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Combining exchangeable P-values
Matteo Gasparin1, Ruodu Wang2, Aaditya Ramdas3
1Department of Statistical Sciences, University of Padova, Padova 35121, Italy.
Summary
Combining P-values, especially when dependent, is improved using exchangeability or randomization. New methods enhance existing rules for P-value combination, offering better statistical power.
Area of Science:
- Statistical inference
- Hypothesis testing
Background:
- Combining P-values is crucial in statistical analysis.
- Independence assumption is often violated in real-world applications.
Purpose of the Study:
- To develop improved methods for combining dependent P-values.
- To enhance existing P-value combination rules.
Main Methods:
- Utilizing exchangeability and external randomization for P-value combination.
- Deriving randomized and exchangeable improvements of established rules (e.g., median, average, geometric, harmonic means).
- Calibrating P-values to e-values, averaging e-values, and applying Markov's inequality variants.
Main Results:
- Demonstrated strict improvements over existing P-value combination rules under exchangeability or randomization.
- Developed sequential combination methods for P-values produced over time.
- Showed that arbitrary dependent P-values become exchangeable when randomly ordered.
Conclusions:
- Exchangeability and randomization offer significant improvements for P-value combination.
- New methods provide enhanced statistical power and flexibility in hypothesis testing.
- The findings advance the field of meta-analysis and combining evidence from multiple studies.
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