Dear Richard, Mly and others

I just thought of another thing. Please don't read further if you already
understand this. I am just trying to convince myself.

While Mly is right that we do assume there is a common component, that common
component will affect only certain parts of the brain (those that we are
interested in detecting). There will be other parts of the brain that are
affected only by some of the constituent contrasts (those that we don't want). So
from the perspective of one of those voxels wouldn't it be true that we have
truly "different" treatments in the different constituent contrasts.

An example, say we have a conjunction consisting of two contrasts, one of which
have a visual component. Lets look at this from the perspective of a voxel in the
visual cortex. In one contrast we will have a huge effect (visual you know), and
the other will be distributed according to the null-distribution. We want to
protect ourselves at a specific p-level  for the conjunction as a whole. In order
to do this we would need to make sure that the contrast for which the
null-hypothesis is true doesn't exceed some threshold, but which threshold should
we pick.
Well, since in the other contrast the null-hypothesis is truly false we shouldn't
really involve that and we would need to use the "usual" (not the minimum t
derived) threshold to make sure that there actually is "activation" in all the
constituent contrasts.

This would suggest that the model we use is correct in the voxels we are
interested in detecting, namely those to which the same "treatment" is applied.
BUT, that the model is not correct in the voxels where different treatments are
applied, i.e. those which are activated only in some of the contrasts. That means
that we use the wrong model for a subset of voxels in which the null-hypothesis
is true, and that we lose control of type 1 error for that subset.

I truly whish I am wrong, and would be grateful if someone could set me straight.

Jesper


Emiliano Macaluso wrote:

> Maybe of interest
>
> >Dear Mly,
> >
> >I think you are absolutely right. We DO assume that there is a common
> component
> >in the contrasts. Also I think that we do not need to assume anything
> about the
> >effect size in the different contrasts, and in that case it would be
> kosher. Why
> >don't you send your mail to the mailbase, I think it would be very useful.
> >
> >Puss Jesper
> >
> >Emiliano Macaluso wrote:
> >
> >> Dear Jesper,
> >>
> >> happy new year.
> >>
> >> As usual I find your e.mails the most "enlightening"!
> >>
> >> My impression on the matter is that it is true
> >> that we usually use 5 different treatments A-E,
> >> but all of these have something in common.
> >> Say A-E are different tasks, all of which share
> >> a common cognitive component "X".
> >>
> >> For a brain area that respond to X,
> >> we are effectively testing 5 time the same effect (X).
> >>
> >> In this case it seeems to me
> >> that the min-t-stats would be approprate!
> >>
> >> What do you think?
> >>
> >> cheers,
> >>
> >> mly
> >>
> >> At 12:24 PM 1/11/2001 +0100, you wrote:
> >> >Dear Pierre, Richard, Joe and everyone,
> >> >
> >> >while certainly not being an expert, I thought I should add my five
> cents to
> >> >this very interesting discussion.
> >> >
> >> >Joe gave a nice explanation of deMorgans inequality, which states that
> if you
> >> >have a set of statements then the "set" is true only if all the statements
> >> >are true. Or conversly the "set" is false if one or more of the statements
> >> >are false.
> >> >
> >> >I think this is in fact precisely what Pierre and Richard (and I) have a
> >> >problem with. That means that we (might) reject the null hypothesis if a
> >> >single one of the individual hypotheses is wrong. This is certainly not in
> >> >accordance with my intuitive interpretation of "conjunctions" which I have
> >> >thought of as testing if they are all wrong (i.e. if we have
> "activations" in
> >> >all of the constituent contrasts).
> >> >
> >> >When does one use a "minimum" statistic? Well, say that we have 5
> independent
> >> >samples of THE SAME effect, for example we have tested treatment A in 5
> >> >groups of 10 subjects. The null hypothesis is that A doesn't work, and we
> >> >might proceed to test this with the minimum t-statistic of these 5
> different
> >> >t values.
> >> >
> >> >Now, say instead we have 5 independent samples testing DIFFERENT
> effects, for
> >> >example treatments with compounds A to E in groups of five subjects.
> The null
> >> >hypothesis is that none of the compounds work, and again we use the
> minimum
> >> >t-statistic to test it. I suggest that if we reject the null hypothesis we
> >> >conclude that at least one of the compunds work. But I suspect we
> cannot say
> >> >that all compounds work, which is what we would say in "neuroimaging
> >> >conjunctions".
> >> >
> >> >So, isn't perhaps the problem that an assumption (one which we never
> test) in
> >> >the use of the minimum t-statistic is that we test THE SAME effect in all
> >> >tests? Whereas this in fact ought to be the hypothesis that we test.
> >> >
> >> >I hope I haven't added to the confusion too much with this.
> >> >
> >> >Jesper
> >> >
> >> >
> >
> >
> >