Enhanced Meta-Analysis: Converting Beta Weights to Correlations
Bibliographic record
Abstract
Meta-analysis is crucial to coping with the contemporary landscape of exponential scientific output. Hindering this effort is effect size variety, with standardized beta coefficients, regression weights, elasticities, or partial correlations proven to be non-equivalent to zero-order correlations, despite that these parameters are often aggregated together. Addressing this challenge, we developed two novel approaches that convert betas to correlations, uninformed and informed estimation, and compare their accuracy and bias against the traditional method of Peterson and Brown (2005). In our simulations, we tested matrices from 3 to 10 variables, finding that Peterson and Brown’s technique is inherently biased, less accurate, and misestimates error variance. Uninformed and informed estimation was on average more accurate, unbiased and, by merging sampling error with imputation error, correctly identifies error variance. Due to imputation error, reporting beta weights alone typically destroys 95% to over 99% of the information originally held by a full correlation matrix. For fields that almost exclusively report betas, such as Economics, it necessarily cripples them from becoming cumulative sciences. We recommend that all previous uses of Peterson and Brown be re-evaluated, future aggregations of partial correlations should use our provided estimation techniques, and correlation matrices be routinely reported.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.244 | 0.630 |
| Meta-epidemiology (narrow) | 0.004 | 0.002 |
| Meta-epidemiology (broad) | 0.006 | 0.012 |
| Bibliometrics | 0.013 | 0.017 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.009 | 0.007 |
| Open science | 0.003 | 0.006 |
| Research integrity | 0.002 | 0.007 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
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; the direct Gemma label and the distilled Codex classifier agree on what is shown here.
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".