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The flexible factorial model in SPM with 3 factors (group, time, and
subject) should work fine for assessing differences in learning between
young/old groups.

The interaction tests whether the change between pre- and post-test is
different between young and old subjects.

The one caveat is that this does not adjust or control for learning
differences if learning is related to pre- learning connectivity. For that,
you'd need a different test as follows:
(1) Compute the difference in pre- and post- connectivity scores;
(2) Create a 2 sample t-test with a covariate and have the covariate
interact with factor 1;
(3) You can test whether the difference in connectivity is different
between groups and/or if the connectivity change with learning is related
to baseline connectivity and/or if the relationship of the connectivity
change to baseline connectivity varies as a function of group.

If the latter is the case, then you should not report the findings of group
differences as the group difference will be dependent on baseline
connectivity. I'd recommend reading the following webpage:
http://mumford.fmripower.org/mean_centering/

Additionally, as you will have an imaging covariate, you will need to use
Biological Parametric Mapping (http://fmri.wfubmc.edu/software/Bpm);
however, the website only lists compatibility with SPM8. There seems to be
another toolbox on the nitrc website, that may be useful (I haven't
downloaded it or tested it): http://www.nitrc.org/projects/rbpm/

One possibility is to pick one connection to use as the baseline
connectivity, this would eliminate the imaging covariate from the model and
you could use SPM without BPM.

Computing a 2 sample ttest for the pre-learning and then for post-learning
will show you group differences for each part of your study; however, there
is no statistical way to say that the effect of learning is different
between groups based on those two ttests. Likewise, 2 paired ttests for
each group wouldn't allow you to say the groups are different. You need to
be able to test the interaction within a single model to be able to say
learning has differential effect between groups.

Hope this helps.

Best Regards, Donald McLaren
=================
D.G. McLaren, Ph.D.
Research Fellow, Department of Neurology, Massachusetts General Hospital and
Harvard Medical School
Postdoctoral Research Fellow, GRECC, Bedford VA
Website: http://www.martinos.org/~mclaren
Office: (773) 406-2464
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On Tue, Mar 17, 2015 at 9:32 AM, Elisabeth Kaminski <[log in to unmask]>
wrote:

> Dear colleagues,
>
> I have problems in finding the best design for a learning study comparing
> old and young participants.
> We acquired pre and post resting state connectivity and now want to do a
> seed-based correlation analysis and compare the pre and post connectivity
> among the 2 subgroups.
> What do you think might be the best design to answer this question?
> Especially because there are definite baseline differences between young
> and old subjects regarding their connectivity. Is there a way to somehow
> control for these baseline differences to only have the pure learning
> difference?
> I already tried to set up a flexible factorial design and look for
> interactions but often there are none. If I compute 2sample ttests pre and
> post, you can see differences between pre and post significant areas but I
> guess this is not the appropriate way to approach this question.
> Any ideas would be highly appreciated.
> Thanks a lot in advance.
> Elisabeth
>