The Bayes factor, HDI-ROPE, and frequentist equivalence tests can all be reverse engineered—Almost exactly—From one another: Reply to Linde et al. (2021).
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
Following an extensive simulation study comparing the operating characteristics of three different procedures used for establishing equivalence (the frequentist "TOST," the Bayesian "HDI-ROPE," and the Bayes factor interval null procedure), Linde et al. (2021) conclude with the recommendation that "researchers rely more on the Bayes factor interval null approach for quantifying evidence for equivalence" (p. 1). We redo the simulation study of Linde et al. (2021) in its entirety but with the different procedures calibrated to have the same predetermined maximum Type I error rate. Our results suggest that, when calibrated in this way, the Bayes factor, HDI-ROPE, and frequentist equivalence tests all have similar-almost exactly-Type II error rates. In general any advocating for frequentist testing as better or worse than Bayesian testing in terms of empirical findings seems dubious at best. If one decides on which underlying principle to subscribe to in tackling a given problem, then the method follows naturally. Bearing in mind that each procedure can be reverse-engineered from the others (at least approximately), trying to use empirical performance to argue for 1 approach over another seems like tilting at windmills. (PsycInfo Database Record (c) 2024 APA, all rights reserved).
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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 | 0.011 | 0.161 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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