Dear Rebecca,
|it is actually present in the active task specification. I assume the
|same logic would apply even when neither condition is a baseline as
|such but both are active task conditions? So I could specify one
|condition only (presumably either A or B) and assess the difference
|between the conditions using 1 0 and -1 0 contrasts.
|
|a) Is this true?
Yes. I can't see that there is anything intrinsically special about brain
activity in a 'rest' condition as occurred to an 'active' condition.
Imagine the two boxcars in the design matrix for A and B. They are both
mean corrected and with your ABABA design the boxcar for A is therefore
just the inverse of the boxcar for B. Thus anything in the data that can
be modelled by a positive weighting on the parameter estimate for A can
also be modelled by a negative weighting on the parameter estimate for B
(or vice-versa). Hence one of the two boxcars is redundant and doesn't
contribute anything 'extra'. The other way of looking at it is that the
sum of the modeled effects of A and B adds up to a constant, so including
the second regressor doesn't change the model.
|b) Is this actually statistically superior or just aesthetically more
|appealling to the cogniscenti? (and if the former - why?)
Specifying an additional column in the design matrix that adds nothing
extra takes away one degree of freedom so reduces the power of the
experiment. But I guess this is only important in short time series. I
can't think of any other reason for superiority...
|c) For future reference, does the logic extend to a design with n
|conditions where n>2, ie: does one always specify n-1 conditions on
|the basis that the nth is implicitly completely specified?
Hmmm...I always wondered about this too but can't figure it out in my
head. Is it that some linear combination of the parameter estimates for
the n-1 conditions can specify the nth? Someone else will have to answer
this one...
best wishes,
Geraint
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