Dear Matthew
Re:

At 04:47 PM 6/29/2001 +0100, you wrote:
>
>Hello all,
>I saw this thread, and it's prompted me into asking about what conjunctions
>mean.  I realised after some discussions in HBM that I didn't understand this
>atall.  The conjunction is of course based on a test on the minimum of the t
>statistics for a set of contrasts.  So here is the question that bothers me:
>what question is that a conjunction is the answer to?
>
>The answer that is sometimes given is that a significant conjunction tells
you
>that all subjects / contrasts have activated, but this can't be the case,
>as you can have a conjunction that is significant with a minimum t value that
>is negative.  Or, in a related vein, imagine that you have six subjects doing
>the same task (and therefore six contrasts), and that, in fact, only one
of the
>six subjects is activating for that contrast.  If you assume that the one
>subject activates enough that their contrast does not contribute to the
minimum
>t statistic, then you are more likely, by chance, to get a significant
minimum
>t statistic from the overall conjunction, even though only one subject has
>activated.  The trivial code snippet below does a little demonstration.
>
>But if the conjunction isn't the answer to the question 'have all subjects/
>contrasts activated', then what is it the answer to?
>
>Sorry to share my confunsion,
>
>Best,
>
>Matthew
>
>
>
>% test conjunction probabilities
>
>% Let us assume that for one or more of the
>% contrasts in the conjunction, there is an effect, and the effect is such
>% that this (these) contrasts have a negligible contribution to the overall
>% minimum t statistic.  Then, if we have 6 contrasts in our conjunction, and
>% one with an effect, the minimum t statistic is effectively being
>% drawn from a minumum of 5 t values.
>
>% corrected height threshold required
>th = [0.05];
>
>% number of contrasts in the conjunction as specified
>n = 6;
>% number of contrasts with no effect, in the conjunction
>% (contrasts with an effect are assumed not to contribute to the min t
>% statistic)
>realn = 5;
>
>% some example resel counts and df (from a PET analysis in fact)
>df = [1.0000   67.0000];
>R = [1.0000   26.7179  180.5031  325.0859];
>STAT = 'T';
>
>for i = 1:length(th)
>  % determine corrected t threshold, if the number H0 t's is as specfied
>  corrpfz = inline(sprintf(...
>      'spm_P(1,0,x,[%f %f],''%s'',[%f %f %f %f],%f)-%f',...
>      df, STAT,R,n,th(i)));
>  Z = fzero(corrpfz,[1 20]);
>  % determine corrected t alpha, if H0 t's is the actual no
>  gth(i) = spm_P(1,0,Z,df,STAT,R,realn);
>  fprintf(['For requested corr threshold %0.2f: predicted alpha:' ...
>                                         ' %0.2f\n'],th(i),gth(i));
>
>end

With respect to your specific question, to look for consistent activation
across subjects,  you need to set the threshold for the minimum T.  This
can be done by using the uncorrected rather than corrected threshold and
specifying the min T that you want to see. Obviously you want the overall
conjunction to reach a corrected level of significance and the minimal T to
be positive.


More generally concerning the use of conjunctions, I think the difference
between a conjunction design and broader uses of conjunction analyses has
become very confused. The reason that we introduced conjunction designs
initially was to try and side-step problems with cognitive subtraction.
The specific motivation originated from language studies where it is
difficult to find baseline tasks that activate all but the process of
interest in the activation task. For instance, if you present word-like
letter strings as a baseline for reading real words, subjects will
automatically attempt to read the control stimuli often resulting in more
"word activation" than the activation task.  The idea behind the
conjunction design was to ensure that the process of interest was activated
by using "low level" baselines that didn't result in "implicit" activation
of the process of interest.  Of course, the problem with a low level
baseline task is that it doesn't control for all other processes.  To get
around this problem, the conjunction design relies on a series of task
pairs that each differ by the process of interest. The trick is that the
only consistent difference between pairs must be the condition of interest.
 The conjunction analysis was therefore implemented to identify common
activation across task pairs.


Once the conjunction analysis was implemented in SPM, we found other uses
for it.  The example you give relates to finding consistent activation
across subjects.  There are indeed several complications using the
conjunction analysis.  Most users seem unaware of what the
prespecifications are and at one stage we were planning on writing a
technical note to address them.  Maybe this would still be a good idea,
what do you think?

Other uses for the conjunction analysis include analysis of classical
factorial designs. Conjunction analysis allows you to segregate the main
effect into components that are consistent or inconsistent over factors.
ALthough you can do this conventionally noting which effects are qualified
by an interaction, the classical approach does not segregate the SPMs which
is useful when you are making figures.

I hope this partially answers your questions?
Do you or does anyone else think that Karl and I should write up an
explanation of conjunctions and masking, include a detailed list of the
prespecifications and clarify the differences between conjunctions in
SPM96, 97 and 99???????

Look forward to hearing your response
Cathy