Maybe this will help. I am thinking of the same distinction discussed by Meehl in Figure 2 of this paper: "The poor social scientist, confronted with the twofo

Maybe this will help. I am thinking of the same distinction discussed by Meehl in Figure 2 of this paper: "The poor social scientist, confronted with the twofold problem of dangerous inferential passage (right-to-left) in Figure 2 is rescued as to the (H → O) problem by the statistician. Comforted by these “objective” inferential tools (formulas and tables), the social scientist easily forgets about the far more serious, and less tractable, (T → H) problem, which the statistics text does not address." http://rhowell.ba.ttu.edu/Meehl1.pdf http://rhowell.ba.ttu.edu/Meehl1.pdf Here, we are not even yet talking about the substantive theory, although that issue will also exist. There is also a difference between the statistical hypothesis (the mathematical object) and what the researcher wants to test. I think you are conflating those two hypotheses.