Understanding decimal proportions: Discrete representations, parallel access, and privileged processing of zero

Varma, Sashank; Karl, Stacy R.

doi:10.1016/j.cogpsych.2013.01.002

Cited by 44 publications

(113 citation statements)

References 43 publications

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“…In general, this conclusion is consistent with the studies of Cohen (2010) and Varma and Karl (2013), demonstrating the uniqueness of decimal representation. Our findings challenge the conversion hypothesis which purports that people convert decimals to natural number expressions by ignoring decimal points and compare the corresponding natural number referents.…”

Section: The Processing Of Two-digit Mixed Decimalssupporting

confidence: 90%

“…In contrast, for integers, the less relevant unit digits came to produce a Stroop-like interference to the more relevant decade digits. Similarly, in the study by Varma and Karl (2013), although decimals produced a positive compatibility effect, the effect was less obvious than in integers. That is, decimals showed less interference than integers.…”

Section: Discussionmentioning

confidence: 66%

“…Integers and pure decimals are visually very similar. It has been found that when understanding a decimal (e.g., 0.32), both the correct referent (e.g., 0.32) and the incorrect natural number referent (e.g., 32) corresponding to the visually similar natural number expression are accessed in parallel (Varma & Karl, 2013). Therefore, it is unclear whether the findings in Experiment 1 can be extended to two-digit pure decimals.…”

Section: Methodsmentioning

confidence: 85%

“…Although "32", "0.32", and "3.2" are visually very similar, they indicate entirely different numerical magnitudes. To our knowledge, only two previous studies have investigated the processing of decimals (Cohen, 2010;Varma & Karl, 2013). Cohen (2010) compared the processing of two-digit integers and decimals between 0 and 1 in numerical comparison tasks.…”

Section: Introductionmentioning

confidence: 99%

“…It was concluded that the processing of decimals is different from that of integers. Varma and Karl (2013) revealed that decimals between 0 and 1 produced the tenths-hundredths compatibility effect and their tenth and hundredth components are processed in parallel when comparing two decimals.…”

Section: Introductionmentioning

confidence: 99%

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Flexible and unique representations of two-digit decimals

Zhang¹,

Chen²,

Lin³

et al. 2014

Acta Psychologica

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We examined the representation of two-digit decimals through studying distance and compatibility effects in magnitude comparison tasks in four experiments. Using number pairs with different leftmost digits, we found both the second digit distance effect and compatibility effect with two-digit integers but only the second digit distance effect with two-digit pure decimals. This suggests that both integers and pure decimals are processed in a compositional manner. In contrast, neither the second digit distance effect nor the compatibility effect was observed in two-digit mixed decimals, thereby showing no evidence for compositional processing of two-digit mixed decimals. However, when the relevance of the rightmost digit processing was increased by adding some decimals pairs with the same leftmost digits, both pure and mixed decimals produced the compatibility effect. Overall, results suggest that the processing of decimals is flexible and depends on the relevance of unique digit positions. This processing mode is different from integer analysis in that two-digit mixed decimals demonstrate parallel compositional processing only when the rightmost digit is relevant. Findings suggest that people probably do not represent decimals by simply ignoring the decimal point and converting them to natural numbers.

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Section: The Processing Of Two-digit Mixed Decimalssupporting

confidence: 90%

Section: Discussionmentioning

confidence: 66%

Section: Methodsmentioning

confidence: 85%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Flexible and unique representations of two-digit decimals

Zhang¹,

Chen²,

Lin³

et al. 2014

Acta Psychologica

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Evaluating the effect of delay spacing on delay discounting: carry‐over effects on steepness and the form of the discounting function

Rung

Frye

DeHart

et al. 2019

J Exper Analysis Behavior

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Most delay discounting studies use tasks that arrange delay progressions in which the spacing between consecutive delays becomes progressively larger. To date, little research has examined delay discounting using other progressions. The present study assessed whether the form or steepness of discounting varied across different delay progressions. Human participants completed three discounting tasks with delay progressions that varied in the time between consecutive delays: a standard (increasing duration between delays), linear (equal duration between delays), and an inverse progression (decreasing duration between delays). Steepness of discounting was generally reduced, and remained so, following experience with the inverse progression. Effects of the delay progression on the best fitting equation were order-dependent. Overall the hyperbola model provided better fits, but the exponential model performed better with data from the inverse progression. Regardless, differences in which model fit best were often small. The finding that the best fitting model was dependent, in some cases, on the delay progression suggests that a single quantitative model of discounting may not be applicable to describe discounting across all procedural contexts. Ultimately, changes in steepness of discounting following experience with the inverse progression appeared similar to anchoring effects, whose mechanism will require further study to delineate.

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