Hi Stephen,
Thanks you very much for your answers. They have been very helpful. I will proceed to answer some of your questions.
Yeah, I have a block design. Each block lasts 9 seconds, after which there is a 3 second "rest" period before the next block. I will talk to the person who designed the experiment about the efficiency issue you raised. For now, our study is sort of preliminary.
I also followed your advice and read some of the older posts on the SPM forum, as well as some presentations from Rik Henson's website. Coupled with what I you explained to me, now get the general idea of how to comduct these analyses.
For example, if I were interested in the difference between Counting and Reasoning in my study, and I were modelling the canonical HRF and its two derivatives, I would use three separate T-contrasts for each individual:
    [1 0 0 -1 0 0] Canonical HRF (Counting - Reasoning)
    [0 1 0 0 -1 0] Temporal derivative (Counting - Reasoning)
    [0 0 1 0 0 -1] Dispersion derivative (Counting - Reasoning)
Then, once I obtained the necessary contrast images, I would perform the following F-contrast to see the overall effect of Counting versus Reasoning.
[1 0 0
 0 1 0
 0 0  1].
I have a few questions.
1. If I were simply interested in knowing where Counting produced activation, would I use:
    [1 0 0 0 0 0] Canonical HRF (Counting)
    [0 1 0 0 0 0] Temporal derivative (Counting)
    [0 0 1 0 0 0] Dispersion derivative (Counting)
Ould the F-contrast of [1 0 0; 0 1 0; 0 0 1] be applocable as it was in the Counting versus Reasoning case?
2. If I were to include the Rest condition, or any 3rd condition, and wanted to know where Counting had higher activation than Reasoning and Rest, would the T-contrasts be:
    [1 0 0 -0.5 0 0 -0.5 0 0] Canonical HRF
    [0 1 0 0 -0.5 0 0 -0.5 0] Temporal derivative
    [0 0 1 0 0 -0.5 0 0 -0.5] Dispersion derivative
3. If I were conducting this study for 2 groups of people, say, controls and Alzheimer's disease patients, what F contrast would I use to compare the two groups once I had completed the individual GLMs?
Is there a book that explains these things in simple terms?
Thank you very much.

From: Stephen J. Fromm <[log in to unmask]>
To: [log in to unmask]; Kwaku Akrofi <[log in to unmask]>
Cc: Stephen J. Fromm <[log in to unmask]>
Sent: Thursday, 25 June, 2009 6:54:23
Subject: Re: Multiple GLM Analysis and F-Contrasts

On Wed, 24 Jun 2009 16:05:57 +0100, Kwaku Akrofi
<[log in to unmask]> wrote:

>My problems with SPM are two-fold.
>Firstly, I don't understand F-contrasts well. I thought I did but now I am not
>sure I do.
>Secondly, I don't know how to do a GLM analysis on multiple subjects. Let
>elaborate further.
>So far, what I'm doing is simple: subjects answered some questions on a
>computer screen; questions were either "counting" questions (they must
>a button to show how many objects they see on the screen) or "reasoning"
>questions (they must choose one of several answer choices that best fit a
>given pattern); a block design was used, a question was displayed for 9
>seconds (during which the subject had to press a button to answer) and
>was a 3-second rest period after each question; 36 questions in all.

How long are the blocks?  Do they consist only of the 9 second trials?  You
might want to check your design for efficiency.

If you have a real block design (as opposed to a "single trial" design, which is
almost like an event-related design), I don't see much point in modeling the
partial derivatives of the HRF.

>From my understanding of what the SPM5 manual says, T-contrasts are
>suitable when I use only the canonical HRF,

t contrasts can be used when testing a single quantity, like a single regressor
(like the canonical HRF itself).  The advantage of a t contrast is that you can
talk about one thing being greater than another thing.  (E.g., "is the amplitude
of the response to stimulus A greater than that to stimulus B?")  The
disadvantage of t contrasts is that you can only test scalar quantities---you
cannot e.g. test the HRF and its derivatives at the same time.

> and F-contrasts are suitable when
>I use the canonical HRF and its partial derivatives.

You have to use F contrasts when you're testing multiple quantities.  (The
HRF plus both partial derivatives is three quantities.)  Of course, you could
model the HRF plus both partial derivatives, and then test them each
separately, but the results might be hard to interpret.

> F-contrasts are also the
>way to go for any analysis of multiple subjects.

That's not true.

>I am also of the understanding that GLM of multiple subjects is a 2-level
>process: I have to do a 1st level analysis on each subject (presumably, using
>only F-contrasts), generate contrast images from each subject, and then
>those contrast images in a 2nd-level analysis.

It's useful to understand why.  A few years ago, the fMRI community generally
did "fixed effect analyses."  Basically, all the subjects' designs were
concatenated into one huge regression, and the statistics were done on that. 
Then people realized that you cannot make "population level inferences" doing
things that way, and so the community decided that in most instances mixed
effects analyses (somewhat erroneously yet more commonly referred to
as "random effects analyses") were more appropriate.

One simple way to effect a random effects analysis (valid in many cases) is to
use the hierarchical method you allude to.

>There is one example in the manual (Chapter 30 of the SPM5 manual) where
>they show how to do a 2nd-level multi-subject analysis. In that example, got
>three con*.img images from each subject; one for the canonical HRF, one for
>its time derivative and one for its dispersion derivative. I really wonder how
>they got those images because it appears SPM doesn't let me choose either
>the derivatives on its own. [In my case, I used an F-contrast for all
>HRF and all its derivatives, and I got ess*.img images and not con*.img

That's because con*.img only come from t contrasts.  ess*.img come from F

>Well, I proceeded with my ess*.img images and did the 2nd-level analysis.

That's actually _NOT_ the right way to go about things.  _Do not take the
ess*.img to the group level (or second level)_.  The right thing to do is to
take con*.img (or beta*.img, if you know what you're doing) to the second
level.  Notice this means that you don't do the F contrast at the subject
level; you do it at the group level.

> I
>got some results but I don't know how to make sense out of them.
>The reason I don't know how to make sense out of them is my understanding
>of T- and F-contrasts. Let's assume I have 3 conditions: counting, reasoning
>and rest. (Another question I have is whether or not to model the "rest" as a
>separate condition. So far, I've been doing that. What do you think?)

Usually people don't model rest (it becomes part of the "implicit baseline"),
although it's not necessarily wrong to do so.

I won't answer the following, because you first need to avoid taking the
ess*.img images to the group level and instead use the appropriate con*.img
or beta*.img.  I would have thought there are posts on this group as to what
should be done in the case of the HRF and its two derivatives.  There also
should be some unpublished monographs floating around out there, particularly
by Rik Henson.  I know Rik has commented at length on designs with partial
derivaties of the HRF.


> Well, if I
>want to, say, know what brain areas are activated during counting, my T-
>contrast vector is [1 0 0]. What would my F-contrast vector be? Since I
>the canonical HRF and its two derivatives, I'm assuming my F-contrast
>would now be [1 0 0 0 0 0 0 0 0; 0 1 0 0 0 0 0 0 0; 0 0 1 0 0 0 0 0 0]. But
>when I did the 2nd-level analysis, I couldn't at all enter such an F-contrast!
>So, in view of all this background, my questions are:
>1. How do I conduct a GLM analysis of multiple subjects? In fact, in
>this question, you'd automatically be answering my other questions....
>2. Is my understanding of F-contrasts correct?
>3. In the study I have above, would you model "rest" as a 3rd condition?
>Thank you very much.