A Remedy for the Overzealous Bonferroni Technique for Multiple Statistical Tests
Bibliographic record
Abstract
Abstract Ecological research often involves multiple statistical tests. It is common practice to employ the Bonferroni technique or its more advanced sequential variant for such multiple tests. Indeed, Moran (Oikos, 100, 2003, 403) found that 13% of ecological papers apply this technique. The seminal paper by Rice (Evolution, 43, 1989, 223) that introduced this technique to the ecological community, is cited to date over 12 000 times. However, these techniques are conservative and some null hypotheses that should be rejected are not. Using order statistics we find that significant results are correlated even when the data consist of independent events. The Bonferroni methods assume independent significant results which results in Type II error with their application. We propose a simple approach, which we term the correlated Bonferroni technique, to rectify this shortcoming, which reduces rejection of significant results. Ecologists may be able to confirm the significance of their results while they are unable to confirm it using the original Bonferroni technique. Researchers may revisit their projects and find that significant results were mistakenly ignored. We provide an Excel file (see supplement) that researchers can easily use. We illustrate the correlated Bonferroni technique with an example.
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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 | 0.224 | 0.545 |
| Meta-epidemiology (narrow) | 0.003 | 0.002 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.004 | 0.007 |
| Science and technology studies | 0.006 | 0.012 |
| Scholarly communication | 0.005 | 0.007 |
| Open science | 0.007 | 0.007 |
| Research integrity | 0.006 | 0.020 |
| Insufficient payload (model declined to judge) | 0.012 | 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".