In this paper, the reconcilability between the P-value and the posterior probability in testing a point null hypothesis against the one-sided hypothesis is considered. Two essential families, non regular and exponential family of distributions, are studied. It was shown in a non regular family of distributions; in some cases, it is possible to find a prior distribution function under which P-va...

Testing a point (sharp) null hypothesis is arguably the most widely used statistical inferential procedure in many fields of scientific research, nevertheless, the most controversial, and misapprehended. Since 1935 when Buchanan-Wollaston raised the first criticism against hypothesis testing, this foundational field of statistics has drawn increasingly active and stronger opposition, including ...

Abstract A perennial objection against Bayes factor point-null hypothesis tests is that the known to be false from outset. We examine consequences of approximating sharp by a hazy ‘peri-null’ instantiated as narrow prior distribution centered on point interest. The peri-null then equals multiplied correction term which itself factor. For moderate sample sizes, relatively inconsequential; howeve...