LLN, le 27/04/05
Dear Sterling,
>2. the contrast -3 -1 1 3 should tell me if there is a linear trend,
>but using equally spaced positive integers (1 3 5 7) in the contrast
>yields a better result when using the ANOVA no constant model, but
>is this contrast valid?
Jesper Andersson already (I don't know when) commented on this. Here
is what he wrote.
Yours,
Mauro.
-------------
In linear constrasts are [-3 -1 1 3] and [ 2 4 6 8 ] equivalent?
When seeking areas that show a linear increase/decrease with
increasing proportions of congruence, one does not want to show areas
where there is simply an activation (common to all block types) over
some implicit baseline.
Let's assume some data for both those cases. In area 1 (area with
linear increase), we have parameter estimates [.5 .9 1.6 2] for the
four block types and in area 2 (area with general activation) we have
[.9 1.1 1.2 0.9 ]. When evaluating a contrast SPM simply multiply the
parameter estimates with the contrast weights, sum them up and
divides with the uncertainty.
For the first contrast ([-3 -1 1 3]):
a1: ((-3*.5)+(-1*.9)+(1*1.6)+(3*2))/uncertainty = 5.2/uncertainty
which would, with a reasonable uncertinaty, indicate a linear increase.
a2: ((-3*.9)+(-1*1.1)+(1*1.2)+(3*.9))/uncertainty = 0.1/uncertainty
which doesn't indicate a linear increase.
The second contrast ([ 2 4 6 8 ]), on the other hand, does not sum to
0 and gives
a1: ((2*.5)+(4*.9)+(6*1.6)+(8*2))/uncertainty = 30.2/uncertainty and
a2: ((2*.9)+(4*1.1)+(6*1.2)+(8*.9))/uncertainty = 20.6/uncertainty.
So, with the second contrast one would conclude that both areas show
a linear increase. The problem here is that by not mean-correcting
the contrast weight vector, the main effect (general activation) is
inflated with the parametric modulation. Thus, contrast 1 is better.
Jesper Anderson
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Mauro PESENTI
Research Associate, National Fund for Scientific Research (Belgium)
Unite de Neurosciences Cognitives
Departement de Psychologie
Universite Catholique de Louvain
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