Dissociation of the Distance Effect and Size Effect in One-Digit Numbers

By Verguts, Tom; Van Opstal, Filip | Psychonomic Bulletin & Review, October 2005 | Go to article overview

Dissociation of the Distance Effect and Size Effect in One-Digit Numbers


Verguts, Tom, Van Opstal, Filip, Psychonomic Bulletin & Review


Magnitude comparison of single digits is robustly characterized by a distance effect (close numbers are more difficult to compare than numbers further apart) and a size effect (for a given distance, comparison difficulty increases with increasing size). The distance effect indicates access to the mental number line (Dehaene, 1997), and the size effect is usually interpreted as indicating that the mental number line represents larger numbers more vaguely than smaller ones. In contrast, we have argued earlier (Verguts, Fias, & Stevens, 2005) that for symbolic numbers (Arabic or verbal notation), the size effect does not originate from the mental number line but, instead, originates from mappings to relevant output components that are specific for magnitude comparison. If the latter is true, it should be possible to dissociate the distance effect from the size effect in tasks other than magnitude comparison. In two experiments, we observed a robust distance effect in same/different judgments, which implies access to the mental number line. Yet the size effect was absent. Consistent with our prediction, this finding establishes a dissociation between the size effect and the distance effect.

Numbers in Arabic and verbal notations are highly abstract: They bear no relation to their magnitudes whatsoever. Yet comparing two such numbers is subject to a distance effect, meaning that it is more difficult to compare two numbers if they are close (e.g., 1 and 2) than if they are far apart (e.g., 1 and 8). This is obtained both when the numerical magnitude is relevant (e.g., Moyer & Landauer, 1967; Schwarz & Stein, 1998) and when it is irrelevant (Dehaene & Akhavein, 1995). A distance effect is also robustly obtained in priming tasks, in the sense that smaller prime-target distances lead to shorter response times (RTs; e.g., Reynvoet & Brysbaert, 1999). The distance effect suggests that a number's magnitude is accessed immediately and that the number is placed on a mental number line (Dehaene, 1997), after which further processing can proceed.

In addition to a distance effect, magnitude comparison (which number is smaller/larger?) is subject to a size effect: Comparison of two numbers is easier for small than for large numbers (e.g., 1 and 2 vs. 8 and 9). The latter finding has led some authors to posit that the number line represents large numbers more vaguely than small numbers, so that discriminating between larger numbers is more difficult. Different implementations of this general idea have been proposed (e.g., logarithmic compression, Dehaene, 1992; scalar variability, Gallistel & Gelman, 1992; see also recent discussions in Carey, 2001, and Dehaene, 2001). Arithmetical operations (e.g., addition or multiplication) typically also exhibit a size effect, but it is controversial whether this size effect has the same origin as that observed in number comparison (Dehaene, Piazza, Pinel, & Cohen, 2003; Gallistel & Gelman, 1992). In the following, we will therefore ignore size effects in arithmetic.

We (Verguts, Fias, & Stevens, 2005) have recently argued that, at least in the range of one-digit numbers, large numbers (e.g., 8 or 9) are represented as exactly (or as vaguely) as small numbers (e.g., 1 or 2). One argument was that with symbolic numbers'-that is, numbers in Arabic or verbal notation-the size effect appears in magnitude comparison, but not in number naming or parity judgment. A second argument was that, in masked priming studies with number naming and parity judgment (e.g., Reynvoet & Brysbaert, 1999; Reynvoet, Caessens, & Brysbaert, 2002), there is a distance effect between the prime and the target, but no size effect (of either the prime or the target). We argued that the size effect in magnitude comparison originates from mappings (connections) from the number line to the task-relevant output component.

To substantiate this, we trained a neural network on magnitude comparison, number naming, and parity judgment. …

The rest of this article is only available to active members of Questia

Already a member? Log in now.

Notes for this article

Add a new note
If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Default project is now your active project.
Project items

Items saved from this article

This article has been saved
Highlights (0)
Some of your highlights are legacy items.

Highlights saved before July 30, 2012 will not be displayed on their respective source pages.

You can easily re-create the highlights by opening the book page or article, selecting the text, and clicking “Highlight.”

Citations (0)
Some of your citations are legacy items.

Any citation created before July 30, 2012 will labeled as a “Cited page.” New citations will be saved as cited passages, pages or articles.

We also added the ability to view new citations from your projects or the book or article where you created them.

Notes (0)
Bookmarks (0)

You have no saved items from this article

Project items include:
  • Saved book/article
  • Highlights
  • Quotes/citations
  • Notes
  • Bookmarks
Notes
Cite this article

Cited article

Style
Citations are available only to our active members.
Buy instant access to cite pages or passages in MLA, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

Cited article

Dissociation of the Distance Effect and Size Effect in One-Digit Numbers
Settings

Settings

Typeface
Text size Smaller Larger Reset View mode
Search within

Search within this article

Look up

Look up a word

  • Dictionary
  • Thesaurus
Please submit a word or phrase above.
Print this page

Print this page

Why can't I print more than one page at a time?

Help
Full screen

matching results for page

    Questia reader help

    How to highlight and cite specific passages

    1. Click or tap the first word you want to select.
    2. Click or tap the last word you want to select, and you’ll see everything in between get selected.
    3. You’ll then get a menu of options like creating a highlight or a citation from that passage of text.

    OK, got it!

    Cited passage

    Style
    Citations are available only to our active members.
    Buy instant access to cite pages or passages in MLA, APA and Chicago citation styles.

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

    1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

    Cited passage

    Thanks for trying Questia!

    Please continue trying out our research tools, but please note, full functionality is available only to our active members.

    Your work will be lost once you leave this Web page.

    Buy instant access to save your work.

    Already a member? Log in now.

    Author Advanced search

    Oops!

    An unknown error has occurred. Please click the button below to reload the page. If the problem persists, please try again in a little while.