# Formulate hypotheses when $\mu_A < \mu_B$ is different from $\mu_A > \mu_B$

I'm testing two different settings (say 'A' and 'B') for a machine. From physical arguments, I know that $\mu_B >= \mu_A$. If really $\mu_B < \mu_A$, there's something fundamentally wrong with my model. So there are three options:

• $H_0: \mu_B = \mu_A$ (setting doesn't make a difference)
• $H_1: \mu_B > \mu_A$ (setting make a difference, according to model)
• $H_2: \mu_B < \mu_A$ (model wrong)

I never see the material treated this way - am I violating some principles of experimental design this way? How do I analyze the results of the experiment?

Edit: I see this is related to the answer in Justification of one-tailed hypothesis testing , but I still would like to know how to analyze the resulting data.

• Is this related to your other question, How to decide whether difference between two conditions is significant?? – chl Jul 14 '11 at 10:31
• Could you give us your model? I think you're a little confused about your hypotheses: Each hypothesis represents a different class of models; the third just happens to be physically impossible. Even if you tested H2 against the composite of H0 and H1, you're not testing "the model is wrong" against "the model is right" unless H2 indexes every possible model except those in H0 and H1... – JMS Jul 14 '11 at 17:13