Reconnecting <i>p</i> -Value and Posterior Probability Under One- and Two-Sided Tests
Bibliographic record
Abstract
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 noninformative 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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.171 | 0.545 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.005 | 0.003 |
| Bibliometrics | 0.006 | 0.007 |
| Science and technology studies | 0.002 | 0.041 |
| Scholarly communication | 0.011 | 0.020 |
| Open science | 0.007 | 0.011 |
| Research integrity | 0.009 | 0.025 |
| Insufficient payload (model declined to judge) | 0.006 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".