I'm running a 2x2 full factorial design on one group of subjects in
Suppose the design is Factor A x Factor B, then the corrsponding cells
A1B1, A1B2, A2B1,A2B2
I assume in my task that Factor A has no independency and unequal
Factor B is independent, and has equal variance.
After reading Nichols et al. (2005) I wonder if I could use a
conjunction within a
factorial design. Since I'm only interested in possible effect within
by Factor A, I want to make a conjunction of both conditions A1 & A2.
I could use the
following contrasts to create the conjuntion:
A1B1+A1B2 (1 1 0 0) with A2B1+A2B2 (0 0 1 1).
This will give me all regions activated by both conditions of Factor A,
including regions possibly activated by Factor B, including a possible
or I could run a conjunction over all cells seperated:
A1B1 (1 0 0 0) + A1B2 (0 1 0 0) + A2B1 (0 0 1 0) + A2B2 (0 0 0 1)
This will give me all regions activated by Factor A, and maybe by
(when there is no main effect of factor B, B1 and B2 could still have
effect on regions activated by A1 and A2)
Which one seems to be the most relevant? And, moreover, does it make
use conjunctions like this within a factorial design? For me, it seems
since I can test if there are any positive effects of Factor A (A1>A2),
interactions effects (A1-A2)x(B1-B2) and positive effects of B (B1>B2)
of interest (those that are activated by Factor A)
However, I also could use a F-test over all cells (1 0 0 0, 0 1 0 0
etc.) but since I'm
only interested in regions activated by both A1 and A2, I thought a
conjunction will be more relevant.
(by the way, I mask the conjunction with a (inclusive) mask p-value of
0.05, and run the test under
p= 0.05 (FWE) to control for multipl. comparisons)
Does this all make any sense?