The normal, Edgeworth, saddlepoint and uniform approximations to the Wilcoxon–Mann–Whitney null-distribution: a numerical comparison
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Bibliographic record
Abstract
In the present paper, we consider four approximations to the null-distribution of the two-sample Wilcoxon–Mann–Whitney statistic, namely a normal, an Edgeworth and a saddlepoint approximation, as well as an approximation by the sum of independent uniform random variables. We make numerical comparisons of these approximations for moderate sample sizes, namely for m = 20 and 20 ≤ n ≤ 80. It turns out that the saddlepoint improves on the Edgeworth and the uniform approximations only very far in the tails, while the Edgeworth outperforms the other three for less extreme cases. We also discuss the practical importance of our results in the era of statistical packages.
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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 | 0.001 | 0.010 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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