Significant Inter-Test Reliability across Approximate Number System Assessments

The approximate number system (ANS) is the hypothesized cognitive mechanism that allows adults, infants, and animals to enumerate large sets of items approximately. Researchers usually assess the ANS by having subjects compare two sets and indicate which is larger. Accuracy or Weber fraction is taken as an index of the acuity of the system. However, as Clayton et al. (2015) have highlighted, the stimulus parameters used when assessing the ANS vary widely. In particular, the numerical ratio between the pairs, and the way in which non-numerical features are varied often differ radically between studies. Recently, Clayton et al. (2015) found that accuracy measures derived from two commonly used stimulus sets are not significantly correlated. They argue that a lack of inter-test reliability threatens the validity of the ANS construct. Here we apply a recently developed modeling technique to the same data set. The model, by explicitly accounting for the effect of numerical ratio and non-numerical features, produces dependent measures that are less perturbed by stimulus protocol. Contrary to their conclusion we find a significant correlation in Weber fraction across the two stimulus sets. Nevertheless, in agreement with Clayton et al. (2015) we find that different protocols do indeed induce differences in numerical acuity and the degree of influence of non-numerical stimulus features. These findings highlight the need for a systematic investigation of how protocol idiosyncrasies affect ANS assessments.