Perceived Numerosity as a Function of Item Size

Abstract

In a sample of 48 subjects, there was a significant inverse relation between item size and estimation of numerosity. This result was shown to be consistent with Gestalt theory. According to this approach, the components of good figures appear more numerous, and smaller items produce better figures.

How might the discrepancy in the effects of perceptual variables on numerosity judgment be reconciled?

“…As is presented in Table 1, the results of experiments in which experienced observers participated have shown little or no effect of element size and array area Burgess & Barlow, 1983). On the contrary, studies that have introduced naive or less experienced observers have shown the effects of element size and array area (Ginsburg & Nicholls, 1988;Shuman & Spelke, 2006;Sophian & Chu, 2008). Apart from human studies, it has been reported that extensive training was required, at least in the initial phase of an experiment, in studies that required animals to respond to numerosity under controls for perceptual variables (e.g., Nieder et al, 2002;Tomonaga, 2008).…”

“…Likewise, Burgess and Barlow (1983) demonstrated that display size and density had little ef-f f fect on precision in numerosity comparison by a 16-fold change of linear dimensions. As for the effect of element size, Ginsburg and Nicholls (1988), Shuman and Spelke (2006), and Sophian and Chu (2008) demonstrated an inverse relationship between item size and the estimation of numerosity, such as when larger items appeared less numerous than small items. By examining Weber fractions in the numerosity discrimination task, Ross (2003) demonstrated that when the size of elements in comparison was altered, the Weber fractions increased, suggesting that the difference in the size of elements elicited the deterioration of precision in numerosity comparison.…”

“…Different processes at the response stage could produce different outcomes for those tasks in numerosity judgments. For example, the recent study by Sophian and Chu (2008) demonstrated that the accuracy of verbal estimates of the numerosities of arrays made upon completion Ginsburg, 1991;Ginsburg & Nicholls, 1988;Krueger, 1972;Shuman & Spelke, 2006;Sophian & Chu, 2008), as well as in young children (Clearfield & Mix, 1999;Cordes & Brannon, 2008Mix, Huttenlocher, & Levine, 2002;Rousselle, Palmers, & Noel, 2004).…”

“…Sophian and Chu demonstrated that numerosity judgments were affected by the amount of open space in the array being compared. In addition, recent studies on Stroop interference between discrete (i.e., numerical) and continuous (i.e., element size, cumulative area, or display area) Burgess & Barlow (1983) 25 Comparative judgment Experienced (2) No effect of array area Ginsburg & Nicholls (1988) 19, 37, 61, 117 Estimation Naive (48) Overestimation of smaller elements Vos, van Oeffelen, Tibosch, & Allik (1988) 36 Comparative judgment Naive (23) Overestimation of elements in larger array area Allik, Tuulmets, & Vos, (1991) 16, 32 Comparative judgment Experienced (2) No effect of array area Ross (2003) 8 observers will show some effects, few studies have explicitly attempted to examine whether and how practice influences the performance of numerosity judgments in a particular experiment. In Experiment 1, we introduced the numerosity comparison task to less experienced adult observers in order to examine the effects of element size and array area.…”

The construction of large number representations in adults

“…Human adults clearly have this ability when dealing with exact quantities labeled with Arabic numerals. Yet judgments of approximate numerosity in humans are consistently found to be highly influenced by sensory properties of the stimulus, such as regularity in a visual array, or frequency in an auditory sequence (Ginsburg, 1991;Ginsburg & Nicholls, 1988;Ginsburg & Pringle, 1988;Massaro, 1976). For example, the density and grouping patterns of large visual arrays affect the numerosity judgments of human adults (Durgin, 1995).…”