One tamed at a time: A new approach for controlling continuous magnitudes in numerical comparison tasks

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.