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Number placement on scales is influenced by range and frequency. Both factors cause compression, but not as much as logarithmic scaling predicts.

Keywords:
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Area of Science:

  • Cognitive Psychology
  • Psychophysics
  • Numerical Cognition

Background:

  • Human number representation often exhibits non-linear scaling on number lines.
  • Parducci's range-frequency theory posits that number placement is affected by the range and distribution of presented stimuli.

Purpose of the Study:

  • To investigate the influence of numerical range and distribution on number line placement.
  • To test the predictions of range-frequency theory in number scaling tasks.

Main Methods:

  • Experiment 1: Participants placed numbers on a line with extreme endpoints (1 to 10^16).
  • Experiment 2: Participants placed logarithmically vs. linearly distributed numbers on a 1-1,000 scale.

Main Results:

  • Significant compressive scaling observed with a wide numerical range (Experiment 1).
  • Logarithmically distributed numbers induced compression, while linearly distributed numbers approximated linear scaling (Experiment 2).
  • Compression effects were present but less pronounced than predicted by pure logarithmic scaling.

Conclusions:

  • Both the range and frequency of numbers significantly impact their perceived scaling on number lines.
  • The observed compression is not adequately explained by participants switching between linear and logarithmic representations.