Meta‐analysis and the reversed <scp>Theorem of the Means</scp>
Bibliographic record
Abstract
Conventional meta-analysis estimators are weighted means of study measures, meant to estimate an overall population measure. For measures such as means, mean differences and risk differences, a weighted arithmetic mean is the conventional estimator. When the measures are ratios, such as odds ratios, logarithms of the study measures are most frequently used, and the back-transform is a weighted geometric mean, rather than the arithmetic mean. For numbers needed to treat, a weighted harmonic mean is the back-transform. The Theorem of the Means effectively states that unless all of the studies have an equal result, the arithmetic mean must be greater than the geometric mean, which must be greater than the harmonic mean. When the weights are fixed sampling weights, the inequalities are in the expected direction. However, when the weights are the usual reciprocal variance estimates, the inequalities go in the opposite direction. The use of reciprocal variance weights is therefore questioned as perhaps having a fundamental flaw. An example is shown of a meta-analysis of frequencies of two classes of drug-resistant HIV-1 mutations.
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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 | 0.176 | 0.298 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.009 | 0.011 |
| Bibliometrics | 0.008 | 0.010 |
| Science and technology studies | 0.001 | 0.010 |
| Scholarly communication | 0.005 | 0.006 |
| Open science | 0.005 | 0.004 |
| Research integrity | 0.005 | 0.011 |
| Insufficient payload (model declined to judge) | 0.007 | 0.003 |
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".