Bibliographic record
Abstract
The visual system is efficient at extracting a range of ensemble statistics. Most research has independently focused on the estimation of the number, the average, or the sum. Since these processes have been studied separately, their relationship is not well understood. Here we explore the interaction among numerosity, mean, and sum perception in one paradigm. In each trial, observers viewed an array of circles varying in size, and estimated the number, the mean size, or the total size of circles in each array in separate blocks (order counterbalanced across observers). Thus, for every array we obtained numerosity, mean, and sum estimates from the same observer. We noticed that there was consistent underestimation in the number, the mean, and the sum judgments. For every array, we also derived the arithmetic number (the estimated sum/the estimated mean), the arithmetic mean (the estimated sum/the estimated number), and the arithmetic sum (the estimated mean*the estimated number) for each observer. We found that the arithmetic mean was significantly closer to the estimated mean than to the objective mean, and the arithmetic sum was significantly closer to the estimated sum than to the objective sum. However, the estimated number was closer to the objective number than to the arithmetic number. This dissociation suggests that observers may have implicitly followed the arithmetic model for mean and sum estimation, but not for number estimation. Moreover, the errors in the sum estimates were highly correlated with the errors in the mean estimates, but the errors in the number estimates were not correlated with either the errors in the sum or the errors in the mean estimates. This provides further evidence that numerosity was calculated independently from the mean or the sum. Taken together, the results suggest that numerosity perception operates in a distinct manner from mean or sum perception. Meeting abstract presented at VSS 2015
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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 | 0.002 | 0.028 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.001 | 0.004 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".