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The aggregation paradox for statistical rankings and nonparametric tests
Haikady N Nagaraja1, Shane Sanders2
1The Ohio State University, Division of Biostatistics, College of Public Health, Columbus, OH, United States of America.
Plos One
|March 13, 2020
Summary
This study proves that aggregating multiple datasets strengthens non-parametric sign test consistency, enhancing statistical robustness. This aggregation method avoids paradoxes, reinforcing overall data analysis reliability.
Area of Science:
- Statistics
- Social Choice Theory
- Data Aggregation
Background:
- The relationship between social choice aggregation and non-parametric tests is known.
- A key question is whether non-parametric tests can consistently aggregate data without paradoxes.
Purpose of the Study:
- To determine if a non-parametric test exists that is consistent upon data aggregation.
- To investigate the robustness and potential paradoxes in aggregating non-parametric test results.
Main Methods:
- Utilizing the cumulative distribution function (CDF) of the binomial(n, p = 0.5) random variable.
- Proving sign test consistency through the aggregation of multiple, qualitatively-equivalent datasets.
- Examining a generalized form of aggregation for broader applicability.
Main Results:
- Aggregation of multiple sign tests for matched pairs reinforces constituent results, demonstrating sign test consistency.
- The magnitude of sign test consistency strengthens with the significance level of constituent results (strong-form consistency).
- Preliminary evidence suggests sign test consistency is preserved under generalized aggregation.
Conclusions:
- Data aggregation can enhance the consistency and robustness of non-parametric sign tests.
- The findings offer a method to mitigate aggregation paradoxes in statistical analysis.
- This research links statistical consistency with information aggregation mechanisms.
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