FIRST design matrix notes

More than 2 groups

There are several possible ways to setup such a design, but the crucial thing is that the mean value of the data (distances) in FIRST are not meaningful and so the mean should not be put into the model.  That is why the +1/-1 column is used in the two-group example.  For three groups you could use a model like this:

1   0
1   0
1   0
0   1
0   1
0   1
-1 -1 
-1 -1
-1 -1

This model the differences in groups A-C and B-C directly, and leaves A-B implicit but is not needed separately as it is given by:  A-B = (A-C) - (B-C)
So you should not add A-B explicitly, since it is completely determined by the other two and would be redundant.

(link)