Dear Saori,

> Now I analyze fMRI experimental data, in which 12 subjects performed same
> task (there were TEST and CONTROL conditions) in different 3 days under
> different pharmacological states (A, B, and C).
>
> In order to check difference of brain activity involved in TEST between
> these 3 days, I think following two ways may be possible:
>
> (1)
> First level:
> I make one design matrix including one day's data, and make contrast [1
> -1]=[TEST-CONTROL] about every subjects and every days.
>
> Second level:
> I perform "one-way ANOVA" with 3 groups using 36 con*.img, and make contrast
> [1 -1 0] if I check [A-B] comparison.
>
> (2)
> First level:
> I make one design matrix including 3 days data, and make contrast [1 -1 -1 1
> 0 0] if I check [A-B] comparison with [TEST-CONTROL].
>
> Second level:
> I perform "one-sample t-test" with some comparison (ex. [A-B]) and make
> contrast [1].
>
> Are these correct?
> Which is statistically more reasonable?
>

As far as I can tell these are both correct. The latter approach corresponds to
the way you "had to do it" in the old SPM99 days. The former approach hinges on
the capability to estimate off-diagonal elements in the second level
variance-covariance matrix (i.e. to take into account that e.g. subject 1's
activation (test-control) when on drug A is not independent of subject 1's
activation when on drug B).

The following is my rather naive take on the issue:

The covariance modelling in SPM2 enables us to (among other things) bring more
than one parameter per subject and trial-type to the second level. This means
that we can now do things that simply wasn't possible before. Notably, we can
use richer basis-sets to model each trial-type, thereby making ourselves less
sensitive to slice-timing issues, inter-subject differences in HRF etc etc. For
example bringing the HRF and the temporal and dispersion derivatives to a
second level and assessing the trial-type differences using an F-test would
potentially be very useful for ER studies. This can be done thanks to the
modelling of the covariance between the estimates of the different parameters
in the same subject.

Still, it IS an estimate. For the cases (such as in your example above) when
the second level analysis can be designed such as not to hinge on those extra
assumptions/estimates it would seem the reasonable thing to do. I.e. I would
suggest using alternative 2 above.

I would welcome any, less naive, opinions on this (Will?).

On the side: I am sure you are aware that it is a good idea to design the study
such that you randomise the assignment of drugs to days.

Good luck Jesper