## Abstract

A classical result indicates that the arithmetic average of p-values multiplied by the factor of 2 is a valid p-value under arbitrary dependence among p-values. Moreover, this constant factor cannot be improved in general without additional assumptions. Given this classical result, we study the average of p-values under exchangeability, which is a natural generalization of the i.i.d. assumption. Somewhat surprisingly, we prove that exchangeability is not enough to improve the constant factor of 2. This negative result motivates us to explore other conditions under which it is possible to obtain a smaller constant factor. Finally, we discuss certain benefits of the average of p-values over the average of statistics in terms of statistical power and provide empirical results that verify our theoretical findings.

Original language | English |
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Article number | 109748 |

Journal | Statistics and Probability Letters |

Volume | 194 |

DOIs | |

Publication status | Published - 2023 Mar |

### Bibliographical note

Funding Information:This work was supported by the Yonsei University Research Fund of 2022-22-0289 as well as the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( 2022R1A4A1033384 ). We thank the anonymous reviewers for their helpful comments and suggestions. We acknowledge that the specific construction of exchangeable -values used in the proof of Theorem 2.1 was suggested by one of the anonymous reviewers. IK is grateful to Richard J. Samworth and Rajen Shah for their helpful discussion that stimulated several results in this paper.

Publisher Copyright:

© 2022 Elsevier B.V.

## All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Statistics, Probability and Uncertainty