Testing Simple Hypotheses
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.
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