Dear SPM community,
Say we have a 2 x 2 design, where each subject has been tested with two
factors in a design like this, where A and B are the two levels of one
factor, and 1 2 3 the two levels of another factor (e.g. A and B could
be men and women, and 1 2 3 three different types of actions, say
grasping a simple object, grasping a more clomplex object and grasping
an even more complex object):
1 2 3
A a1 a2 a3
B b1 b2 b3
The univariate statistic approach to test that kind of design would be
to do an anova 2x3, and then do post-hocs.
In spm I thus defined contrasts at the first level that combine the
beta-weights of each basic condition. I then included these 6 con images
into a within subject anova at the second level. I can then calculate
all the usual effects using Ftests, like main effect, interactions etc.
My puzzlement came when I used a simple t-test to say compare a2 against
b2. If I do that within the Anova, the t-test uses the unexplained
variance of the entire design to divide the contrast, and I get
relatively little activation
If I would use an more classical RFX approach, I would define the a2-b2
contrast at the first level, and use a one-sample t-test at the second
level to check if the difference is significant. That uses a much
smaller unexplained variance of course.
My motivation for using the ANOVA is in part, that it is very convenient
to use: I can mask results of one contrast directly with another. If
a-priori I'm interested in certain comparisons more than in others
though, I feel that using the unexplained variance of the whole ANOVA is
not legitimate to test planned contrasts though...
So I have two questions:
a) why use the full unexplained variance in the ANOVA for the t-tests.
b) could SPM incorporate an option for planned contrasts within an
ANOVA-type design, such that one could bring all the basic effects into
a single second level design, while keeping the statistical power of
planned comparisons? or is that a silly question?
Christian
--
Christian Keysers, PhD
Assistant Professor
BCN Neuro-Imaging Center
University of Groningen
Antonius Deusinglaan 2 (room 120)
9713 AW Groningen
Phone: +31 50 3638794
Fax: +31 50 3638875
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