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Q&A Notation for one-sided hypothesis testing

posted 1y ago by Glen_b‭  ·  edited 1y ago by Glen_b‭

Answer
#2: Post edited by user avatar Glen_b‭ · 2023-08-26T06:39:06Z (about 1 year ago)
  • A partial answer may be better than none.
  • Not requiring that two hypotheses exhaust the parameter space is fairly clearly present in Neyman and Pearson (1933) - the origin of the Neyman Pearson lemma, so arguably no later than that.
  • They don't explicitly lay out hypotheses in that form you have though, this is still pretty early on.
  • Fisher was more focused on the null rather than laying out an explicit alternative or multiple alternatives.
  • A partial answer may be better than none.
  • Not requiring that two hypotheses exhaust the parameter space is fairly clearly present in Neyman and Pearson (1933), so arguably no later than that. This paper is the origin of the Neyman-Pearson lemma.
  • They don't explicitly lay out hypotheses in that form you have though, this is still pretty early on. To find an explicitly laid out simple null and one-sided composite alternative, you might need to go a bit later, perhaps, to the generalizations of it.
  • Fisher was more focused on the null rather than laying out an explicit alternative or multiple alternatives.
#1: Initial revision by user avatar Glen_b‭ · 2023-08-26T06:30:20Z (about 1 year ago)
A partial answer may be better than none.

Not requiring that two hypotheses exhaust the parameter space is fairly clearly present in Neyman and Pearson (1933) - the origin of the Neyman Pearson lemma, so arguably no later than that. 

They don't explicitly lay out hypotheses in that form you have though, this is still pretty early on.  

Fisher was more focused on the null rather than laying out an explicit alternative or multiple alternatives.