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02-08-2018 | Original Article

On the linear representation of numbers: evidence from a new two-numbers-to-two positions task

Auteurs: Hofit Bar, Martin H. Fischer, Daniel Algom

Gepubliceerd in: Psychological Research | Uitgave 1/2019

Abstract

In the number-to-position methodology, a number is presented on each trial and the observer places it on a straight line in a position that corresponds to its felt subjective magnitude. In the novel modification introduced in this study, the two-numbers-to-two-positions method, a pair of numbers rather than a single number is presented on each trial and the observer places them in appropriate positions on the same line. Responses in this method indicate not only the subjective magnitude of each single number but, simultaneously, provide a direct estimation of their subjective numerical distance. The results of four experiments provide strong evidence for a linear representation of numbers and, commensurately, for the linear representation of numerical distances. We attribute earlier results that indicate a logarithmic representation to the ordered nature of numbers and to the task used and not to a truly non-linear underlying representation.

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In order to control for confounds, an inclusive ANOVA was performed, including gender (male, female) and hand (left, right) as between-subjects variables, in addition to the main reported variables. For both number and distance estimation, the ANOVA did not yield main effects or interactions for gender and hand (p > 0.05). A similar analysis with respect to RT did not yield effects.

We did not record any systematic differences between our German and Israeli participants.

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Titel: On the linear representation of numbers: evidence from a new two-numbers-to-two positions task
Auteurs: Hofit Bar
Martin H. Fischer
Daniel Algom
Publicatiedatum: 02-08-2018
Uitgeverij: Springer Berlin Heidelberg
Gepubliceerd in: Psychological Research / Uitgave 1/2019
Print ISSN: 0340-0727
Elektronisch ISSN: 1430-2772
DOI: https://doi.org/10.1007/s00426-018-1063-y

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