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.

翻译：偏相关系数在社会科学中被广泛应用，用于评估在控制其他变量影响后两个变量之间的关系。本文提出用于评估偏相关系数存在性的贝叶斯因子函数。BFFs 是基于检验统计量推导出的贝叶斯因子，并表示为标准化效应量的函数。虽然基于 $p$ 值的传统频率学派方法因无法提供支持真实假设的累积证据而受到批评，但贝叶斯方法常因其计算需求和对先验分布的敏感性而面临挑战。BFFs 克服了这些限制，当备择假设在标准化效应的一系列先验分布上变化时，能够提供假设检验的概括性结果。它们还支持跨多个研究的证据整合。