Bayesian t tests for accepting and rejecting the null hypothesis

Psychon Bull Rev. 2009 Apr;16(2):225-37. doi: 10.3758/PBR.16.2.225.


Progress in science often comes from discovering invariances in relationships among variables; these invariances often correspond to null hypotheses. As is commonly known, it is not possible to state evidence for the null hypothesis in conventional significance testing. Here we highlight a Bayes factor alternative to the conventional t test that will allow researchers to express preference for either the null hypothesis or the alternative. The Bayes factor has a natural and straightforward interpretation, is based on reasonable assumptions, and has better properties than other methods of inference that have been advocated in the psychological literature. To facilitate use of the Bayes factor, we provide an easy-to-use, Web-based program that performs the necessary calculations.

Publication types

  • Research Support, N.I.H., Extramural
  • Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

  • Analysis of Variance*
  • Bayes Theorem*
  • Data Interpretation, Statistical*
  • Humans
  • Likelihood Functions
  • Mathematical Computing*
  • Probability
  • Psychology, Experimental / statistics & numerical data*
  • Software*