Dear Joe
>
> I have a few questions of clarification.
>
> 1) Regarding SPM contrasts.... Since contrasts need to be orthogonal, I
> would assume this means each contrast uses unique sum of squares
> (what some statistical programs like SAS refer to as Sum of Squares III)
> and, therefore, the F-statistics for a given contrast take into account
> (partition out) the variance associated with the other contrasts. Is this the
> case???
>
SPM Contrasts are just like any statistical package contrasts exept that
it padds with zeros in front of the functions of no interests. In general
they need not be orthogonal, unless you are doing conjunctions or
corrections for the number of contrasts tested...
In any case, each contrast uses unique sum of squares and the F statistics
is simply the square of the t-stat. (I don't think there is an easy way to
get the F for a particular contrast in spm96, you would have to do a bit
of hand work, but that's coming with spm99)
>
> 2) Regarding construction of covariate vectors...
> I have a covariate of interest related to accuracy of performance. The
> accuracy score was only available and collected during one condition. I
> plan to use the PET multi-subject, different conditions, covariate design for
> analysis. Can the covariate vector be constructed with zeros when the
> accuracy score is not available as in Condition 2 below???
>
> Subject # Experimental Condition/Scan Covariate Vector
> (Accuracy Score)
> 01 Condition 1, Mean Brain Volume 11.3
> 01 Condition 2, Mean Brain Volume 0
> 02 Condition 1, Mean Brain Volume 18.6
> 02 Condition 2, Mean Brain Volume 0
> 03 Condition 1, Mean Brain Volume 15.4
> 03 Condition 2, Mean Brain Volume 0
> etc. for 6 subjects
>
> I am concerned that the covariate vector is closely related to the
> expeimental condition column. Should I transform the covariate vector so
> that it sums to zero by subtracting the mean score from each value (this
> would still preserve the relative rank of the subject's accuracy scores)????
>
> I would then test two contrasts reflecting the condition 1 and the
> covariate effects.
> Condition1 Condition2 Covariate
> Contrast 1 1 -1 0
> Contrast 2 0 0 1
> Will contrast 2 then reflect the activation associated with the accuracy
> of performance during condition 1 ???
>
This is a question that arises often (and may be less easy than it looks...)
I will take the example of a contrast that looks like [1 0 0 ....]
testing for the first covariate. Testing for this contrast only tests
for the part of the first covariate that is uncorrelated with other
covariates, exatly in the same way a F-test on that first covariate
would test for the *additional* variance explained by this first
covariate.
Coming back to your example, you shouldn't need to do anything more than
what you have done already. You could check, however, that rewritting the model
with a first covariate [1 -1 1 -1 1 -1 ... ]' modeling the conditions
difference, a second covariable [score_1 0 score_2 0 score_3 0 ...] with
score_i = your_original_score_i - mean(your_original_scores) , plus
a covariable introduced by spm modeling the mean ([1 1 1 ...]') and then testing
with contrast [1 0] and [0 1] should give you the same answer than [1 -1 0 ]
and [0 0 1] of your original model. In the rewritten model, covariables
are orthogonal and therefore the estimated parameters and contrast easier
to interpret. (I should be discussing these matters and relation to F-tests at
the forthcoming spm course).
hope this helps
JB
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