Differentiating the Cochran‐Armitage Trend Test and Pearson's χ<sup>2</sup> Test: Location and Dispersion
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Bibliographic record
Abstract
Summary In genetic case‐control association studies, a standard practice is to perform the Cochran‐Armitage (CA) trend test with 1 degree‐of‐freedom (d.f.) under the assumption of an additive model. However, when the true genetic model is recessive or near recessive, it is outperformed by Pearson's χ 2 test with 2 d.f. In this article, we analytically reveal the statistical basis that leads to the phenomenon. First, we show that the CA trend test examines the location shift between the case and control groups, whereas Pearson's χ 2 test examines both the location and dispersion shifts between the two groups. Second, we show that under the additive model, the effect of location deviation outweighs that of the dispersion deviation and vice versa under a near recessive model. Therefore, Pearson's χ 2 test is a more robust test than the CA trend test, and it outperforms the latter when the mode of inheritance evolves to the recessive end.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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