Interpreting the Stars in Precise Hypothesis

Summary The problem of testing a precise null hypothesis is considered when available information is limited to knowledge of either the P-value or that the P-value is in some interval (e.g., the classical one or two 'stars'). Because of the recognized conflict between classical and Bayesian measures of evidence in testing a precise null hypothesis, the interpretation of a P-value or of 'stars', from a Bayesian perspective, is explored. This is done by treating the P-value or the 'stars' as the data, and computing corresponding posterior probabilities or Bayes factors. Of particular interest are lower bounds on these measures over wide classes of prior distributions. Comparisons are also made between classical meta-analysis techniques for combining many tests of statistical significance and lower bounds on Bayes factors and posterior probabilities.

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