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Dear Dr Friston,
hello all,

we would like to seek your advice on a question regarding a conjunction
analysis performed on VBM data. In brief, we are not sure whether it is
the global or the conjunction null hypothesis to test to answer a specific
question.

Background: repeated measures of psychopathological ratings were
decomposed into orthogonal polynomials that were then used for correlation
analysis with GM maps to inform about predictions of the clinical course
from morphology.

We have calculated separate T-maps for voxels correlating with the linear
trend and voxels correlating with the cubic trend. From another analysis
with clinical data we know that when combined, the linear and cubic trend
excellently reflect "early response".

The idea was to identify regions that support this "early response" -
which we thought would mean that the test should show voxels that
correlate into the defined directions to some degree (however, not
necessarily as much as in the separate tests) and that 'work together' to
explain this very specific clinical pattern.

We have had a look at your paper on conjunction analysis, 2005, and
understood that the 'rejection region' shown in figure 2 implies that if
the global null hypothesis is rejected, both T-values still have a certain
height. Expectedly, testing the global null gives a stronger contrast than
testing the conjunction null hypothesis.

The question now arised, if a voxel survived the global null testing, how
much of the  second effect is 'minimally' contained? Intuitively it seems
that testing the conjunction hypothesis is too conservative, we are very
grateful on any opinion on this.

Thank you very much in advance,

Philipp Saemann