Research Article: Unbounded number line estimation as a measure of numerical estimation

Date Published: March 14, 2019

Publisher: Public Library of Science

Author(s): Regina Miriam Reinert, Matthias Hartmann, Stefan Huber, Korbinian Moeller, Jérôme Prado.

http://doi.org/10.1371/journal.pone.0213102

Abstract

Number magnitude estimation has been investigated over the last decades using different tasks including non-symbolic numerosity but also number line estimation tasks. Recently, a bi-directional mapping process was suggested for numerosity estimation accounting for underestimation in a perception version of the task (i.e., indicating the number of non-symbolic dots in a set) and overestimation in the corresponding production task (i.e., produce the number of dots indicated by a symbolic number). In the present study, we evaluated the generalizability of these estimation biases in perception and production tasks to bounded and unbounded number line estimation. Importantly, target numbers were underestimated/overestimated by participants in the perception/production version of numerosity estimation as well as unbounded number line estimation. However, this pattern was reversed for bounded number line estimation. Thereby, the present data indicate a conceptual similarity of unbounded number line estimation and the established non-symbolic numerosity estimation task as a measure of numerical estimation. Accordingly, this corroborates the notion that unbounded number line estimation may reflect a purer measure of number magnitude representation than the bounded task version. Furthermore, our findings strengthen the bi-directional mapping hypothesis for numerical estimation by providing evidence for its generalizability to unbounded number line estimation for the first time.

Partial Text

Magnitude estimation tasks are typically employed to investigate numerical cognition. On the one hand, non-symbolic stimuli like collections of dots or sequences of sounds are used to assess the underlying representation of number magnitude. Usually, participants have to estimate their numerosity producing symbolic outputs such as Arabic or oral verbal numerals (e.g., [1],[2]). On the other hand, the (spatial) representation of number magnitude is often investigated using symbolic stimuli in tasks such as number line estimation (e.g., [3]). So far, however, similarities and differences in performance patterns for non-symbolic numerosity estimation and number line estimation have hardly been investigated. Therefore, the current study set off to evaluate whether results on non-symbolic numerosity estimation (e.g., [4]) can be generalized to bounded (e.g., [3]) as well as unbounded number line estimation (e.g., [5]). Generalizable patterns of results would provide further evidence that bounded and/or unbounded number line estimation indeed rely on number magnitude estimation processes. In the following, we will first elaborate on the specifics of number line estimation and non-symbolic numerosity estimation before outlining the details of the present study.

In a first step, individual trials that differed more than ± 4 standard deviations from the overall mean estimates were excluded from the analysis (0.25% of the data). Moreover, we used the average mean of both versions of the perception numerosity estimation task as dependent variable for the ANOVA because the correlation between REE in both versions was r(75) = .89, p < .001, and therefore sufficiently high to pool the respective means. The present study set off to systematically investigate similarities and differences between non-symbolic numerosity estimation (e.g., [4]) and bounded (e.g., [3]) as well as unbounded number line estimation (e.g., [5]). In particular, the aim of our study was to examine the generalizability of patterns of underestimation in the perception and overestimation in the production version of non-symbolic numerosity estimation to bounded and unbounded number line estimation. This approach seems promising to evaluate whether unbounded number line estimation is more similar to non-symbolic estimation and thus reflects a purer measure of magnitude representation. In the following, we will first discuss the results with respect to unbounded number line estimation as a measure of number magnitude representation before elaborating on the broader implications of these findings for the bi-directional mapping hypothesis. Taken together, to the best of our knowledge, the present study is the first to systematically assess different types of estimation tasks (i.e., numerosity, as well as bounded and unbounded number line estimation) in both their perception and production version in adults to evaluate similarities and differences between these tasks. We replicated the pattern of systematic biases of under- and overestimation for numerosity estimation and also found that this pattern generalized to unbounded but not bounded number line estimation. Therefore, our results indicated conceptual similarity of unbounded number line and non-symbolic numerosity estimation. As such, these findings provide converging evidence from results of an established magnitude estimation task that unbounded number line estimation might be a purer and more valid measure of (spatial) number magnitude representation as compared to bounded number line estimation.   Source: http://doi.org/10.1371/journal.pone.0213102

 

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