired.
> Raj's analogous contrast
> weight vector of [0 1 -1]  corresponds to a contrast
> of (Task B mean) -
> (Rest mean), which is desired.
> 
> Eric
> 
> 
> ----- Original Message ----- 
> From: "George Towne" <[log in to unmask]>
> To: <[log in to unmask]>
> Sent: Tuesday, June 21, 2005 4:49 PM
> Subject: Re: [SPM] Contrasts for a design matrix
> 
> 
> > Hi Raj, with the given design matrix, I would have
> > thought that instead of the contrasts
> >
> >     [ 1 1 -2 ]
> >     [ 1 0 -1 ] and
> >     [ 0 1 -1 ]
> >
> > you should instead use the contrasts
> >
> >     [ 1/3 1/2 -1/4 ]
> >     [ 1/3 0 -1/4 ] and
> >     [ 0 1/2 -1/4 ]
> >
> > to take into account the differing numbers of
> scans in
> > the TaskA, TaskB, and Rest groups.  E.g., if c
> were
> > set to [ 0 1/2 -1/4 ] and X was your given design
> > matrix, then c'X would contrast the mean of the
> two
> > TaskB scans versus the mean of the four Rest
> scans.
> >
> >
> > George
> >
> >
> > --- RJ <[log in to unmask]> wrote:
> >
> > > I am trying to find out if there are any
> specific
> > > rules when setting up contrasts in SPM2 for an
> fMRI
> > > analysis where different conditions have
> differing
> > > number of samples.
> > >
> > > Suppose I have a de-meaned fMRI data set with
> three
> > > conditions A, B and Rest with unequal number of
> > > scans
> > > say 3, 2 and 4 respectively.
> > >
> > > If my design matrix were as shown below
> (orthogonal,
> > > full rank, simple box car)
> > >
> > > TaskA TaskB Rest
> > >   1    0     0
> > >   1    0     0
> > >   1    0     0
> > >   0    0     1
> > >   0    0     1
> > >   0    0     1
> > >   0    0     1
> > >   0    1     0
> > >   0    1     0
> > >
> > > My questions are:
> > >
> > > Do the regressors need to be normalized in some
> way
> > > (de-meaned/other) considering the fact that the
> > > actual
> > > dataset (Y) is already de-meaned ? My concern
> here
> > > being the differing number of samples for the
> > > conditions.
> > >
> > > Also, is it important to have the sum of the
> > > contrast
> > > weighted regressors equal to zero i.e sum(c1*X1
> +
> > > c2*X2 + c3*X3) = 0 ? In other words is it ok to
> have
> > > t-statistic contrasts such as [1 1 -2], [1 0 -1]
> and
> > > [0 1 -1] in the case of the above design matrix
> ?
> > >
> > > I did run an analysis comparing both ways i.e
> > > regressors with zero mean and non-zero mean
> > > regressors
> > > and got results which were very close but am
> trying
> > > to
> > > verify whether it is ok to do so.
> > >
> > > ....Raj
> > >
> > >
> > >
> > >
> > >
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