The median and the mode as robust meta‐analysis estimators in the presence of small‐study effects and outliers
Bibliographic record
Abstract
Meta-analyses based on systematic literature reviews are commonly used to obtain a quantitative summary of the available evidence on a given topic. However, the reliability of any meta-analysis is constrained by that of its constituent studies. One major limitation is the possibility of small-study effects, when estimates from smaller and larger studies differ systematically. Small-study effects may result from reporting biases (ie, publication bias), from inadequacies of the included studies that are related to study size, or from reasons unrelated to bias. We propose two estimators based on the median and mode to increase the reliability of findings in a meta-analysis by mitigating the influence of small-study effects. By re-examining data from published meta-analyses and by conducting a simulation study, we show that these estimators offer robustness to a range of plausible bias mechanisms, without making explicit modelling assumptions. They are also robust to outlying studies without explicitly removing such studies from the analysis. When meta-analyses are suspected to be at risk of bias because of small-study effects, we recommend reporting the mean, median and modal pooled estimates.
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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 | 0.243 | 0.566 |
| Meta-epidemiology (narrow) | 0.003 | 0.002 |
| Meta-epidemiology (broad) | 0.009 | 0.013 |
| Bibliometrics | 0.010 | 0.008 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.007 | 0.008 |
| Open science | 0.006 | 0.004 |
| Research integrity | 0.005 | 0.006 |
| Insufficient payload (model declined to judge) | 0.004 | 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".