Comparing Numerical Comparison Tasks: A Meta-Analysis of the Variability of the Weber Fraction Relative to the Generation Algorithm

Abstract

Since more than 15 years, researchers have been expressing their interest in evaluating the Approximate Number System (ANS) and its potential influence on cognitive skills involving number processing, such as arithmetic. Although many studies reported significant and predictive relations between ANS and arithmetic abilities, there has recently been an increasing amount of published data that failed to replicate such relationship. Inconsistencies lead many researchers to question the validity of the assessment of the ANS itself. In the current meta-analysis of over 68 experimental studies published between 2004 and 2017, we show that the mean value of the Weber fraction (w), the minimal amount of change in magnitude to detect a difference, is very heterogeneous across the literature. Within young adults, w might range from < 10 to more than 60, which is critical for its validity for research and diagnostic purposes. We illustrate here the concern that different methods controlling for non-numerical dimensions lead to substantially variable performance. Nevertheless, studies that referred to the exact same method (e.g., Panamath) showed high consistency among them, which is reassuring. We are thus encouraging researchers only to compare what is comparable and to avoid considering the Weber fraction as an abstract parameter independent from the context. Eventually, we observed that all reported correlation coefficients between the value of w and general accuracy were very high. Such result calls into question the relevance of computing and reporting at all the Weber fraction. We are thus in disfavor of the systematic use of the Weber fraction, to discourage any temptation to compare given data to some values of w reported from different tasks and generation algorithms.

A robust electrophysiological marker of spontaneous numerical discrimination

“…It should be noted here that previous works highlighted comparable responses only from a ratio of 1.4 onwards 42 , 43 . This slight discrepancy might be explained by the present participants’ high ability to discriminate between numerosities, which was reflected by the comparably low Weber fraction of 0.116 in the number comparison task (this value is on average 0.22 in typical adult samples 62 . Such an elevated sensitivity to numerical discrimination at the behavioural level in the present sample might then account for the observation that the cerebral responses capturing the numerical change already reached significance at the group level at the early ratio of 1.2.…”

“…First, we computed Baseline-Corrected Amplitudes (BCA) by subtracting from the 5 Hz bin the mean amplitude of its twenty surrounding bins (ten on each side, excluding the immediately adjacent bins, and the two extreme values). BCA are thus expressed in microvolt and can therefore be considered to quantify changes within the EEG signal 35 , 36 , 60 – 62 . BCA were used to depict the scalp topographies in Fig.…”

Numerosity discrimination in deep neural networks: Initial competence, developmental refinement and experience statistics

“…Indeed, it is well‐known that different experimental protocols and testing conditions (e.g. lab settings vs. on‐line crowdsourcing platforms) induce differences in the estimated Weber fraction, leading some authors to question the inter‐test reliability of this measure (Clayton, Gilmore, & Inglis, ; Guillaume & Van Rinsveld, ; Price, Palmer, Battista, & Ansari, ). Furthermore, variability in individual estimates is very high even within the same experimental study, for example ranging from 0.15 to 0.3 in Revkin et al (), from 0.1 to 0.5 in Halberda et al (), from 0.1 to 0.4 in Piazza et al () and from 0.15 to 0.5 in DeWind et al ().…”

Cognitive Research and Mathematics Education—How Can Basic Research Reach the Classroom?

“…Examples of more applied research on numerical cognition include evaluations of effectiveness of interventions in early childhood (Mononen et al, 2014;Wang et al, 2016;Christodoulou et al, 2017;Nelson and McMaster, 2019); for older students (Jitendra et al, 2018;Stevens et al, 2018); across age groups (Dennis et al, 2016); and across different regions of the world (Conn, 2017). Other examples include interventions for students with emotional difficulties (Losinski et al, 2019); math anxiety (Namkung et al, 2019); or on attitudes toward achievement (Savelsbergh et al, 2016); the impact of homework (Fan et al, 2017); and specific teaching strategies (Capar and Tarim, 2015;Rittle-Johnson et al, 2017;Guillaume and Van Rinsveld, 2018).…”