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The Sign Test, Paired Data, and Asymmetric Dependence: A Cautionary Tale
1Roswell Park Comprehensive Cancer Center, Department of Biostatistics and Bioinformatics, Elm and Carlton Streets, Buffalo, NY 14623.
The American Statistician
|June 19, 2023
Summary
The sign test may misinterpret paired data when distributions are asymmetric. This study shows the median of differences can differ from the difference of medians, leading to incorrect conclusions in statistical analysis.
Area of Science:
- Statistics
- Biostatistics
- Data Analysis
Background:
- The sign test is commonly used in textbooks for comparing medians of paired data.
- It relies on the assumption that the median of differences equals the difference of medians.
Purpose of the Study:
- To investigate the validity of the sign test assumption in paired data analysis.
- To demonstrate scenarios where the median of differences deviates from the difference of medians.
Main Methods:
- Theoretical analysis of bivariate distributions.
- Simulation studies to assess test performance.
- Application to real-world breast cancer RNA sequencing data (TCGA).
Main Results:
- Asymmetry in bivariate distributions can cause the median of differences to not equal the difference of medians.
- This inequality leads to a misinterpretation of the sign test's results.
- The findings were validated through simulations and a TCGA dataset.
Conclusions:
- The sign test's application to paired data requires careful consideration of distributional symmetry.
- Textbook assumptions may not hold, potentially leading to erroneous statistical inferences.
- Researchers should be aware of this limitation when analyzing asymmetric paired data.
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