Abstract
The left digit effect in number line estimation refers to the phenomenon where numerals with similar magnitudes but different leftmost digits (e.g., 19 and 22) are estimated to be farther apart on a number line than is warranted. The effect has been studied using a bounded number line task, a task in which a line is bounded by two endpoints (e.g., 0 and 100), and where one must indicate the correct location of a target numeral on the line. The goal of the present work is to investigate the left digit effect in an unbounded number line task, a task that involves using the size of one unit to determine a target numeral’s location, and that elicits strategies different from those used in the bounded number line task. In a preregistered study, participants (N = 58 college students) completed four blocks of 38 trials each of an unbounded number line task, with target numerals ranging between 0 and 100. We found a medium and statistically reliable left digit effect (d = 0.70). The study offers further evidence that the effect is not driven by response strategies specific to the bounded number line task. We discuss other possible sources of the effect including conversion of symbols to magnitudes in these and other contexts.
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Notes
The strategy used to perform the task is also often referred to as a subtraction-division strategy because either of these arithmetic skills can be used to place the target in relation to the two boundary values.
One might expect this bias to be negatively accelerating, especially based on some past work with children (e.g., Siegler & Opfer, 2003). However, this is not what is typically found for adults once task strategy is considered and experimental bias is reduced (e.g., Cohen & Blanc-Goldhammer, 2011; see Cohen & Ray, 2020, for discussion).
Put differently, this means estimating the length of 10 units, then estimating the length of 24 units, and then adding the second length to the end of the first length. It does not mean iterating by single units.
As in past work (e.g., Williams et al., 2022b), the boundary of ‘10’ was not used in left digit analyses, in case single-digit target numerals (numerals below the boundary) are evaluated differently than two-digit ones.
Using the formula of Cohen and Ray (2020), we calculated that a canvas of the size we used (5,011 × 2,771 px) with a starting point at 327 px, unit lines 4 px wide, and a unit width of a maximum of 14 px, could accommodate a 0–108 number line task (i.e., larger than the 0–100 line used here), assuming accelerating bias of β = 1.2.
In this example, as with some proposed models, it is the underweighting of the rightward digit that leads to the relative overweighting of the leftmost digit (rather than a direct overweighting of the leftmost digit).
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Acknowledgements
We thank Wesleyan Reasoning and Decision Making Lab researchers Gina Gwiazda, Anjali Prabhu, and Gillian Weeks for their assistance
KK is now in the Department of Psychology, Ohio University, Athens, OH.
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This work was supported by NSF DRL-1920445 and benefited from NSF DRL-1561214, both to HB and ALP.
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Kayton, K., Fischer, G., Barth, H. et al. The left digit effect in an unbounded number line task. Psychon Bull Rev (2024). https://doi.org/10.3758/s13423-024-02486-4
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DOI: https://doi.org/10.3758/s13423-024-02486-4