Nonparametric tests for equality of psychometric functions

Area of Science:

• Psychology
• Statistics
• Psychophysics

Background:

• Psychometric functions are crucial for understanding how performance changes with stimulus magnitude.
• Current parametric methods for analyzing these functions have limitations and may yield misleading results.
• There is a need for robust, assumption-free methods to compare psychometric functions across conditions.

Purpose of the Study:

• To compare the statistical properties of three nonparametric tests for assessing psychometric function equality.
• To introduce a generalization of the Berry-Mielke test and a split variant of the generalized Mantel-Haenszel test.
• To provide practical recommendations for analyzing psychometric data using these nonparametric approaches.

Main Methods:

• Comparison of three nonparametric tests: generalized Mantel-Haenszel, generalized Berry-Mielke, and split generalized Mantel-Haenszel.
• Statistical properties (accuracy and power) were evaluated using simulation studies.
• Empirical validation through the analysis of published datasets.

Main Results:

• All three nonparametric tests demonstrated comparable accuracy in assessing psychometric function equality.
• The tests showed non-uniform differences in statistical power.
• The study provides practical guidance and available computational code for implementing these tests.

Conclusions:

• Nonparametric tests offer a reliable alternative to parametric methods for analyzing psychometric functions.
• The generalized Berry-Mielke and split generalized Mantel-Haenszel tests are valuable additions to the analytical toolkit.
• These methods enhance the ability to accurately assess experimental condition effects on observer performance.