Nonparametric equivalence testing with respect to the median difference

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.