ROC asymmetry is not diagnostic of unequal residual variance in Gaussian signal detection theory
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Signal detection theory (SDT) is used to analyze yes/no judgment accuracy in many research domains of psychology. SDT yields separate estimates for response bias/criterion (c) and for sensitivity/discriminability (d'). Discrimination performance can be displayed in Receiver Operating Characteristics (ROCs) plotting hit and false alarm rates at various levels of confidence. We provide formal proof and simulations showing that asymmetric ROCs in Gaussian SDT are not exclusively diagnostic of unequal residual variance but may as well result from equal-variance models with c and d' systematically varying across subjects and/or items. Falsely attributing zROC slopes to unequal residual variance while neglecting true group-level variability introduces systematic and unsystematic statistical error. We show that ordinal regression models minimize such errors while estimating all SDT parameters and statistical criteria in a single model.
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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 | 0.008 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 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) | 0.001 | 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