Fechnerian metrics in unidimensional and multidimensional stimulus spaces

Area of Science:

• Psychology
• Psychophysics
• Sensory Perception

Background:

• Subjective distances in stimulus spaces are crucial for understanding perception.
• Fechner's original theory proposed a framework for quantifying these subjective distances.
• Previous models faced challenges in arbitrary dimensional spaces and resolving specific controversies.

Purpose of the Study:

• To propose a new theory for subjective (Fechnerian) distances in continuous stimulus spaces.
• To develop a method for calculating these distances that is invariant to response bias.
• To resolve controversies regarding just-noticeable differences in sensory perception.

Main Methods:

• Associating each stimulus with a psychometric function.
• Computing a measure of discriminability from the psychometric function's local shape.
• Integrating discriminability along paths to define psychometric length.
• Defining Fechnerian distance as the infimum of psychometric lengths between stimuli.

Main Results:

• The proposed Fechnerian distances are invariant under changes in response bias for many models.
• A systematic construction of the Fechnerian metric resolves controversies about just-noticeable differences.
• The theory closely approximates Fechner's original intent for unidimensional continua.

Conclusions:

• The new theory provides a robust framework for subjective distance measurement in multidimensional stimulus spaces.
• It offers a unified approach to understanding discriminability and response bias.
• The findings contribute to a deeper understanding of sensory perception and psychophysical scaling.