Decomposing the Mean: Using Distributional Analyses to Provide a Detailed Description of Addition and Multiplication Latencies
Bibliographic record
Abstract
In the current paper, distributional analyses were used to provide a detailed description of addition and multiplication latencies.University students (n = 32) solved single-digit problems and reported their solution methods.Mean response times were decomposed into mu, reflecting the position of the distribution, and tau, reflecting the skew of the distribution (mean RT = mu + tau) for retrievers, occasional procedure users, and frequent procedure users.By decomposing the mean we were able to determine if observed effects of problem size and group reflected an overall slowing of responses (reflected in mu) or a slowing on some trials only (reflected in tau).Findings provide evidence for tau as an index of procedure use and highlight differences across operations in the locus of the problem-size effect, a robust finding that larger problems (e.g., 8 x 7, 9 + 6) take longer to solve than smaller problems (e.g., 4 x 3, 2 + 4).
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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 | 0.009 | 0.072 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.007 | 0.005 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.008 | 0.001 |
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".