Except such a data set is also inconsistent with an infinite number of models, so ruling one out via rejecting a null also provides practically no information value and moves us no closer to understanding. /devils advocate
In practical terms, we're not interested in true models, but useful ones, so the description of a model's consistency with observed data is often the more useful metric in practice than rejecting nulls :/ especially in applications where you can't set up repeated experiments.
OK, I realise its more nuanced than that too, but given how many papers and practitioners seem incapable of understanding that evidence against the null it's not explicit evidence for an arbitrary alternative, practically and consequentially I don't think that's how we should be working...
> Except such a data set is also inconsistent with an infinite number of models, so ruling one out via rejecting a null also provides practically no information value and moves us no closer to understanding.
No, that's not true, because experiments are not done in a (figurative) vacuum. They are done in the context of an explanatory theory that has already gone through a vigorous filter and shown to be consistent with the all prior experimental data and has better explanatory power than all of its competitors. It is only when more than one theory survives this filter that an experiment is done, and the experiment is designed specifically to distinguish between the surviving theories.
So while it is true that an experiment allows you to eliminate an infinite number of theories, it's irrelevant, because by the time the experiment is done nearly all of those theories have already been eliminated anyway.
In practical terms, we're not interested in true models, but useful ones, so the description of a model's consistency with observed data is often the more useful metric in practice than rejecting nulls :/ especially in applications where you can't set up repeated experiments.
OK, I realise its more nuanced than that too, but given how many papers and practitioners seem incapable of understanding that evidence against the null it's not explicit evidence for an arbitrary alternative, practically and consequentially I don't think that's how we should be working...