I have a question about contrasts that I'm sure is easily answered, but I
seem to be coming up with conflicting answers and was hoping someone here
could clarify for me.
If you have a 2x3 ANOVA modeled in a full factorial design with just
interaction columns in the design matrix (for simplicity), then it seems
like there are a number of possible ways to test an interaction between the
factors.
The design matrix looks something like this:
A1 A2 A3 B1 B2 B3
Now, one way to test the interaction in a t-test is: -1 0 1 1 0 -1 (or for
the other direction 1 0 -1 -1 0 1)
Another way is: -1 .5 .5 1 -.5 -.5
These obviously lead to 2 different results, but what are the different
interpretations? Is the first method just a comparison of the difference
between A3-A1 and B3-B1, completely ignoring any difference between A2-A1
and B2-B1? Does the second method account for the A2-A1 and B2-B1
difference as well as A3-A1 and B3-B1, and thus is a "more complete" test of
the interaction among the levels? Any advice folks could give would be
greatly appreciated.
- DC
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