A Minority pulls the sample mean: on the individual prevalence of robust group-level cognitive phenomena – the instance of the SNARC effect

Abstract

The aim of cognitive psychology is to obtain insights into human cognition in general. For this purpose, group-studies are typically conducted on representative samples so that the results can be generalized to the population. Using this approach, individual differences in such group-level cognitive phenomena are typically neglected and not much is known about their prevalence at the individual level. Such information is nevertheless important for claims about the universality of phenomena, as in theory, significant effects at the group-level can in principle be driven by a minority of participants. Here we used a uniform analysis of 18 existing data sets revealing a well-replicated phenomenon in numerical cognition: the SNARC (Spatial-Numerical Association of Response Codes) effect, in order to investigate the prevalence of the effect at the individual level. Three methods of analyzing the presence of the effect at the individual level were utilized: one psychometric and two bootstrapping methods. The results show that the group-level SNARC effect is driven by a minority of individuals (≤ 45%) who reveal the effect. This finding demonstrate an important theoretical issue: whether group-level effects really reflect general principles of cognition. We discuss advantages and drawbacks of the present methods and their usefulness for investigating the prevalence of other cognitive phenomena. We posit that testing the presence of robust group-level cognitive effects at the individual level as well as ensuring their reliable measurement is an important step towards integrating two traditionally separate approaches of scientific psychology proposed back in 50’ by Cronbach: experimental and correlational.

A gifted SNARC? Directional spatial-numerical associations in gifted children with high level math skills do not differ from controls

“…Indeed, our data also seems to be quite stable on a group level. In our data preparation process, the trimming eliminated the outlier reaction times, and the values of mean, and in particular the intraindividual variance in RTs were similar to those reported in adult studies (Cipora et al, 2019b). As we discussed in detail before, despite being problematic for correlation analysis, the reliability is not such a problem for between group comparisons.…”

“…The determinants of left-toright directionality are also debated and opposing views emphasize the role of innate biases (e.g., Rugani, Regolin & Vallortigara, 2010) or cultural factors such as dominant reading / writing direction and other implicit spatial biases in a society (e.g., Patro, Fischer, Nuerk, & Cress, 2016;Shaki, Fischer & Petrusic, 2009). Interestingly, as typically quantified, the SNARC effect can be observed in about 70-80% of individuals (e.g., Wood et al, 2008;Cipora et al, 2016, Cipora et al, 2019b. Since individual differences can be observed, another vital question in the debate is: which variables correlate with the SNARC effect?…”

Professional mathematicians do not differ from others in the symbolic numerical distance and size effects

“…This was done using a split-half method (Spearman-Brown corrected for double test length). A detailed description of the algorithm can be found in the Supplementary Material to Cipora et al 's work 75 .…”

Do preliterate children spontaneously employ spatial coding for serial order in working memory?

“…Here, we investigated the OPE in 5‐year‐old children who only received training in preliterate skills (e.g., letter/symbol detection, story reconstructing using images, and flipping books), without dedicated and intensive formal literacy education at school. Besides performing group‐level analyses, we also applied a novel statistical technique that can be used to determine the presence of the OPE at the individual level 19 . As such, we can obtain a more detailed view on the prevalence of individual differences in the orientation of the OPE.…”