Thanks, Ged! I appreciate the input. I suspected as much but every once in
a while it helps to reconfirm one's suspicions.
Your response actually helped address an early question I posed to the list
about modifying the contrast weight to account for task error for any
particular response type. Now, I'm back on track and will enter the error
as a nuisance variable and not monkey with the contrast weights.
Cheers,
Jeff
-----Original Message-----
From: SPM (Statistical Parametric Mapping) [mailto:[log in to unmask]] On
Behalf Of Ged Ridgway
Sent: Thursday, October 05, 2006 2:16 PM
To: [log in to unmask]
Subject: Re: [SPM] Do contrast weights = signal variance proportionality?
Hi Jeff,
My understanding is that overall scaling of contrasts has no effect on
t- or F-values. Scaling every contrast element by a certain factor
will scale the "con" images by that factor, and it will also scale the
ResMS images by the same factor. The scaling will therefore cancel out
in the statistics.
An alternative way of interpreting this is that the contrasts just
specify a particular null hypothesis, in the general form c'*beta = d,
and SPM's t and F contrasts/hypotheses always assume d = 0, so scaling
c simply multiplies zero and leaves the actual hypothesis unchanged.
So in concrete terms, [-1 1] and [-0.5 0.5] should give the same
t-test results (with the con/ResMS images for the first having twice
the value of those for the second), while [-0.3333 0.6667] would test
a different hypothesis -- relative scaling does matter.
Best,
Ged.
Jeff Browndyke wrote:
> Currently, we have three runs concatenated and we have constructed our
> fixed-effect contrasts for a particular response type relative to
> baseline in each run for each subject in the following way:
>
> [0.33333 0 0 0 ... 0.33333 0 0 0 ... 0.33333 0 0 0]
>
> Just want to double check that this is correct, or whether we should be
> using the following instead:
>
> [1 0 0 0 .... 1 0 0 0 .... 1 0 0 0]
>
> Would it matter if a contrast between two response types in a three run
> concatenation was represented as:
>
> [1 -1 0 0 0 ... 1 -1 0 0 0 ... 1 -1 0 0 0]
>
> or
>
> [0.33333 -0.33333 0 0 0 ... 0.33333 -0.33333 0 0 0 ... 0.33333 -0.33333
> 0 0 0]
>
> I suspect we're on the right path, but worry that the 0.33333 is
> reflecting that we are only weighting the particular response type in
> any one run at .33 of the total signal. In the contrast between two
> response types examples above the sum is zero in both cases, so which is
> more appropriate? Am I completely offbase in understanding that the
> contrast weights are reflecting how one portions signal variance
> associated with a particular response type (i.e., a [1 -1] contrast
> means 100% of signal variance in one response condition vs. 100% of
> signal variance in another response condition)?
>
> Not too proud to be completely wrong, so please comment as needed.
> I will value the feedback.
>
> Thanks,
> Jeff
>
>
>
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