Bayesian t-tests for correlations and partial correlations

Min Wang, Fang Chen, Tao Lu, Jianping Dong

Research output: Contribution to journalArticlepeer-review


In this paper, we develop Bayes factor based testing procedures for the presence of a correlation or a partial correlation. The proposed Bayesian tests are obtained by restricting the class of the alternative hypotheses to maximize the probability of rejecting the null hypothesis when the Bayes factor is larger than a specified threshold. It turns out that they depend simply on the frequentist t-statistics with the associated critical values and can thus be easily calculated by using a spreadsheet in Excel and in fact by just adding one more step after one has performed the frequentist correlation tests. In addition, they are able to yield an identical decision with the frequentist paradigm, provided that the evidence threshold of the Bayesian tests is determined by the significance level of the frequentist paradigm. We illustrate the performance of the proposed procedures through simulated and real-data examples.

Original languageEnglish
Pages (from-to)1820-1832
Number of pages13
JournalJournal of Applied Statistics
Issue number10
StatePublished - Jul 26 2020


  • Bayes factor
  • Zellner's g-prior
  • restricted most powerful Bayesian tests
  • statistical evidence
  • t-test


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