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A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

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Nonparametric equivalence testing with respect to the median difference.

¹Department of Medical Data Services, Boehringer Ingelheim Pharma GmbH & Co. KG, Ingelheim am Rhein, Germany. meieru@ing.boehringer-ingelheim.com

Pharmaceutical Statistics

|July 1, 2009

Summary

This study introduces a new nonparametric method for equivalence testing between two independent groups. The approach focuses on the median of the difference distribution, offering a flexible alternative to traditional methods.

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Area of Science:

Statistics
Nonparametric Statistics

Background:

Comparing independent groups is crucial in statistical analysis.
Traditional methods often assume specific distributional properties (e.g., shift models) or normality.
Existing nonparametric methods may lack flexibility for complex data distributions.

Purpose of the Study:

To develop a fully nonparametric equivalence testing procedure for two independent univariate data groups.
To avoid assumptions about the nature of distributional differences between groups.
To propose a method applicable to data with mixed continuous and discrete components.

Main Methods:

The procedure centers on the median of the independent difference distribution.
It employs an asymptotic equivalence test, symmetric for test and reference groups.
The method can be framed as a two-one-sided-tests (TOST) approach or a confidence interval inclusion rule.

Main Results:

An asymptotic equivalence test is provided for nonparametric settings.
The test is robust to various distributional differences, avoiding shift model assumptions.
A one-sided variant is suitable for non-inferiority testing.

Conclusions:

The proposed method offers a flexible and robust approach to nonparametric equivalence testing.
It extends to testing equivalence for quantiles beyond the median.
The procedure is closely linked to tolerance interval inference, enhancing its applicability.