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Reconnecting p-Value and Posterior Probability Under One- and Two-Sided Tests
| Content Provider | Scilit |
|---|---|
| Author | Shi, Haolun Yin, Guosheng |
| Copyright Year | 2020 |
| Description | As a convention, p-value is often computed in frequentist hypothesis testing and compared with the nominal significance level of 0.05 to determine whether or not to reject the null hypothesis. The smaller the p-value, the more significant the statistical test. Under non-informative prior distributions, we establish the equivalence relationship between the p-value and Bayesian posterior probability of the null hypothesis for one-sided tests and, more importantly, the equivalence between the p-value and a transformation of posterior probabilities of the hypotheses for two-sided tests. For two-sided hypothesis tests with a point null, we recast the problem as a combination of two one-sided hypotheses along the opposite directions and establish the notion of a “two-sided posterior probability”, which reconnects with the (two-sided) p-value. In contrast to the common belief, such an equivalence relationship renders p-value an explicit interpretation of how strong the data support the null. Extensive simulation studies are conducted to demonstrate the equivalence relationship between the p-value and Bayesian posterior probability. Contrary to broad criticisms on the use of p-value in evidence-based studies, we justify its utility and reclaim its importance from the Bayesian perspective. |
| Related Links | http://arxiv.org/pdf/1809.08503 |
| Ending Page | 275 |
| Page Count | 11 |
| Starting Page | 265 |
| ISSN | 00031305 |
| e-ISSN | 15372731 |
| DOI | 10.1080/00031305.2020.1717621 |
| Journal | The American Statistician |
| Issue Number | 3 |
| Volume Number | 75 |
| Language | English |
| Publisher | Informa UK Limited |
| Publisher Date | 2020-02-25 |
| Access Restriction | Open |
| Subject Keyword | Statistics and Probability Bayesian Analysis Clinical Trial Hypothesis Testing One-sided Test Posterior Probability P-value Two-sided Test |
| Content Type | Text |
| Resource Type | Article |
| Subject | Statistics and Probability Statistics, Probability and Uncertainty |
