Bayes factor functions for testing partial correlation coefficients

Partial correlations are widely used in psychology and related fields to evaluate the relationship between two variables while controlling for others. In this article, we extend Bayes Factor Functions (BFFs; Johnson, Pramanik, & Shudde) to the assessment of partial correlation. BFFs provide Bayes factors derived from test statistics and expressed as functions of standardized effect sizes. Unlike p-values, which have been criticized for failing to accumulate evidence for the true hypothesis, and unlike conventional Bayesian methods, which can be computationally demanding and sensitive to prior specification, BFFs offer a practical objective alternative. They summarize evidence across a range of prior distributions on standardized effects and allow researchers to integrate results across studies. We further emphasize that the proposed test for partial correlations differs from conventional (t/F) tests, since the distribution of the test statistic under the alternative hypothesis follows a nonstandard form. We demonstrate how BFFs can be applied to partial correlation testing to provide interpretable and cumulative evidence in psychological research.