When comparisons among means provide independent information, the comparisons are called "orthogonal." If an experiment with four groups were conducted, then a comparison of Groups 1 and 2 would be orthogonal to a comparison of Groups 3 and 4. There is nothing in the comparison of Groups 1 and 2 that provides information about the comparison of Groups 3 and 4. These two comparisons are orthogonal.

Now consider the following two comparisons: Group 1 with Group 2 and Group 1 with the mean of Groups 2 and 3. These two comparisons are clearly not orthogonal: both involve a comparison of Groups 1 and 2, although the second comparison also involves Group 3. If Group 1 is larger than Group 2, then it is probably (but not necessarily) larger than the mean of Groups 2 and 3. The information conveyed by the two comparisons overlaps; the comparisons are not independent.