How might the discrepancy in the effects of perceptual variables on numerosity judgment be reconciled?

It has been claimed that a genuinely abstract numerical representation would be capable of representing the numerosity of any set of discrete elements independently of the attributes of the individual elements. In practice, however, perceptual variables, such as element size, density, and others, affect numerosity judgment. In this study, we examined how perceptual variables affect the performance of numerosity judgments under the control of factors such as amount of practice and set size. In Experiment 1, we introduced the numerosity comparison task to less experienced observers in order to examine the effect of element size and array area. In Experiment 2, we examined whether and how practice would influence precision and accuracy in numerosity comparison and demonstrated that the effects of perceptual variables mostly disappeared. In Experiment 3, we examined whether the effect of practice could transfer to the performance in different stimulus conditions. Taking the results together, we demonstrate that differences in practice might be the source of inconsistent results for perceptual variables.