Using Bayes to get the most out of non-significant results
- PMID: 25120503
- PMCID: PMC4114196
- DOI: 10.3389/fpsyg.2014.00781
Using Bayes to get the most out of non-significant results
Abstract
No scientific conclusion follows automatically from a statistically non-significant result, yet people routinely use non-significant results to guide conclusions about the status of theories (or the effectiveness of practices). To know whether a non-significant result counts against a theory, or if it just indicates data insensitivity, researchers must use one of: power, intervals (such as confidence or credibility intervals), or else an indicator of the relative evidence for one theory over another, such as a Bayes factor. I argue Bayes factors allow theory to be linked to data in a way that overcomes the weaknesses of the other approaches. Specifically, Bayes factors use the data themselves to determine their sensitivity in distinguishing theories (unlike power), and they make use of those aspects of a theory's predictions that are often easiest to specify (unlike power and intervals, which require specifying the minimal interesting value in order to address theory). Bayes factors provide a coherent approach to determining whether non-significant results support a null hypothesis over a theory, or whether the data are just insensitive. They allow accepting and rejecting the null hypothesis to be put on an equal footing. Concrete examples are provided to indicate the range of application of a simple online Bayes calculator, which reveal both the strengths and weaknesses of Bayes factors.
Keywords: Bayes factor; confidence interval; highest density region; null hypothesis; power; significance testing; statistical inference.
Figures
![FIGURE 1](https://cdn.statically.io/img/www.ncbi.nlm.nih.gov/pmc/articles/instance/4114196/bin/fpsyg-05-00781-g001.gif)
![FIGURE 2](https://cdn.statically.io/img/www.ncbi.nlm.nih.gov/pmc/articles/instance/4114196/bin/fpsyg-05-00781-g002.gif)
![FIGURE 3](https://cdn.statically.io/img/www.ncbi.nlm.nih.gov/pmc/articles/instance/4114196/bin/fpsyg-05-00781-g003.gif)
Similar articles
-
Inappropriate use of statistical power.Bone Marrow Transplant. 2023 May;58(5):474-477. doi: 10.1038/s41409-023-01935-3. Epub 2023 Mar 3. Bone Marrow Transplant. 2023. PMID: 36869191
-
Empirical Bayes interval estimates that are conditionally equal to unadjusted confidence intervals or to default prior credibility intervals.Stat Appl Genet Mol Biol. 2012 Feb 21;11(3):Article 7. doi: 10.1515/1544-6115.1765. Stat Appl Genet Mol Biol. 2012. PMID: 22499708
-
P value and the theory of hypothesis testing: an explanation for new researchers.Clin Orthop Relat Res. 2010 Mar;468(3):885-92. doi: 10.1007/s11999-009-1164-4. Clin Orthop Relat Res. 2010. PMID: 19921345 Free PMC article.
-
Reverse-Bayes methods for evidence assessment and research synthesis.Res Synth Methods. 2022 May;13(3):295-314. doi: 10.1002/jrsm.1538. Epub 2021 Dec 30. Res Synth Methods. 2022. PMID: 34889058 Free PMC article. Review.
-
A Bayesian analysis of non-significant rehabilitation findings: Evaluating the evidence in favour of truly absent treatment effects.Ann Phys Rehabil Med. 2021 Jul;64(4):101425. doi: 10.1016/j.rehab.2020.07.008. Epub 2020 Oct 6. Ann Phys Rehabil Med. 2021. PMID: 32805456 Review.
Cited by
-
Cognitive control training with domain-general response inhibition does not change children's brains or behavior.Nat Neurosci. 2024 Jul;27(7):1364-1375. doi: 10.1038/s41593-024-01672-w. Epub 2024 Jun 4. Nat Neurosci. 2024. PMID: 38834704 Free PMC article. Clinical Trial.
-
Tactile memory impairments in younger and older adults.Sci Rep. 2024 May 23;14(1):11766. doi: 10.1038/s41598-024-62683-y. Sci Rep. 2024. PMID: 38783038 Free PMC article.
-
Slower Learning Rates from Negative Outcomes in Substance Use Disorder over a 1-Year Period and Their Potential Predictive Utility.Comput Psychiatr. 2022 Jun 8;6(1):117-141. doi: 10.5334/cpsy.85. eCollection 2022. Comput Psychiatr. 2022. PMID: 38774781 Free PMC article.
-
Replication of null results: Absence of evidence or evidence of absence?Elife. 2024 May 13;12:RP92311. doi: 10.7554/eLife.92311. Elife. 2024. PMID: 38739437 Free PMC article.
-
Baseline Pupil Size Seems Unrelated to Fluid Intelligence, Working Memory Capacity, and Attentional Control.J Cogn. 2024 May 10;7(1):41. doi: 10.5334/joc.365. eCollection 2024. J Cogn. 2024. PMID: 38737819 Free PMC article.
References
-
- American Psychological Association [APA] (2010). Publication Manual of the American Psychological Association 5th Edn. Washington, DC: AP.
-
- Armitage P., McPherson C. K., Rowe B. C. (1969). Repeated significance tests on accumulating data. J. R. Stat. Soc. Ser. A 132 235–244 10.2307/2343787 - DOI
LinkOut - more resources
Full Text Sources
Other Literature Sources