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Partial correlation coefficients are widely applied in the social sciences to evaluate the relationship between two variables after accounting for the influence of others. In this article, we present Bayes Factor Functions (BFFs) for assessing the presence of partial correlation. BFFs represent Bayes factors derived from test statistics and are expressed as functions of a standardized effect size. While traditional frequentist methods based on p-values have been criticized for their inability to provide cumulative evidence in favor of the true hypothesis, Bayesian approaches are often challenged due to their computational demands and sensitivity to prior distributions. BFFs overcome these limitations and offer summaries of hypothesis tests as alternative hypotheses are varied over a range of prior distributions on standardized effects. They also enable the integration of evidence across multiple studies.
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This content will become publicly available on June 20, 2026
On Bayes factor functions
We describe Bayes factors functions based on the sampling distributions of z, t, χ2, and F statistics, using a class of inverse-moment prior distributions to define alternative hypotheses. These non-local alternative prior distributions are centered on standardized effects, which serve as indices for the Bayes factor function. We compare the conclusions drawn from resulting Bayes factor functions to those drawn from Bayes factors defined using local alternative prior specifications and examine their frequentist operating characteristics. Finally, an application of Bayes factor functions for replicated experimental designs in psychology are provided.
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- Award ID(s):
- 2311005
- PAR ID:
- 10609508
- Publisher / Repository:
- arXiv: arXiv:2506.16674
- Date Published:
- Subject(s) / Keyword(s):
- Bayes factor based on test statistic, Meta-analysis, Non-local prior density, Inverse moment prior density
- Format(s):
- Medium: X
- Institution:
- Texas A&M University
- Sponsoring Org:
- National Science Foundation
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