A Note on Rescaling the Arithmetic Mean for Right-skewed Positive Distributions
Bibliographic record
Abstract
When the arithmetic mean (mean) is used as a measure of location for a set of rightskewed positive observations, it is subject to being pulled upward. This upward movement tends to move the mean away from the bulk of the observations, making it less representative of them. One way to deal with this loss of representativeness is to transform the data. A Box-Cox power transformation can make a right-skewed distribution more symmetrical and then a measure of location for the original observations is found by applying an inverse transformation to the center of the transformed data. This approach was used in a series of papers dealing with the Mean Absolute Percent Error (MAPE) as a measure of forecast and estimation error. In this paper, we show that the Box-Cox power transformation can be used more generally with any mean computed for a set of right-skewed positive observations to develop R-MEAN (Rescaled-Mean). We provide a set of examples to illustrate this approach and show its use in an actual application.
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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 | 0.029 | 0.130 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.003 | 0.004 |
| Science and technology studies | 0.001 | 0.007 |
| Scholarly communication | 0.004 | 0.010 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.003 | 0.011 |
| Insufficient payload (model declined to judge) | 0.006 | 0.004 |
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".