Abstract
The approximate number system (ANS) is believed to be an essential component of numerical understanding. The sensitivity of the ANS has been found to be correlating with various mathematical abilities. Recently, Chesney (2018, Attention, Perception, & Psychophysics, 80[5], 1057–1063) demonstrated that if the ANS sensitivity is measured with the ratio effect slope, the slope may measure the sensitivity imprecisely. The present work extends her findings by demonstrating that mathematically the usability of the ratio effect slope depends on the Weber fraction range of the sample and the ratios of the numbers in the used test. Various indexes presented here can specify whether the use of the ratio effect slope as a replacement for the sigmoid fit is recommended or not. Detailed recommendations and a publicly available script help the researchers to plan or evaluate the use of the ratio effect slope as an ANS sensitivity index.
Highlights
The aim of the present study is to extend the analysis of Chesney (2018), and instead of suggesting mainly to avoid the ratio effect slope, it is investigated how (1) the expected Weber fraction range and (2) the used number ratio range influence whether the ratio effect slope is recommended to use or not by measuring (a) the expected ratio effect slope, (b) the expected range of ratio effect slopes in a group, and (c) the expected decay of the correlation coefficient in a correlational study
It was measured what correlation could be observed if an index is perfectly correlating (i.e., r = 1) with the approximate number system (ANS) sensitivity, but the ANS sensitivity is measured with the ratio effect slope
The correlation of the ratio effect slope and the Weber fraction was calculated (Weber fraction was considered as the index of a property that is perfectly correlating with the ANS sensitivity, which in turn is validly measured with the Weber fraction). (One can consider this as sampling from a population showing a function displayed in Fig. 3 or Fig. 5, and the correlation of the two variables is calculated.) Sampling and calculation of the correlation was repeated 10,000 times, and the distribution of the correlations are displayed
Summary
When the mean is large enough with relatively small range, when most of the population is beyond the peak, the ratio effect is again a straightforward index to measure the ANS sensitivity, the relation of the ratio effect slope and the Weber fraction is reversed. Relation of the Weber fraction and the ratio effect slope as a function of ratio pairs In a comparison task simulation, overlaps of two normal distributions were calculated.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
