Numerical distance effect size is a poor metric of approximate number system acuity

The Interaction between Congruency and Numerical Ratio Effects in the Nonsymbolic Comparison Test

The nonsymbolic comparison task is used to investigate the precision of the Approximate Number Sense, the ability to process discrete numerosity without counting and symbols. There is an ongoing debate regarding the extent to which the ANS is influenced by the processing of non-numerical visual cues. To address this question, we assessed the congruency effect in a nonsymbolic comparison task, examining its variability across different stimulus presentation formats and numerical proportions. Additionally, we examined the variability of the numerical ratio effect with the format and congruency. Utilizing generalized linear mixed-effects models with a sample of 290 students (89% female, mean age 19.33 years), we estimated the congruency effect and numerical ratio effect for separated and intermixed formats of stimulus presentation, and for small and large numerical proportions. The findings indicated that the congruency effect increased in large numerical proportion conditions, but this pattern was observed only in the separated format. In the intermixed format, the congruency effect was insignificant for both types of numerical proportion. Notably, the numerical ratio effect varied for congruent and incongruent trials in different formats. The results may suggest that the processing of visual non-numerical parameters may be crucial when numerosity processing becomes noisier, specifically when numerical proportion becomes larger. The implications of these findings for refining the ANS theory are discussed.

Symbolic number comparison and number priming do not rely on the same mechanism

In elementary symbolic number processing, the comparison distance effect (in a comparison task, the task is more difficult with smaller numerical distance between the values) and the priming distance effect (in a number processing task, actual number is easier to process with a numerically close previous number) are two essential phenomena. While a dominant model, the approximate number system model, assumes that the two effects rely on the same mechanism, some other models, such as the discrete semantic system model, assume that the two effects are rooted in different generators. In a correlational study, here we investigate the relation of the two effects. Critically, the reliability of the effects is considered; therefore, a possible null result cannot be attributed to the attenuation of low reliability. The results showed no strong correlation between the two effects, even though appropriate reliabilities were provided. These results confirm the models of elementary number processing that assume distinct mechanisms behind number comparison and number priming.

Ratio effect slope can sometimes be an appropriate metric of the approximate number system sensitivity

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.