Efficiency of locating centres of dot-clusters by human observers

A spatial interval acuity task was used to determine the efficiency with which observers located the centroids of circular clusters of individually-small elements. A cluster was defined by its radius and by the number of elements within it. The observer's task was to compare the horizontal distance between the centres of two such clusters to a standard distance, and to decide whether it was greater or smaller. The standard distance was made explicit by two markers on the display screen. As expected on statistical grounds, thresholds increased with the radius of the clusters, and decreased as a function of the number of elements. There were considerable individual differences in efficiency between observers, but the best observers achieved efficiencies close to 100% in many of the conditions. One anomalous observer showed virtually no decrease in thresholds as the number of elements increased, and thus her efficiencies declined to as little as 10%. The ability to combine positional information over spatially-separated elements to obtain an estimate of their central tendency appears in general to be high, and may underlie the perceptual biases revealed in certain geometric illusions, such as the Müller-Lyer.