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. 2017 Apr 4;7:630. doi: 10.1038/s41598-017-00680-0

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© The Author(s) 2017

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Experimental Design. (A) On a given trial, participants were presented with a word (“durée”, “nombre” or “surface”) indicating the dimension to estimate. In Experiment 1, one magnitude dimension could vary +/− 25%, 10%, and 5% of its mean value, while the second one was set to its minimal or maximal value, and the third one to its mean value (Table 1). At the end of the stimulus presentation, participants used a vertical scale to estimate the target magnitude. (B) Three distributions were used for evidence accumulation: while D linearly accumulates over time (black trace), the rate of dot presentation could be manipulated to control N and S. Experiment 1 tested a linear distribution (filled black trace); Experiment 2 tested two distributions: a fast-slow (filled grey trace) and a slow-fast (dotted grey trace) distribution. The different stimulus distributions can be experienced with the videos Linear, FastSlow and SlowFast in Supp. Material. (C) Equated task difficulty across magnitudes. For illustration purposes, the psychometric curve captures the grand average performance obtained for the estimation of Duration, Number and Surface when all non-target dimensions were kept at their mean value. The task difficulty was equated across magnitude dimensions so that no differences in discriminability (PSE and WR) existed between the tested dimensions. Bars are 2 s.e.m. (D) Predictions for the effect of non-target manipulations on the estimation of the target magnitude dimension. Left panel: varying the target magnitude while keeping the non-target dimensions to their mean values provided the control central tendency and intercept. In a common Bayesian magnitude estimation system [4], comparable tendency and intercept should be predicted pending controlled matching between magnitudes and task difficulty (panel C). Right panel: estimation of D while N is set to its maximal value (in green, Nmax). Maximal value in non-target magnitude may affect the central tendency and the intercept if an amodal global prior common to D and N is implicated in the estimation of duration. In this example, N_max would bias the lowest (highest) duration values towards larger (smaller) values and lead the intercept to move upwards.