Combining Correlated P-values From Primary Data Analyses
Bibliographic record
Abstract
Research results on the same subject, extracted from scientific papers or clinical trials, are combined to determine a consensus. We are primarily concerned with combining p-values from experiments that may be correlated. We have two methods, a non-Bayesian method and a Bayesian method. We use a model to combine these results and assume the combined results follow a certain distribution, for example, chi-square or normal. The distribution requires independent and identically distributed (iid) random variables. When the data are correlated or non-iid, we cannot assume such distribution. In order to do so, the combined results from the model need to be adjusted, and the adjustment is done “indirectly” through two test statistics. Specifically, one test statistic (TS** ) is obtained for the non-iid data and the other is the test statistic (TS) is obtained for iid data. We use the ratio between the two test statistics to adjust the model test statistic (TS**) for its non-iid violation. The adjusted TS** is named as “effective test statistics” (ETS), which is then used for statistical inferences with the assumed distribution. As it is difficult to estimate the correlation, to provide a more coherent method for combining p-values, we also introduce a novel Bayesian method for both iid data and non-iid data. The examples are used to illustrate the non-Bayesian method and additional examples are given to illustrate the Bayesian method.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.041 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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 teacher head, 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".