Precision and Bias in Approximate Numerical Judgment in Auditory, Tactile, and Cross-modal Presentation

Many studies have claimed that the numerosity of any set of discrete elements can be depicted by a genuinely abstract number representation, irrespective of whether they are presented in a visual, auditory, or tactile modality. However, in behavioral studies, some inconsistencies have been observed in the performance of number comparisons among different modalities. In this study, we have tested whether numerical comparisons of auditory, tactile, and cross-modal presentations would differ under adequate control of stimulus presentation, and, if so, how they would differ. The unimodal and cross-modal stimuli pairs were presented in sequential manner. We measured the Weber fractions (i.e., precision) and points of subjective equality (i.e., accuracy) of numerical discriminations in auditory, tactile, and crossmodal conditions. The results showed that the Weber fractions are constant over standard stimuli, indicating that the Weber's law holds for the range of numerical values that was tested. Furthermore, the Weber fractions are consistent over unimodal and cross-modal comparisons, and this indicates that there is no additional noise involved in the cross-modal comparisons. Interestingly, the bias measure showed that the number of auditory stimuli is systematically overestimated compared with that of tactile stimuli.