Refining the law of practice.
Bibliographic record
Abstract
The "law of practice"-a simple nonlinear function describing the relationship between mean response time (RT) and practice-has provided a practically and theoretically useful way of quantifying the speed-up that characterizes skill acquisition. Early work favored a power law, but this was shown to be an artifact of biases caused by averaging over participants who are individually better described by an exponential law. However, both power and exponential functions make the strong assumption that the speedup always proceeds at a steadily decreasing rate, even though there are sometimes clear exceptions. We propose a new law that can both accommodate an initial delay resulting in a slower-faster-slower rate of learning, with either power or exponential forms as limiting cases, and which can account for not only mean RT but also the effect of practice on the entire distribution of RT. We evaluate this proposal with data from a broad array of tasks using hierarchical Bayesian modeling, which pools data across participants while minimizing averaging artifacts, and using inference procedures that take into account differences in flexibility among laws. In a clear majority of paradigms our results supported a delayed exponential law. (PsycINFO Database Record
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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 | 0.081 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.010 | 0.002 |
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".