Mapping numerical magnitudes along the right lines: differentiating between scale and bias

Area of Science:

• Cognitive psychology
• Psychophysics
• Numerical cognition

Background:

• Previous studies assumed subjective scale type directly from stimulus-response mapping.
• This assumption is flawed due to potential nonlinear mapping and response biases.

Purpose of the Study:

• To develop a method differentiating linear and logarithmic hypotheses robust to distorting processes.
• To investigate how participants represent numerical magnitudes in line-marking and line-construction tasks.

Main Methods:

• Developed a novel method based on transformational rules and closure properties of subjective scales.
• Implemented the method using variants of the number line task: line-marking and line-construction.
• Analyzed data using numerical and analytical approaches to evaluate linear and logarithmic components.

Main Results:

• Results support a linear hypothesis for subjective numerical scales.
• Observed a consistent bias: overestimation of small magnitudes and underestimation of large magnitudes.
• Task-specific biases were noted: overestimation with increasing interval start in line-marking, and overconstruction with increasing interval length in line-construction.

Conclusions:

• The developed method effectively differentiates scale types despite response biases.
• Numerical magnitudes appear to be encoded differently across tasks: absolute values in line-marking and numerical differences in line-construction.