The Visual Perception of Correlation in Scatterplots
Why this work is in the frame
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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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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it