For each subject, we repeatedly measure 3 conditions for a scalar dependent variable. The research hypothesis is that there is a monotonic positive trend - that is, either 1<2<3 or 1=2<3 or 1<2=3.
Preferably, I would like both a hypothesis test for this condition relationship (i.e., can we reject the hypothesis that there is some monotonic trend?), and one for its opposite (can we reject the hypothesis that there is no or a negative or a non-monotonic trend?).
I've come up with a few naive ways of testing for this, but I wonder what the optimal way would be.