Hi experts

I want to know how to make the design matrix in the following situation.

Assume that there are three groups, group A, group B and group C.
Then each group consists of 4,3,2 participants.
If we want to look at the pairwise group difference, is the following way of constructing the design matrix OK?

[ 1 0 0
  1 0  0
  1  0  0
  1  0  0
  0  1  0
  0  1  0
  0  1  0
  0  0  1
  0  0  1]

Then if you want to know the difference between group A and B,
you can make the contrast as follows. [1 -1 0]

Similarly, if you want to know the difference between B and C, you can make the contrast like [0 1 -1].

Finally, if you want to know the difference between C and A, you can make the contrast like [-1 0 1].

Any comment is appreciated.

Thank you
Takuya

Hi Takuya, 

yes - this looks correct. Note that the contrast [1 -1 0], will specifically test whether A is greater than B. You can then use [-1 1 0] to test B>A. 

You can also do a single F-test using the contrast [1 1 1] to test whether any of the three group differ from each other. 

Andrew
Originally posted by Takuya Ishida:

Dear Andrew

Thank you very much for your reply.
It help me a lot.

Best 
Takuya 
Originally posted by Andrew Zalesky: