Testing Simple Hypotheses

Robert L. Wolpert

Duke University Institute of Statistics and Decision Sciences

Pre-experimental Frequentist error probabilities do not summarize adequately the strength of evidence from data. The Conditional Frequentist paradigm overcomes this problem by selecting a "neutral" statistic S to reflect the strength of the evidence and reporting a conditional error probability, given the observed value of S.

We introduce a neutral statistic S that makes the Conditional Frequentist error reports identical to Bayesian posterior probabilities of the hypotheses. In symmetrical cases we can show this strategy to be optimal from the Frequentist perspective. A Conditional Frequentist who uses such a strategy can exploit the consistency of the method with the Likelihood Principle-- for example, the validity of sequential hypothesis tests even if the stopping rule is informative or is incompletely specified.

Cite as:

@InProceedings{wolp:1996,
      Author = "Robert L. Wolpert",
       Title = "Testing Simple Hypotheses",
   BookTitle = "Studies in Classification, Data Analysis, and Knowledge
                Organization",
      Volume = 7,
      Editor = "Hans Hermann Bock and Wolfgang Polasek",
   Publisher = "Springer-Verlag",
     Address = "Berlin, DE",
       Pages = "289--297",
        Year = 1996,
}

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