The mythologization of regression towards the mean
Bibliographic record
Abstract
In the quantitative methodology literature, there now exists what can be considered a received account of the enigmatic phenomenon known as regression towards the mean (RTM), the origins of which can be traced to the work of Sir Francis Galton circa 1885. On the received account, RTM is, variably, portrayed as a ubiquitous, unobservable property of individual-level difference and change phenomena, a force that impacts upon the characteristics of individual entities, an explanation for difference and change phenomena, and a profound threat to the drawing of correct conclusions in experiments. In the current paper, we describe the most essential components of the received account, and offer arguments to the effect that the received account is a mythologization of RTM. In particular, we: (a) describe the scientific and statistical setting in which a consideration of RTM is embedded; (b) translate Galton’s discussion of RTM into modern statistical terms; (c) excavate a definition of the concept regression towards the mean from Galton’s discussion of RTM; and (d) employ the excavated definition to dismantle certain of the most essential components of the received account.
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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 | 0.047 | 0.068 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.005 | 0.003 |
| Science and technology studies | 0.002 | 0.046 |
| Scholarly communication | 0.007 | 0.012 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.004 | 0.010 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".