Spontaneous and directed attention to number and proportion.

Abstract

Although difficulties processing both symbolic and nonsymbolic proportion compared with absolute number are well established, the mechanisms involved remain unclear. We investigate four potential explanations to account for better number processing in adulthood: (a) number is more salient than proportion, (b) number is encoded more automatically than proportion, (c) proportion is more effortfully processed than number, and (d) number competes with proportion during decision making. Across three experiments, we used a delayed match-to-sample paradigm in which adults were asked which of two alternatives matched a sample set of red and blue dots. We systematically manipulated which dimension of the sample participants matched (number of red dots, total number of dots, proportion of red dots), the presence/absence of the competing quantity in the choice alternatives, and when they were told which quantitative dimension to encode (before vs. after the sample presentation, or not at all). Overall, data reveal that proportion was less salient than the numerical subset. Additionally, the number of items within the subset, but not the total number of items in the superset, interfered with proportion-based responding. Last, even in the absence of response competition and costly task demands, proportion matching took longer than number matching, highlighting basic processing differences. Together, results reveal pervasive difficulties in representing proportion compared with number, even when task demands are unambiguous. However, this varied depending on the numerical set involved and across encoding, processing, and decision processes. We discuss the implications of these findings for theories of ratio processing and of quantity more generally.