Orthogonal Comparisons (2 of 5)

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There is a simple rule for determining if two comparisons are orthogonal: they are orthogonal if and only

if Σa_ib_i= 0

where a_i is the ith coefficient of the first comparison and b_i is the ith coefficient of the second comparison. Again consider the comparisons:

Group 1 with Group 2
Group 1 with the average of Groups 2 and 3

The coefficients for the first comparison are: 1, -1, 0, 0.
The coefficients for the second comparison are: 1, -.5, -.5, 0.

Σa_ib_i = (1)(1)+(-1)(-.5)+0+0 ≠0.

Therefore, these two comparisons are not orthogonal. For the comparisons:

Group 1 with Group 2
Group 3 with Group 4

the coefficients are: 1, -1, 0, 0 and 0, 0, 1, -1. Therefore,

Σa_ib_i = (1)(0) + (-1)(0) + (0)(1) + (0)(-1) = 0

and the comparisons are orthogonal.