The p-value interpreted as the posterior probability of explaining the data: Applications to multiple testing and to restricted parameter spaces

David R. Bickel ()
Additional contact information
David R. Bickel: University of North Carolina at Greensboro, The Graduate School

Sankhya A: The Indian Journal of Statistics, 2024, vol. 86, issue 1, No 14, 464-493

Abstract: Abstract Failures to replicate the results of scientific studies are often attributed to misinterpretations of the p-value. The p-value may be interpreted as an approximate posterior probability, not that the null hypothesis is true but rather that it explains the data as well as the data-generating distribution. That posterior probability modifies the p-value in the following two broad areas of application, leading to new methods of hypothesis testing and effect size estimation. First, when corrected for multiple comparisons, the posterior probability that the null hypothesis adequately explains the data overcomes both the conservative bias of corrected p-values and the anti-conservative bias of commonly used false discovery rate methods. Second, the posterior probability that the null hypothesis adequately explains the data, conditional on a parameter restriction, transforms the p-value in such a way as to overcome difficulties in restricted parameter spaces.

Keywords: Approximate confidence distribution; Multiple comparison procedures; Multiple testing; Null hypothesis significance testing; Restricted parameter space; Replication crisis; Reproducibility crisis; Primary 62A01; Secondary 62F03 (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s13171-023-00328-4 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sankha:v:86:y:2024:i:1:d:10.1007_s13171-023-00328-4

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/13171

DOI: 10.1007/s13171-023-00328-4

Access Statistics for this article

Sankhya A: The Indian Journal of Statistics is currently edited by Dipak Dey

More articles in Sankhya A: The Indian Journal of Statistics from Springer, Indian Statistical Institute
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().