title: One tamed at a time: A new approach for controlling continuous magnitudes in numerical comparison tasks.
abstract: Non-symbolic stimuli (i.e., dot arrays) are commonly used to study numerical cognition. However, in addition to numerosity, non-symbolic stimuli entail continuous magnitudes (e.g., total surface area, convex-hull, etc.) that correlate with numerosity. Several methods for controlling for continuous magnitudes have been suggested, all with the same underlying rationale: disassociating numerosity from continuous magnitudes. However, the different continuous magnitudes do not fully correlate; therefore, it is impossible to disassociate them completely from numerosity. Moreover, relying on a specific continuous magnitude in order to create this disassociation may end up in increasing or decreasing numerosity saliency, pushing subjects to rely on it more or less, respectively. Here, we put forward a taxonomy depicting the relations between the different continuous magnitudes. We use this taxonomy to introduce a new method with a complimentary Matlab toolbox that allows disassociating numerosity from continuous magnitudes and equating the ratio of the continuous magnitudes to the ratio of the numerosity in order to balance the saliency of numerosity and continuous magnitudes. A dot array comparison experiment in the subitizing range showed the utility of this method. Equating different continuous magnitudes yielded different results. Importantly, equating the convex hull ratio to the numerical ratio resulted in similar interference of numerical and continuous magnitudes.
authors.affiliation: Zlotowski Center for Neuroscience, Ben-Gurion University of the Negev, Beer-Sheva, Israel. motisalti@gmail.com.|Brain Imaging Research Center, Ben-Gurion University of the Negev, Beer-Sheva, Israel. motisalti@gmail.com.
authors.forename: Moti
authors.initials: M
authors.lastname: Salti
authors.affiliation: Zlotowski Center for Neuroscience, Ben-Gurion University of the Negev, Beer-Sheva, Israel.|Department of Psychology, Ben-Gurion University of the Negev, Building 95, P.O.B. 653, Beer Sheva, 84105, Israel.
authors.forename: Naama
authors.initials: N
authors.lastname: Katzin
authors.affiliation: School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv, Israel.
authors.forename: David
authors.initials: D
authors.lastname: Katzin
authors.affiliation: Brain Imaging Research Center, Ben-Gurion University of the Negev, Beer-Sheva, Israel.|Numerical Cognition Laboratory, The University of Western Ontario, Toronto, Ontario, Canada.
authors.forename: Tali
authors.initials: T
authors.lastname: Leibovich
authors.affiliation: Zlotowski Center for Neuroscience, Ben-Gurion University of the Negev, Beer-Sheva, Israel.|Department of Psychology, Ben-Gurion University of the Negev, Building 95, P.O.B. 653, Beer Sheva, 84105, Israel.
authors.forename: Avishai
authors.initials: A
authors.lastname: Henik
mesh_terms: D003071:Cognition; D005260:Female; D006801:Humans; D008297:Male; D055641:Mathematical Concepts; D055815:Young Adult
keywords: Matlab toolbox; Non-symbolic number; Ratio effect