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SPM  March 2009

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Subject:

Re: Paired t-test with covariates

From:

Jonathan Peelle <[log in to unmask]>

Reply-To:

Jonathan Peelle <[log in to unmask]>

Date:

Thu, 12 Mar 2009 18:22:02 +0000

Content-Type:

text/plain

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Parts/Attachments

text/plain (103 lines)

Hi Steve

I'm going to restate what I think the problem is to make sure we are
on the same page.  You can let me know if I've misunderstood.

Let's say you have 6 scans and a covariate for each of them
(10,20,30,40,50,60).  You enter these in your design, and by default
SPM will mean-center this vector, so instead of [10 20 30 40 50 60]
you have [-25 -15 -5 5 15 25].  This is what you want, because a high
parameter estimate for this regressor would tell you that the first
scan contributed less than average, and the last scan more than
average---the relative differences of all your covariates.

The problem arises when you don't have values for all scans.  So now,
say you have 6 scans, but only 3 numbers (10,20,30).  If you then
enter [10 20 30 0 0 0], mean-centering gives you [0 10 20 -10 -10
-10], so a high parameter estimate would indicate that the last 3
scans contribute less to the mean than the first three----not what you
want.

The solution is to set up your vector so that the values for the scans
you want are mean-centered before adding the 0s for the other scans.
In other words, mean-center [10 20 30], which gives you [-10 0 10],
and then add the extra zeros, for [-10 0 10 0 0 0].  Now, data in the
last 3 scans can't have any influence on the fitting of this parameter
estimate, because no matter how large the beta value is, it is
multiplied by 0.

[Note that, since you have mean-centered this vector yourself outside
of SPM, it makes no difference whether you tell SPM to mean-center it
or not.]

The columns of your design matrix relating to subjects will scale to
fit variance associated with a subject across both scans; this
covariate will reflect the values over the first scans.  I think this
will answer the question you are asking...hopefully someone will
correct me if I'm wrong. :)

Hope this helps,
Jonathan

On Thu, Mar 12, 2009 at 4:23 PM, Cramer, Steven <[log in to unmask]> wrote:
> Hi
> Thanks for below.  There is another layer of complexity.  The covariates are
> scan-specific, and the covariate score exists for the first scan only.
> When prompted by SPM5 for the pair of covariate values, if one enters the
> covariate value for scan 1 and a zero for scan 2, this is inaccurate, as the
> model would use the difference (zero minus scan 1 covar value) as a change
> in score, which is not accurate, as the scan 1 value is the score at
> baseline not the change over time.
> Is there a way to enter the covariate value at time 1 when no value exists
> at time 2, in a manner that does not suggest that the time 1 value is a
> change over time?
> Thanks,
> Steve
>
>
> At 10:25 PM +0000 3/10/09, Jonathan Peelle wrote:
>
> Hi Steve
>
> Are your covariates subject-specific, or scan specific?  I.e. do you
> enter the same number for the subject on both scan 1 and scan 2?  With
> a paired samples t-test, I think any part of your data that can be
> explained in a subject-specific manner would be modeled out; so, if
> your covariates are subject-specific, they aren't helping you explain
> any more of your data.  This would explain why your results are the
> same.
>
> If your covariates aren't set up this way, then something else is
> likely to be the culprit...
>
> Hope this helps,
> Jonathan
>
> On Tue, Mar 10, 2009 at 8:22 PM, Steve Cramer <[log in to unmask]> wrote:
>> I have scanned 24 subjects with fMRI twice per person.  I am trying to
>> examine a paired t-test while controlling for effects of two covariates.
>>  I
>> am able to generate a paired t-test in SPM5 without the covariates, and
>> the
>> activation looks proper.
>>
>> However, the results (glass brain, cluster analysis) do not change when I
>> add 1 or 2 covariates to the model.  When I made the second model (paired
>> t-test that has the two covariates), I used all the same choices (same
>> pairs, no change in Grand mean scaling choices, etc) for the paired
>> t-test,
>> and note too that the covariates are entered without error (vector entered
>> ok, variable named OK, no interactions, etc).  In the second model (with 2
>> covariates), I entered a zero for both of these covariates in the contrast
>> manager.
>>
>> Thus, it appears that in SPM5, a paired t-test with no covariates produces
>> identical results as a paired t-test with 2 covariates properly specified.
>>
>> I would expect that the second model, with the two covariates that have a
>> zero in contrast manager, would have a different result than the first
>> model, with the difference reflecting removal of the signal accounted for
>> by
>> these two covariates.  What am I missing, or doing wrong ?  Thanks--Steve
>

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