A Consideration of Alternative Sample Spaces Used in Coin-Toss Problems
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
This paper examines coin-toss comparison questions from two recent studies involving undergraduate students and high school teachers and connects to findings from two prior studies in the literature. Considering possible sample spaces employed by participants, this is a reflection on whether one sequence could be more likely depending on the interpretation of the question. To critique the choice of sequences and determine possible scenarios in which one sequence may be more likely than the other, three alternative sample spaces were explored. It was determined that different sample spaces can lead to one sequence being more likely to occur than the other. Further evaluation discusses whether alternative sample spaces may have been utilised by the participants in each of the studies, and hence, the paper concludes with an advocacy to enquire deeper into participants' reasoning when investigating coin-toss questions.
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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 | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| 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 it