Scientific Reporting and Personal Probabilities: Student's Hypothesis

Summary It is suggested here that a scientific researcher can report his statistical data by summarizing the application of Bayes's theorem to whole ranges of prior distributions, devised to include the opinions of his readers. The Jeffreys-Savage view is taken that interesting actual prior opinions can be usefully approximated by assuming positive probability on a sharp null hypothesis (point hypothesis). Graphical tools and bounds are given for reporting the weighted likelihood ratio, or Bayes factor, the ratio of the posterior odds to the prior odds, for a vague alternative to a null value for the mean of a Normal distribution.