A pluralistic framework for measuring, interpreting and decomposing heterogeneity in meta‐analysis
Bibliographic record
Abstract
Abstract Measuring heterogeneity, or inconsistency, among effect sizes is a crucial step for interpreting meta‐analytic evidence across diverse taxonomic groups and spatiotemporal contexts. However, ecologists and evolutionary biologists often interpret overall mean effects (mean population effects) as consistent across contexts, either explicitly or implicitly, without properly quantifying and interpreting heterogeneity. Here, we present a pluralistic approach that aims to quantify heterogeneity by introducing complementary metrics, each of which decomposes heterogeneity into within‐study, between‐study and between‐species (species and phylogenetic) variances. These metrics include the traditional I 2 (variance‐standardized metric), the newly derived coefficient of variation for heterogeneity ( CVH family; mean‐standardized metric), the second‐order coefficient of variation ( M family; variance–mean‐standardized metric) and their stratified variants. To demonstrate the benefits of the combined use of these measures, we synthesize heterogeneity estimates from 512 ecological and evolutionary meta‐analyses. We show that total heterogeneity (variance of true effects) is, on average, 10 times larger than statistical noise (sampling error variance), contributing to 91% of the observed variance (median I 2 = 91%). This amount of heterogeneity is nearly twice the size of the mean population effect (median CVH = 1.8 and M = 0.6), indicating substantial variation among studies within a meta‐analysis. Moreover, different effect size types yield different values of heterogeneity metrics because they are inherently influenced by statistical properties of their effect size estimators. As such, comparisons of heterogeneity across effect size types should be made with caution, albeit the proposed heterogeneity metrics are unit‐free. Our large‐scale synthesis also provides new benchmarks for the interpretation of heterogeneity and recommendations on how to quantify and report heterogeneity. New extensions for stratifying heterogeneity metrics will clarify our understanding of the generalisability, and at what level of meta‐analytic effects in ecology and evolution.
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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 | 0.268 | 0.408 |
| Meta-epidemiology (narrow) | 0.003 | 0.002 |
| Meta-epidemiology (broad) | 0.006 | 0.011 |
| Bibliometrics | 0.020 | 0.015 |
| Science and technology studies | 0.002 | 0.006 |
| Scholarly communication | 0.010 | 0.006 |
| Open science | 0.005 | 0.008 |
| Research integrity | 0.004 | 0.008 |
| 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; 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".