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Bayesian t tests for accepting and rejecting the null hypothesis

  • Theoretical and Review Articles
  • Published: April 2009
  • Volume 16, pages 225–237, (2009)
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Bayesian t tests for accepting and rejecting the null hypothesis
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  • Jeffrey N. Rouder1,
  • Paul L. Speckman1,
  • Dongchu Sun1,
  • Richard D. Morey1 &
  • …
  • Geoffrey Iverson2 
  • 23k Accesses

  • 2676 Citations

  • 23 Altmetric

  • 2 Mentions

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Abstract

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.

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Authors and Affiliations

  1. Department of Psychological Sciences, University of Missouri, 210 McAlester Hall, 65211, Columbia, MO

    Jeffrey N. Rouder, Paul L. Speckman, Dongchu Sun & Richard D. Morey

  2. University of California, Irvine, California

    Geoffrey Iverson

Authors
  1. Jeffrey N. Rouder
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  2. Paul L. Speckman
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  3. Dongchu Sun
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  4. Richard D. Morey
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  5. Geoffrey Iverson
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Corresponding author

Correspondence to Jeffrey N. Rouder.

Additional information

This research was supported by NSF Grant SES-0720229 and NIMH Grant R01-MH071418.

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Cite this article

Rouder, J.N., Speckman, P.L., Sun, D. et al. Bayesian t tests for accepting and rejecting the null hypothesis. Psychonomic Bulletin & Review 16, 225–237 (2009). https://doi.org/10.3758/PBR.16.2.225

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  • Received: 04 June 2008

  • Accepted: 27 August 2008

  • Issue Date: April 2009

  • DOI: https://doi.org/10.3758/PBR.16.2.225

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Keywords

  • Akaike Information Criterion
  • Marginal Likelihood
  • Posterior Odds
  • Subliminal Priming
  • Prior Standard Deviation
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