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. Author manuscript; available in PMC: 2016 Sep 1.
Published in final edited form as: Cognition. 2015 Jun 6;142:247–265. doi: 10.1016/j.cognition.2015.05.016

Fig. 2. The internal representation of numerosity in a hypothetical participant according to the new model.

Fig. 2

This hypothetical participant has the following coefficients: w = 0.3 (βnum ≈ 2.36), βSize = 0.5, βSpacing = 0.5, βside = 0. Stimulus S1 and S2 are represented internally as normally distributed random variables on a logarithmically compressed mental number line. The standard deviation of these representations is fixed and equal to w. When Size and Spacing are equal in S1 and S2, the model is equivalent to the logarithmic model (equation 4; Piazza et al., 2010). However, when Size and Spacing are incongruent to number as in S2′ the perceived numerical ratio decreases and confusability increases (as represented by the overlap of the distributions). When Size and Spacing are congruent (S2″) perceived numerical ratio increases and confusability decreases. The shift of the mean of the S2 distribution is given by equation (10).