Decimal Dust, Significant Digits, and the Search for Stars
Bibliographic record
Abstract
The practice of rounding statistical results to two decimal places is one of a large number of heuristics followed in the social sciences. In evaluating this heuristic, the authors conducted simulations to investigate the precision of simple correlations. They considered a true correlation of .15 and ran simulations in which the sample sizes were 60, 100, 200, 500, 1,000, 10,000, and 100,000. They then looked at the digits in the correlations’ first, second, and third decimal places to determine their reproducibility. They conclude that when n < 500, the habit of reporting a result to two decimal places seems unwarranted, and it never makes sense to report the third digit after the decimal place unless one has a sample size larger than 100,000. Similar results were found with rhos of .30, .50, and .70. The results offer an important qualification to what is otherwise a misleading practice.
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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 | 0.035 | 0.332 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.005 | 0.006 |
| Science and technology studies | 0.003 | 0.015 |
| Scholarly communication | 0.008 | 0.010 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.011 | 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; 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".