HOW GOOD IS A NORMAL APPROXIMATION FOR RATES AND PROPORTIONS OF LOW INCIDENCE EVENTS?
Why this work is in the frame
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Bibliographic record
Abstract
Decisions about how to best analyze rare events need to be made in many investigations. For binary events, a normal approximation is often said to be satisfactory when the expected number of events is larger than 5 and the binomial proportion is not too close to zero or one. In most empirical research, the commonly employed large-sample method for determining a confidence interval or for testing a hypothesis for a parameter is based on its logarithmic transformed estimator. In this article, we investigate how much the logarithmic transformation improves the approximation of the distribution of a sample proportion to a normal distribution. We also investigate the performance of the arcsine square root transformation. We find that the success of a normal approximation has less to do with the size of the event rates than the values of np. Further, we find that the transformations do not substantially improve the normal approximation of the distribution of a sample proportion in computing coverage probabilities, that the untransformed results with continuity correction are just about as good as the first-order logarithmic transformation, and that the arcsine transformation is inferior to the logarithmic transformation.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it