In what follows a statistical hypothesis shall be an hypothesis about the distribution of outcomes from trials of kind $K$ on some set-up $X$.
–Ian Hacking, Logic of Statistical Inference (1965), p. 27
This formulation does seem to allow the notion of a statistical hypothesis to do the work I would like it to do: the hypothesis that a point randomly selected from a surface of a sphere lies on a particular great circle is not a hypothesis about the distribution of outcomes from any trial.
What I don’t like about this formulation is that it relies on the unclear notion of a hypothesis “being about” a distribution of outcomes. My formulation is clearer because it is expressed in terms of what a hypothesis allows one to infer under what conditions. Unfortunately, I might need to sacrifice clarity for the sake of successful functioning.
I am on the lookout for other formulations.By Greg Gandenberger