Bibliographic record
Abstract
The problem of combining P -values is an old and fundamental one, and the classic assumption of independence is often violated or unverifiable in many applications. There are many well-known rules that can combine a set of arbitrarily dependent P -values (for the same hypothesis) into a single P -value. We show that essentially all these existing rules can be strictly improved when the P -values are exchangeable, or when external randomization is allowed (or both). For example, we derive randomized and/or exchangeable improvements of well-known rules like “twice the median” and “twice the average,” as well as geometric and harmonic means. Exchangeable P -values are often produced one at a time (for example, under repeated tests involving data splitting), and our rules can combine them sequentially as they are produced, stopping when the combined P -values stabilize. Our work also improves rules for combining arbitrarily dependent P -values, since the latter becomes exchangeable if they are presented to the analyst in a random order. The main technical advance is to show that all existing combination rules can be obtained by calibrating the P -values to e-values (using an α -dependent calibrator), averaging those e-values, converting to a level- α test using Markov’s inequality, and finally obtaining P -values by combining this family of tests; the improvements are delivered via recent randomized and exchangeable variants of Markov’s inequality.
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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 | 0.195 | 0.544 |
| Meta-epidemiology (narrow) | 0.004 | 0.003 |
| Meta-epidemiology (broad) | 0.006 | 0.005 |
| Bibliometrics | 0.008 | 0.006 |
| Science and technology studies | 0.002 | 0.008 |
| Scholarly communication | 0.010 | 0.013 |
| Open science | 0.009 | 0.009 |
| Research integrity | 0.005 | 0.015 |
| Insufficient payload (model declined to judge) | 0.007 | 0.004 |
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".