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Notes -
I agree that's not the definition of "null hypothesis" and I have never claimed otherwise.
Here is a thought experiment to demonstrate my point:
Suppose that a previously unknown species of bird is discovered; 6 members of the new species are exposed to a high dose of radiation, a level that is known to kill roughly half of birds which are exposed. After the radiation exposure, 2 of the six die within a few weeks. There is a debate over whether or not this new species is invulnerable to radiation. There is no special reason to think that this new species is different from any other species of bird, but for some obscure political reason, there are people who insist that this new species is invulnerable to radiation.
Concerning our experiment, what should the null hypothesis be?
H0 (null): no difference between populations
H1 (alternative): radiation resistance of the new population > radiation resistance of the reference bird population
This is the typical formulation. Null typically assumes no effect or no difference between the populations being considered.
I tend to agree with you as to this particular example, but consider some of the formulations which have been floating around. Such as the "hypothesis that no relationship exists" Given that we are looking at (1) radiation being administered to the new bird population; and (2) deaths among that population, one could argue that the null hypothesis is that no relation exists between the radiation and the deaths.
I think that your formulation does not necessarily work either. For example, suppose there is an obscure un-contacted tribe of people in some remote rain forest and for whatever reason, the question on the table is whether the male members of the tribe are taller than the female members. Suppose further that we meet (and measure) only 4 members of the tribe -- 2 males and 2 females -- and that both of the males are significantly taller than either female. What's the null hypothesis here? Is it simply "no difference between the populations being considered"?
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