# ANS measurement

The sensitivity of the Approximate Number System (ANS) is believed to influence math grades, mathematical competence, or mathematical learning problems. 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 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.

(We note again that according to our other results ANS is not a fundamental system in symbolic number processing and many phenomena that have been attributed to the ANS are actually backed up by a discrete representation. See more details about our alternative DSS account here. Still, if the ANS model should be tested, it should be done right.)

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

See a presentation about this work.

Find a Python script with which you can estimate whether the ratio effect slope could be used with given expected Weber fractions and given number ratios.