Bibliographic record
Abstract
Since the groundbreaking work by Cleveland and McGill in 1984, studies have revealed the difficulties humans have extracting quantitative data from visualizations as simple as bar graphs. As a first step toward understanding this situation, this paper proposes a mathematical model of the interpretation effort of a bar graph using concepts drawn from eye tracking. First, three key areas of interest (AOIs) are identified, and fixations are modeled as random point clouds within the AOIs. Stochastic geometry is introduced via random triangles connecting fixations within the adjacent key visual regions. The so-called landmark methodology provides the basis for the probabilistic analysis of the constructed system. It is found that the random length of interest in a stochastic triangle has a noncentral chi distribution with a known mean. Unique to this model, in terms of previous landmark applications, is the inclusion of a correlation between fixations, which is justified by physiological studies of the eyes. This approach introduces several model parameters, such as the noncentrality parameter, variance of the fixation cloud, correlation between fixations, and a visualization scale. A detailed parametric analysis examining the dependence of the mean on these parameters is conducted. The paper ties this work to the visualization via a definition of the expected visual measurement error. An asymptotic analysis of the visual error is performed, and a simple expression is found to relate the expected visual measurement error to the key model parameters. From this expression, the influence these parameters have on a visualization’s interpretation is considered.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.005 | 0.025 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.006 | 0.009 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.003 | 0.002 |
| Insufficient payload (model declined to judge) | 0.008 | 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".