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

if Σa

where a

Group 1 with Group 2The coefficients for the first comparison are: 1, -1, 0, 0.

Group 1 with the average of Groups 2 and 3

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

Σa

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

Group 1 with Group 2the coefficients are: 1, -1, 0, 0 and 0, 0, 1, -1. Therefore,

Group 3 with Group 4

Σa

and the comparisons are orthogonal.