Participants judged the number of dots in visual displays with brief presentations (200 msec), such that the numerosity judgment was based on an instantaneous impression without counting. In some displays, pairs of adjacent dots were connected by line segments, whereas, in others, line segments were freely hanging without touching the dots. In Experiments 1, 2A, and 2B, connecting pairs of dots by line segments led to underestimation of dot numbers in those patterns. In Experiment 3, we controlled for the number of freely hanging line segments, whereas Experiment 4 showed that line segments that were merely attached to dots without actually connecting them did not produce a considerable underestimation effect. Experiment 5 showed that a connectedness effect existed when stimulus duration was reduced (50 msec) or extended (1,000 msec). We conclude that connectivity affects dot numerosity judgments, consistent with earlier findings of a configural effect in numerosity processing. Implications of the role of connectedness in object representation are discussed.
The term numerosity judgment refers to the estimation of the number of dots in a pattern made of a multitude of dots, or to comparing the dot numbers of two such patterns, under a short presentation duration to preclude overt or covert counting, with the judgment based solely on an instantaneous impression of numerosity. In a typical numerosity comparison task, a participant is briefly presented with two visual displays of dots and is asked to indicate which contains more dots. In a typical numerosity estimation task, a participant is asked to provide an estimate of the dot number in a display without actually performing one-by-one counting. Earlier researchers (Indow & Ida, 1977; Krueger, 1972, 1984) constructed psychophysical scales and described numerosity as a power function of the number of items in the stimulus (with an exponent of around 0.85). A participant's ability to discriminate numerosity was found to be invariant against (i.e., irrespective of) dot size (Allik, Tuulmets, & Vos, 1991), although his or her ability to estimate numerosity bore an inverse relationship to dot size (Ginsburg & Nicholls, 1988). Errors in discrimination of numerosity were shown to be related not only to the randomness (external variance) of dots-per-unit area in the dot patterns themselves but also to the internal noise (observer variance) generated by the observer (Burgess & Barlow, 1983).
A well-documented finding in numerosity research is that spatial configuration of elements (dots) exerts a profound influence on perceived numerosity: Compared with dots in random distribution, dots in regular arrangements (such as in concentric circles) tend to be overestimated, whereas dots forming clusters are underestimated (Allik & Tuulmets, 1991; Ginsburg, 1978; Ginsburg & Goldstein, 1987). The same pattern of results was replicated in children 5.8-14.6 years of age (Ginsburg & Deluco, 1979). These findings were explained by the so-called "occupancy model" (Allik & Tuulmets, 1991), which claimed that perceived numerosity depended on the subjective area covered by the totality of dots in a dot pattern; the impact of each dot was postulated to have some local spatial spread into its immediate neighborhood. Each dot supposedly occupied a circular territory of a fixed radius larger than its physical size, so when two dots were close to one another, there was an overlap in their individual territory such that the total effective region covered by the dots was smaller than it would have been if the two dots had been more widely separated. Decreasing the distance of adjacent dots-according to the occupancy model- caused more overlapping apparent area, leading to underestimation of dot numerosity.
In addition to the effect of the spatial arrangement of dots on perceived numerosity, there are nonspatial, structural factors affecting numerosity perception. …