# ANS measurement

The sensitivity of the Approximate Number System (ANS) is believed to influence math grades, mathematical competence, or mathematical learning problems. It is fundamental that ANS sensitivity should be measured validly and reliably for the empirical works, otherwise, the results and their interpretations will be invalid and biased.

We note again here that according to our other line of research, ANS is not a fundamental system in symbolic number processing, and many phenomena that have been attributed to the ANS are backed up by a discrete representation. However, nonsymbolic numbers are processed primarily by the ANS, and it is possible that this nonsymbolic ANS affects symbolic number processing, even if its effect can not be overwhelming, as assumed in the original ANS model. See more details about our alternative DSS account here.

See also our related projects about the role of the ANS in children on our project page.

## Measuring the ANS sensitivity in children

Many works discuss specific issues of ANS sensitivity, and reviews discuss ANS measurement in general. Here, in a new review, we focus on the issues that arise when measuring ANS sensitivity in children. We raise several issues often ignored in the literature; we provide solutions for many of those issues or identify key open questions; and we identify critical problems about the incorrect interpretations of the data that rely on suboptimal ANS precision measurement. We provide recommendations for measuring ANS sensitivity in children.

Krajcsi, A., Chesney, D., Cipora, K., Coolen, I., Gilmore, C., Inglis, M., Libertus, M., Nuerk, H.-C., Simms, V., & Reynvoet, B. (2024). Measuring the acuity of the approximate number system in young children. Developmental Review, 72, 101131. https://doi.org/10.1016/j.dr.2024.101131 Or find the preprint here.

## Using the ratio/distance effect slope

ANS sensitivity is sometimes measured as the Weber fraction (calculated with psychophysical methods), but sometimes it is measured with the ratio/distance effect (calculated as the slope of the linear fit on the performance as a function of the ratio/distance of the numbers). In an illuminating work, Dana Chesney argued that this linear slope is not only an imprecise approximation of the Weber fraction, but the relation of the slope and the Weber fraction may be nonmonotonic. Depending on the parameters, the Weber fraction and the ratio effect may correlate either positively or negatively. This nonmonotonic relation may question the validity of many former correlational studies where ANS sensitivity was measured with ratio or distance effect indexes.

In the present follow-up work, it was investigated under what circumstances (expected range of Weber fractions and ratios of the stimuli in a study) the ratio/distance slope works correctly. A script is also provided to estimate whether former or planned studies could utilize the ratio/distance slope appropriately.

Krajcsi, A. (2020). Ratio effect slope can sometimes be an appropriate metric of the approximate number system sensitivity. Attention, Perception, & Psychophysics, 82(4), 2165–2176. https://doi.org/10.3758/s13414-019-01939-6