Differences in Variance, Skewness, and Kurtosis Can Account for Differences in Binary Outcomes
Bibliographic record
Abstract
When researchers consider the relation between continuous predictors (e.g., perceived threat) and binary outcomes (e.g., being stopped by police), they typically adopt a means-focused approach, (a) attributing observed differences in binary outcomes to expected mean differences in continuous predictors and/or (b) predicting expected differences in binary outcomes using observed mean differences in continuous predictors. Because non-mean distribution moments of the continuous predictor (variance/skewness/kurtosis) also predict binary outcomes, this means-based approach can lead researchers to make inaccurate inferences about the relation between continuous predictors and binary outcomes and overlook viable cognitive explanations for individual or group differences in binary outcomes. We describe the extent to which differences in non-mean distribution moments for continuous predictors translate to differences in binary outcomes (Part I). We show that modeling non-mean distribution moments can change predicted binary outcomes (Part II) and inform existing psychological theory (Part III).
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How this classification was reachedexpand
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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".