Dear Gisela,

good to hear from you! Hope all is well.

> Dear spm-xperts,
>
> we are analyzing a data set from 5 subjects that participated in 4 sessions,
> each with 4 different tasks and would like to know whether there is
> any task related effects, that is not confounded by session or subject.
> We are  interested in any difference between tasks (i.e. both task1>task2
>  and task2>task1, etc) and we thus supposed that F-tests is the preferred
> method of analysis.
>
> Our questions are:
>
> Can the F-contrasts be created in analogy with a plain 3way ANOVA, with 3
> main effects and 4 interaction terms?
> In that case, are the contrasts proposed below correct for the main effect
> of "task", and the interaction term (subject by session by task)?

I am slightly confused here. Are you sure you are interested in this effect.
What that interaction would give you is areas where "the difference in
task-effects, betweeen sessions differ between subjects". So for example say in
a specific area of the brain one subject has the same task effect (say
task2-task1) in all sessions, whereas in another subject that same task effect
differs in magnitude from session to session. That is the type of area that
would get high F-values in a contrast effectuating that interaction.

From your original description above (i.e. are there any task related effects
(i.e. both task1>task2 and task2>task1 etc) it seems you could just use the
"effects of interest" F-contrast that SPM automatically generates.

>
> Is it possible to pursue the analysis on the 2nd level, on the basis of
> observations made using the F-tests? (i.e. after creating the relevant
> T-contrasts) to assess differences in task, related to this particular
> population of 5 subjects, assuming that the result from the 4 sessions are
> representative of these 5 subjects?

Is your question "can I use the fixed-effects results as a prior hypothesis
with regard to location in my random-effects analysis"? If so, the answer is
no.

>
> Would it be preferable to use the approach in the paper by McGonigle
> (Neuroimage, 11,708 2000), i.e. with one regressor describing a single
> "task" and 4 different regressors that describing the sub-divisions of the
> task (1-4), assessing the additional variance modeled by these 4 latter
> regressors in an F-test. In this case, how are the additional confounds
> (session and subject) handled?
>

I don't remember the details of McGonigle et al, but I suspect they did in the
following way. They might have used a single long "task-regressor" that spanned
all sessions. In addition they would have included session-specific
task-regressors. Then, performing an F-test where the F-contrast span the
columns with the session specific task-regressors would test the
null-hypothesis that these columns weren't really necessary, i.e. the
hypothesis that there were no task-by-session interactions.

If I understand your initial question right that's not what you want. You
wanted to know what areas that exhibited task-related effects, but which didn't
exhibit any task-by-session or task-by-subject interactions. That speaks more
to something like a conjunction, where you search for effects that are common
across different contrasts. These contrasts would then in this case not span
across sessions or subjects.
I think you can actually do that, conjunctions across F-contrasts that is. This
would give you minimum F-fields rather than the "usual" minimum t-fields. I
have had no experience of such entities though, and intuitively they do seem a
bit weird. Basically, a given F-value in two different F-contrasts (even when
sinply reflecting task-effects in two identical sessions) could in principle
mean two completely different things in terms of the underlying effect sizes.
How would you then interpret a conjunction across them?

I hope I have been of more help than confusion. If I understood better what you
want to do, perhaps I could be of better help.

Good luck Jesper