Undergraduate students’ difficulties assessing empirical sampling distributions
Bibliographic record
Abstract
Our research reveals that introductory college statistics students experience considerable difficulty applying their classroom knowledge when assessing empirical sampling distributions. In a task-based survey, students were asked to judge the likelihood of four empirical sampling distributions (presented to them in graphical form), from a known skewed population. Two graphs were obtained through simulation and two were created to be unreasonable representations of the sampling situation. Students struggled to identify the reasonable graphs in this sampling situation, and seventy-five percent made two or fewer correct identifications, performing no better than one would by guessing. Student responses are described with reference to a five-tiered framework for statistical reasoning: idiosyncratic (0), additive (1), transitional (2), proportional (3), and distributional (4). This model, which describes types of student reasoning, emerged from the work of Shaughnessy, Ciancetta, and Canada (2004), and Shaughnessy, Ciancetta, Best, and Noll (2005). Briefly, additive responses rely on frequencies and individual data points, transitional responses tend to focus on one particular aspect of the distribution such as shape, proportional responses are primarily focused on the population proportion, and distributional responses use multiple aspects of the distribution, such as center and spread. Students were able
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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 | 0.013 | 0.105 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.006 | 0.002 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".