statistical problem: building orthogonal contrasts in excel ( pairwise mean comparison)

Hi all;

A way to pairwise comparing of mean of several groups can be orthogonal comparisons. to do this we need to define a set of contrast coefficients to accomplish mean comparisons. consider we have 2 groups for compare. the orthogonal coefficients will be as below:

all possible pairwise groups c1 c2

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group 1 vs group 2 +1 -1

this is a 1*2 matrix(consider that c1+c2=0)

this tells us that mean of group 1 statistically is comparing with the mean of group 2. in the case of 3 groups we seezero means that the related group not involved in mean comparison)


all possible pairwise groups c1 c2 c3
group 1 vs group 2 1 -1 0
group 1 vs group 3 1 0 -1
group 2 vs group 3 0 1 -1

again ( c1+c2+c3=0) and we have a 3*3 matrix

comparing 4 groups:

all possible pairwise groups c1 c2 c3 c4
group 1 vs group 2 1 -1 0 0
group 1 vs group 3 1 0 -1 0
group 1 vs group 4 0 1 0 -1
group 2 vs group 3 0 1 -1 0
group 2 vs group 4 0 1 0 -1
group 3 vs group 4 0 0 1 -1
we have a 6*4 matrix

For the case of N groups the matrix dimension is: (N*(N-1)/2) rows and N collumns.

as the groups increased the dimension of matrix of pairwise coefficients are rises. writing a set of these coefficients seems to be very boring for 150 or 200 groups.
The question is: Is a macro available to build these coefficients for comparing N groups ?

I will be appreciated beforehand for your helps or hints

Cheers.....
Ramin