The Visual Perception of Correlation in Scatterplots
Bibliographic record
Abstract
A set of experiments investigated the precision and accuracy of the visual perception of correlation in scatterplots. These used classical psychophysical methods applied directly to these relatively complex stimuli. Scatterplots (of extent 5.0 deg) each contained 100 normally-distributed values. Means were set to 0.5 of the range of the scatterplot, and standard deviations to 0.2 of this range. 20 observers were tested. Precision was determined via an adaptive algorithm that found the just noticeable differences (jnds) in correlation, i.e., the difference between two side-by-side scatterplots that could be discriminated 75% of the time. Accuracy was determined by direct estimation: reference scatterplots were created with fixed upper and lower values, and a test scatterplot adjusted so that its correlation appeared to be midway between these two. This process was then recursively applied to yield several further estimates. Results show that jnd(r) = k (1/b − r), where r is the Pearson correlation, and k and b are parameters such that 0 <k, b <1; typical values are k = 0.2 and b = 0.9. Integration yields the subjective estimate of correlation g(r) = ln (1 − br) / ln (1 − b); this closely matches the results of the direct estimation method. As such, the perception of correlation in a scatterplot is completely specified by just two easily-measured parameters.
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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 | 0.008 | 0.072 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".