Converting between measures of slope of the psychometric function

Area of Science:

• Psychology
• Psychophysics
• Statistics

Background:

• The slope of the psychometric function is crucial for assessing the reliability of psychophysical threshold estimates.
• Comparing thresholds across studies with varying performance criteria is challenging due to diverse slope measures.
• Lack of standardized slope measures hinders empirical validation and cross-study comparisons.

Purpose of the Study:

• To provide conversion formulas for commonly used psychometric function slope measures.
• To facilitate the comparison of psychophysical thresholds obtained under different experimental conditions.
• To standardize the reporting and interpretation of psychometric function slope estimates.

Main Methods:

• Derivation of conversion formulas for analytic functions (logistic, Weibull, Quick, cumulative normal, hyperbolic tangent).
• Formulas provided for both linear and log coordinates, and various log bases.
• Inclusion of conversion formulas for practical units like decibels and empirical measures like interquartile range and d'.

Main Results:

• A comprehensive set of conversion formulas is presented for popular psychometric function representations.
• The formulas enable transformation between different slope units and coordinate systems.
• Standardized methods are provided for slope measures in linear, log, decibel, interquartile range, and d' units.

Conclusions:

• The provided conversion formulas address the heterogeneity of psychometric function slope measures.
• Standardization through these formulas will enhance the reliability and comparability of psychophysical threshold research.
• This work facilitates more robust meta-analyses and a deeper understanding of perceptual sensitivity.