Permuting Incomplete Paired Data: A Novel Exact and Asymptotic Correct Randomization Test

TL;DR

This paper introduces a new randomization test for matched pairs with missing data that is robust to distributional deviations and heteroscedasticity, providing both exact and asymptotic validity.

Contribution

It develops a novel randomization approach for incomplete paired data that is robust and valid under minimal assumptions, improving upon existing methods.

Findings

The test is asymptotically correct and finitely exact under certain conditions.

Simulation studies show superior small sample performance compared to existing methods.

An illustrative example demonstrates practical applicability.

Abstract

Various statistical tests have been developed for testing the equality of means in matched pairs with missing values. However, most existing methods are commonly based on certain distributional assumptions such as normality, 0-symmetry or homoscedasticity of the data. The aim of this paper is to develop a statistical test that is robust against deviations from such assumptions and also leads to valid inference in case of heteroscedasticity or skewed distributions. This is achieved by applying a novel randomization approach. The resulting test procedure is not only shown to be asymptotically correct but is also finitely exact if the distribution of the data is invariant with respect to the considered randomization group. Its small sample performance is further studied in an extensive simulation study and compared to existing methods. Finally, an illustrative data example is analyzed.