Dear Doug,

this msg is somewhat related to another posting on the subject, so apologies for the overlap.

If one had a factor that assumed a set of increasing values (say low, medium, high, very high), we could test for a parametric increase by having the following contrast: -2 -1 1 2

However, if we had 3 levels only, then (-1 0 1) would be problematic because we are essentially testing whether we can refute the null hypothesis that beta1 = beta3. Is this interpretation correct? Or do we have an "implicit" parametric test even when beta2 is zeroed?

Also, even in the first case with 4 levels, the situation is not so simple as we are really testing whether 2*beta1 + beta2 = beta3 + 2*beta4. Here a linear increase would rejetc the null hypothesis, but so would several other combinations! (some of which we perhaps are not interested in)

Perhaps we could follow Bob's suggestion in the earlier posting of doing pairwise tests and conjunctive masks: (beta2 > beta1) && (beta3 > beta2) && (beta4 > beta3). This seems fine to me, but I'm not sure what statistitians would say (maybe something like "you should use orthogonal polynomials and test it hierarchically for the highest order that is significant...").

Anyway, your thoughts on this are much appreciated,

Luiz