How much does the typical ecological meta‐analysis overestimate the true mean effect size?
Bibliographic record
Abstract
Many primary research studies in ecology are underpowered, providing very imprecise estimates of effect size. Meta-analyses partially mitigate this imprecision by combining data from different studies. But meta-analytic estimates of mean effect size may still remain imprecise, particularly if the meta-analysis includes a small number of studies. Imprecise, large-magnitude estimates of mean effect size from small meta-analyses likely would shrink if additional studies were conducted (regression towards the mean). Here, I propose a way to estimate and correct this regression to the mean, using meta-meta-analysis (meta-analysis of meta-analyses). Hierarchical random effects meta-meta-analysis shrinks estimated mean effect sizes from different meta-analyses towards the grand mean, bringing those estimated means closer on average to their unknown true values. The intuition is that, if a meta-analysis reports a mean effect size much larger in magnitude than that reported by other meta-analyses, that large mean effect size likely is an overestimate. This intuition holds even if different meta-analyses of different topics have different true mean effect sizes. Drawing on a compilation of data from hundreds of ecological meta-analyses, I find that the typical (median) ecological meta-analysis overestimates the absolute magnitude of the true mean effect size by ~10%. Some small ecological meta-analyses overestimate the magnitude of the true mean effect size by >50%. Meta-meta-analysis is a promising tool for improving the accuracy of meta-analytic estimates of mean effect size, particularly estimates based on just a few studies.
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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 | 0.330 | 0.617 |
| Meta-epidemiology (narrow) | 0.004 | 0.004 |
| Meta-epidemiology (broad) | 0.014 | 0.016 |
| Bibliometrics | 0.011 | 0.010 |
| Science and technology studies | 0.001 | 0.007 |
| Scholarly communication | 0.009 | 0.011 |
| Open science | 0.006 | 0.005 |
| Research integrity | 0.006 | 0.008 |
| Insufficient payload (model declined to judge) | 0.003 | 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; 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".