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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>
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