### Abstract

In everyday scenes, objects rarely appear in isolation. Clustered objects in a scene are less readily identified than objects in isolation. We form a summary representation of the group as a whole. What properties characterize this summary? Likely candidates are statistical descriptors including the mean, the range and the variance. Understanding how these statistics are extracted is one goal for the study of perception. In a series of experiments, we investigated the accuracy of judgments of the mean size of circles. First, participants adjusted a test circle to the estimated mean size of two target circles. Judgments of the perceived mean size followed a power function with an exponent of 0.76, consistent with results obtained by Teghtsoonian (1965). We used this psychological estimate of the mean in the remaining experiments. Next we measured thresholds for discriminating the mean size of a heterogeneous array, and compared them with thresholds for discriminating the size of elements in a homogeneous array, and the size of a single element. We found little difference between these three measures, suggesting that extracting the mean size might be an automatic process. We varied the exposure duration, and found much less Improvement with duration in thresholds for the mean size than in those for single elements or homogeneous displays. There may be internal noise in the averaging process that sets a ceiling on the improvement that is possible. In another experiment, we varied the distributions of sizes (normal, uniform, two peaks, and homogeneous). Thresholds were only slightly higher for comparing the means across two different distributions compared to within the same distribution, confirming that subjects were indeed averaging sizes. Finally, we investigated how many elements participants used in averaging by running a simulation, randomly sampling different numbers of elements. We found that samples of six elements gave the closest match to human performance.

Original language | English |
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Pages (from-to) | 216a |

Journal | Journal of Vision |

Volume | 2 |

Issue number | 7 |

DOIs | |

Publication status | Published - 2002 Dec 1 |

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### All Science Journal Classification (ASJC) codes

- Ophthalmology
- Sensory Systems

### Cite this

*Journal of Vision*,

*2*(7), 216a. https://doi.org/10.1167/2.7.216

}

*Journal of Vision*, vol. 2, no. 7, pp. 216a. https://doi.org/10.1167/2.7.216

**Representation of statistical properties.** / Chong, Sang C.; Treisman, Anne.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Representation of statistical properties

AU - Chong, Sang C.

AU - Treisman, Anne

PY - 2002/12/1

Y1 - 2002/12/1

N2 - In everyday scenes, objects rarely appear in isolation. Clustered objects in a scene are less readily identified than objects in isolation. We form a summary representation of the group as a whole. What properties characterize this summary? Likely candidates are statistical descriptors including the mean, the range and the variance. Understanding how these statistics are extracted is one goal for the study of perception. In a series of experiments, we investigated the accuracy of judgments of the mean size of circles. First, participants adjusted a test circle to the estimated mean size of two target circles. Judgments of the perceived mean size followed a power function with an exponent of 0.76, consistent with results obtained by Teghtsoonian (1965). We used this psychological estimate of the mean in the remaining experiments. Next we measured thresholds for discriminating the mean size of a heterogeneous array, and compared them with thresholds for discriminating the size of elements in a homogeneous array, and the size of a single element. We found little difference between these three measures, suggesting that extracting the mean size might be an automatic process. We varied the exposure duration, and found much less Improvement with duration in thresholds for the mean size than in those for single elements or homogeneous displays. There may be internal noise in the averaging process that sets a ceiling on the improvement that is possible. In another experiment, we varied the distributions of sizes (normal, uniform, two peaks, and homogeneous). Thresholds were only slightly higher for comparing the means across two different distributions compared to within the same distribution, confirming that subjects were indeed averaging sizes. Finally, we investigated how many elements participants used in averaging by running a simulation, randomly sampling different numbers of elements. We found that samples of six elements gave the closest match to human performance.

AB - In everyday scenes, objects rarely appear in isolation. Clustered objects in a scene are less readily identified than objects in isolation. We form a summary representation of the group as a whole. What properties characterize this summary? Likely candidates are statistical descriptors including the mean, the range and the variance. Understanding how these statistics are extracted is one goal for the study of perception. In a series of experiments, we investigated the accuracy of judgments of the mean size of circles. First, participants adjusted a test circle to the estimated mean size of two target circles. Judgments of the perceived mean size followed a power function with an exponent of 0.76, consistent with results obtained by Teghtsoonian (1965). We used this psychological estimate of the mean in the remaining experiments. Next we measured thresholds for discriminating the mean size of a heterogeneous array, and compared them with thresholds for discriminating the size of elements in a homogeneous array, and the size of a single element. We found little difference between these three measures, suggesting that extracting the mean size might be an automatic process. We varied the exposure duration, and found much less Improvement with duration in thresholds for the mean size than in those for single elements or homogeneous displays. There may be internal noise in the averaging process that sets a ceiling on the improvement that is possible. In another experiment, we varied the distributions of sizes (normal, uniform, two peaks, and homogeneous). Thresholds were only slightly higher for comparing the means across two different distributions compared to within the same distribution, confirming that subjects were indeed averaging sizes. Finally, we investigated how many elements participants used in averaging by running a simulation, randomly sampling different numbers of elements. We found that samples of six elements gave the closest match to human performance.

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U2 - 10.1167/2.7.216

DO - 10.1167/2.7.216

M3 - Article

AN - SCOPUS:4243160735

VL - 2

SP - 216a

JO - Journal of Vision

JF - Journal of Vision

SN - 1534-7362

IS - 7

ER -