The second elbow in number perception

Abstract

Lurking in the number estimation data of Volkman et al. (1949) are two elbows, only one of which has been a focus of previous research. Volkman et al. distinguished the subitizing range from the estimation range based in part on a sharp inflection in the response-time function between numbers less than and numbers greater than about 5. Here we show that a second elbow, hitherto unnoticed in Volkman's estimation data occurs at about 20 in number estimation. Magnitude estimation data were collected for numerosity from participants tested individually in the laboratory (N=78). Undergraduates estimated the numbers of large luminance-balanced annular spots in one of four quasi-logarithmic ranges (Expt. 1: 1-224 or 26-224; Expt. 2: 1-72 or 9-224). Displays were circular with enclosing diameters varying in size by a factor of 1.5 (17° to 25°). Random spot arrays were flashed for 400 ms, after which the participant typed in a numeric estimate. Each participant saw each number in the range 6 times, for a total of either 192 trials (Expt. 1) or 144 trials (Expt. 2). When only numbers above 25 were presented, we replicated Krueger's (1972) observation that number estimates follow a power function with an exponent of about 0.7, but when ranges crossing 20 were presented, estimates changed over from being accurate (with exponents equal to or greater than 1) for numbers up to about 16 to underestimation with an exponent between 0.5 and 0.6 for numbers above 20. Both the sharp elbow in the estimation functions and the compressed scaling for higher numerosities were replicated in all three conditions where the ranges spanned across a numerosity of 20. Modeling based on occupancy (Allik & Tuulmets, 1991) did not account for the elbows. This second number elbow suggests that number estimation may be divisible into three regimes rather than two. Meeting abstract presented at VSS 2017