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Title: The effect of Euclidean length between the end-points of a line on perceived numerosity of the line
Authors: Krishna, Aradhna
Raghubir, Priya
Keywords: Euclidean length
Fix-point estimation
Issue Date: Mar-1995
Series/Report no.: Marketing Working Paper Series ; MKTG 95.033
Abstract: Estimates of number of objects in lines are made in many different situations. For example, radio traffic reports use helicopters to estimate the number of cars in a freeway traffic jam for determining how long the road will take to clear. Also, estimates of migrating geese are mde by looking at the formation of geese in the sky and making a judgment. This paper demonstrates that the Euclidean length between the end points of a line of dots biases the perceived numerical length (numerosity) of the line. Study 1 provides evidence that highly studied "clutter effect" found in distance perception research is moderated by the Euclidean length between the end-points of a line. Thus, while dotted lines with features such as turns, intersections and gaps are perceived to be more numerous than those without this "clutter" effect, cluttering features which lead to a longer (vs. shorter) Euclidean length between end points of the line magnify (vs. diminish) the clutter effect. Follow up studies examine the effect of three factors that affect Euclidean length: the relative length of subsegments (Study 2), the angle between segments (Studies 3 and 4), and the general direction of segments (Study 5). Study 6 conceptually replicates the reseults of studies 2-5 utilizing different experimental procedures and measures. Finally, we propose and test a model describing how people estimate numerosity of lines. The results reported in this paper support the hypothesis that the shorter the Euclidean length between two end points of a line, the lower is its perceived numerosity.
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