# Weber Fraction (Experienced Users)

### From Panamath

In the ANS, it is generally agreed that each numerosity, or relative quantity, is mentally represented by a distribution of activation on an internal "number line." This can be modeled by a Gaussian function with a mean of whatever numerosity is presented. Furthermore, as the numerosity represented increases, the standard deviation of the representing Gaussian also steadily increases.

This relationship shows that the quantitative discrimination between two numerosities in the ANS is a function of their ratio, thus instantiating Weber's law.

The degree of overlap between any two numerosities must be taken into account when considering the Weber fraction. The probability of correct discrimination between two similar numerosities always approaches, but never becomes, zero--which is shown by the fact that, no matter how much overlap there is between two different numerosities, there will always be a non-overlapping area whereby a larger numerosity will be perceived of as larger.

The Weber fraction is a constant that describes the standard deviations of all the numerosity representations on the mental number line. The fraction determines the spread with the following formula: standard deviation = number * Weber fraction. From this, the amount of overlap between any (not just those near threshold) two functions that represent numerosities, as well as a smoothly increasing curve depicting the idealized subject's "Percent Correct," can be determined.

Although the fraction can be thought of as basis for a threshold beyond which an individual will succeed at discrimination, or as the midpoint between subjective equality and asymptotic performance, these only focus on certain aspects of the "Percent Correct" curve derived from the Weber fraction, which is unspecific to two-numerosity discriminations and comparisons near threshold.