Dear FS list, (dear Martin!)
I have a longitudinal design, 3 groups, 2 timepoints,
and I created three different QDEC tables (two groups at
a time) in order to be able to compare each pair of
groups in terms of percentage change from pre to post
(what's referred to as "pc1" in the first stage of the
two-stage-model). I look at thickness, area and lGI as
dependent variables. Group is a categorical factor of
interest, gender as the other categorical factor (not
interested in its effect), and age as (continuous)
nuisance. I'm interested in the contrast "Does the
average ..., accounting for gender, differ between G1
and G2?"
Say that, for some analysis (e.g. group 1 vs group 2,
thickness, LH) I get a certain cluster that survives the
MonteCarlo Null-Z correction. If the cluster is redish, I
take it to mean that group 1 has a higher signed value of
pc1 than group 2, and vice-versa if the cluster is
blueish. However, because pc1 is (I think) a signed
statistic, i.e. is negative for thickness decrease and
positive for thickness increase, this makes me unsure how
to interpret the stage2 (cross-sectional) result. As I
understand it, having a significant red cluster in the
group comparison can mean either of these 3 scenarios:
- Both groups have pc1>0
- G1 has pc1>0 and G2 has pc1<0
- Both groups have pc1<0
..but that the pc1 of G1 is always greater, as a signed
number, than that of G2, since that is what defines the
cluster.
The problem is that, when I run the same analysis but
keeping only subjects of one group in at one time, i.e.
for each group separately and looking at the contrast
"Does the average ... differ from zero?", in most cases I
don't get the same cluster that appeared in the group
comparison.
My question is therefore: can a cluster appearing in the
between-groups analysis be trusted if the same (or similar)
cluster does
appear in each of the two
within-groups (one-sample test) analyses? And if the latter
analysis produces null results but the former does have sig
clusters, does it still make sense to look at the sign of
each group's mean pc1 in order to find the effect of the
longitudinal treatment (atrophy or increase), even if that
group in fact did not have a pc1 that was significantly
different from zero?