The DOI matches its Crossref record; 59 of the 60 references it cites were found in a registry or an index.
Bayesian Versus Orthodox Statistics: Which Side Are You On?
Open accessAbstract
Researchers are often confused about what can be inferred from significance tests. One problem occurs when people apply Bayesian intuitions to significance testing—two approaches that must be firmly separated. This article presents some common situations in which the approaches come to different conclusions; you can see where your intuitions initially lie. The situations include multiple testing, deciding when to stop running participants, and when a theory was thought of relative to finding out results. The interpretation of nonsignificant results has also been persistently problematic in a way that Bayesian inference can clarify. The Bayesian and orthodox approaches are placed in the context of different notions of rationality, and I accuse myself and others as having been irrational in the way we have been using statistics on a key notion of rationality. The reader is shown how to apply Bayesian inference in practice, using free online software, to allow more coherent inferences from data.
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“In terms of statistics, a Bayesian approach might be more appropriate than Fisherian statistics [56] as the Fisher approach is not appropriate with limited data [48].”
From Agile science: creating useful products for behavior change in the real world (2016) · cites this paper as [56]
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“Bayesian t-tests were also conducted, using the procedure recommended by Dienes (2011) and implemented as R code by Baguley and Kaye (2010).”
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“The error-statistical perspective employed in this article is that of Deborah Mayo, sometimes in collaboration with Aris Spanos (Mayo, 1996, 2018; Mayo & Spanos, 2010, 2011).”
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“…evidence for the experimental hypothesis; values around 1 indicate no substantial support either way and suggest insufficient sensitivity in the experimental design (Jeffreys, 1961; see Dienes, 2008b, 2011, for discussions on the relative merits and drawbacks of Bayesian and Orthodox statistics).”
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Eitam, B., Glass-Hackel, R., Aviezer, H., Dienes, Z. P., Shoval, R., & Higgins, E. T. (2014) · Journal of Experimental Psychology Human Perception & Performance · doi:10.1037/a0037627 · Cited by 15
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“As the frequentist approach to statistical hypothesis testing has recently received criticism (Dienes, 2011; Jarosz and Wiley, 2014), hypotheses were tested using both frequentist and Bayesian methods.”
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“Bayesian factors and posterior probabilities of our hypotheses in relation to the data [15].”
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“The Cauchy prior width was set to default prior of 0.707 and report BF 10 , which gives the ratio at which the alternative hypothesis is favored over the null hypothesis (Dienes, 2011; Hu et al., 2018), that is, a larger BF 10 argues in favor of the alternative hypothesis.”
InfluentialObedience to authority reduces cognitive conflict before an action
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“Data were analyzed with both frequentist and Bayesian statistics (Dienes, 2011).”
Kuehn, N. M., Campbell, K. W., & Bozorgnia, Y. (2025) · Bulletin of the Seismological Society of America · doi:10.1785/0120240115 · Cited by 14
Can prepared fear conditioning result from verbal instructions?
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Prototypes, exemplars and the response scaling parameter: A Bayes factor perspective
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“Thus, one of the main benefits of calculating the BF is that for non-significant group comparisons we can use the BF to conclude that the two groups indeed do not differ, and the acquired evidence supports H0 rather than H1 (Dienes, 2011, 2014; Wagenmakers, 2007).”
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“One is only able to conclude, after a single experiment, that the final decision was made by a standard procedure that controls error frequencies in the long run (Dienes, 2011).”
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“Not only are p-values more likely to produce significant findings when the null is true; they also are likely to produce nonsignificant results despite that there is a true effect [85].”
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“Data yielding Bayes factors between 1/3 and 3 can be considered equivocal (23).”
BackgroundMethodInfluentialHas speech and language therapy been shown not to work?
Leff, A. P., & Howard, D. (2012) · Nature Reviews Neurology · doi:10.1038/nrneurol.2012.211 · Cited by 13
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“We also conducted Bayesian analyses to overcome the limitations of the frequentist approach (i.e., null-hypothesis significance testing) and gain statistical evidence for nullresults where relevant (Dienes, 2011; Wagenmakers, 2007).”
Enhancing groundwater vulnerability assessment through Bayesian inference
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Świątkowski, W., & Carrier, A. (2020) · Basic and Applied Social Psychology · doi:10.1080/01973533.2020.1792297 · Cited by 15
“Conventions for using Bayes Factors [Paper presentation].”
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“It has been suggested that Bayesian approaches are resistant to multiple comparison problems (Dienes, 2011).”
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“…the alternative hypothesis is favored over the null hypothesis (i.e., larger BFs argue in favor of the alternative hypothesis, with values above 3 denoting ‘substantial evidence’ in favor of the alternative hypothesis; by contrast, values less than 1 support the null hypothesis; see Dienes, 2011).”
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“17, all of which were above 3 and hence can be interpreted as evidence for the null [83,84].”
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“Using null-hypothesis significance tests, it is not possible to “top up” with additional data and re-test at the same significance level, since the tests are sensitive to the stopping rule used to gather the data (Dienes 2011, p278).”
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“00 was considered as a substantial evidence in favor of the null or the alternative hypothesis accordingly (Dienes, 2011).”
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“We report both frequentist statistics and equivalent Bayesian statistics (Dienes, 2011).”
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“TD RTs (ms) 1046 (37) 1021 (33) 1073 (35) 1036 (39) 1044 (34)”
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“3 is regarded as evidence for the alternative hypothesis (Dienes, 2011; Jeffreys, 1961).”
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“33) (Dienes, 2011) or the maximum sample size (40) was reached, as occurred.”
BackgroundResultInfluentialChang, B. P. I., Mulders, M. D. G. H., Cserjési, R., Axel Cleeremans, B., & Klein, O. (2018) · Appetite · doi:10.1016/j.appet.2018.08.013 · Cited by 11
“…a half-normal distribution of effect sizes centered on zero (i.e., suggesting that small effect sizes are more frequent than larger ones, cf. Dienes, 2011).3 These analyses revealed a Bayes factor of 0.34, which is conventionally considered as strong support for the null hypothesis (see,…”
InfluentialMajerus, S., & Oberauer, K. (2019) · Journal of Experimental Psychology Learning Memory and Cognition · doi:10.1037/xlm0000792 · Cited by 13
“All the statistical analysis conducted in the present study adopted a Bayesian and model comparison approach (see, e.g., Dienes, 2011, 2016; Wagenmakers, 2007; Wagenmakers, Lee, Lodewyckx, & Iverson, 2008).”
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“Our use of Bayesian estimation instead allows us to think probabilistically, which aligns with rising concerns about binary significance testing because it encourages us to think distributionally rather than in binary terms (Wagenmakers, 2007; Dienes, 2011).”
BackgroundWehrle, S., Vogeley, K. T., & Grice, M. (2023) · Language and Cognition · doi:10.1017/langcog.2023.21 · Cited by 14
“We chose a Bayesian rather than a frequentist approach mainly because it is (1) better suited to exploratory work as well as limited sample sizes, (2) more conservative, more robust andmore transparent when properly applied and (3)more closely aligned with common human intuitions about the interpretation of statistica…”
BackgroundMethodMoore, T. E., Schlichting, C. D., Aiello‐Lammens, M. E., Mocko, K., & Jones, C. S. (2018) · New Phytologist · doi:10.1111/nph.15196 · Cited by 11
Estimating neural response functions from fMRI
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“The use of Bayes factors provides a Bayesian alternative to hypothesis testing using classical inference (Dienes, 2011).”
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Adaptive scaling of reward in episodic memory: a replication study
Mason, A., Ludwig, C. J. H., & Farrell, S. (2016) · Quarterly Journal of Experimental Psychology · doi:10.1080/17470218.2016.1233439 · Cited by 11
“Bayes factors are well suited to quantify strength of evidence as they allow the researcher to state evidence in favour of both the null and the alternative hypothesis (Dienes, 2011; Rouder, Speckman, Sun, Morey, & Iverson, 2009; Wagenmakers, 2007).”
BackgroundReporting in Experimental Philosophy: Current Standards and Recommendations for Future Practice
Polonioli, A., Vega‐Mendoza, M., Blankinship, B., & Carmel, D. (2018) · Review of Philosophy and Psychology · doi:10.1007/s13164-018-0414-3 · Cited by 12
“…that, along with simply adding another set of tests to choose from, increase researcher degrees of freedom; several other authors (e.g., Dienes 2011, 2014; Kruschke 2013; Rouder et al. 2009), focus instead on the usefulness of Bayesian analyses for establishing whether the evidence…”
BackgroundTiming of mirror system activation when inferring the intentions of others
Cole, E. J., & Barraclough, N. E. (2018) · Brain Research · doi:10.1016/j.brainres.2018.07.015 · Cited by 12
“Pearson’s correlation coefficients were calculated alongside all linear regressions and were additionally tested using Bayesian analyses (Dienes, 2008, 2011) to quantify the evidence in favor for or against each correlation.”
BackgroundMethodExploring the role of context on the existing evidence for reconsolidation of episodic memory
Capelo, A. M. D. A. B., Albuquerque, P. B., & Cadavid, S. E. (2018) · Memory · doi:10.1080/09658211.2018.1507040 · Cited by 14
“Taking into account the limitations of null-hypothesis significance testing (Dienes, 2011), Bayesian analyses were conducted (Cauchy prior, width 1.0) to examine the evidence in favour of null hypothesis (H0: No differences in performance between no-reactivationABC and reactivationAAC groups)…”
MethodInfluentialEvaluations of clinical tobacco cessation interventions in Arab populations: A systematic review
Alzahrane, A., West, R., Ubhi, H. K., Brown, J., Abdulqader, N., & Samarkandi, O. A. (2018) · Addictive Behaviors · doi:10.1016/j.addbeh.2018.08.017 · Cited by 11
Bayesian Approaches to Testing a Point (“Null”) Hypothesis
Kruschke, J. K. (2014) · Elsevier eBooks · doi:10.1016/b978-0-12-405888-0.00012-x · Cited by 11
Fear‐specific enhancement of tactile perception is disrupted after amygdala lesion
Bertini, C., Starita, F., Passamonti, C., Santoro, F., Zamponi, N., Michelucci, R., & Scarpazza, C. (2019) · Journal of Neuropsychology · doi:10.1111/jnp.12178 · Cited by 12
Practice-induced functional plasticity in inhibitory control interacts with aging
Hartmann, L., Wachtl, L., Marzia De Lucia, E., & Spierer, L. (2019) · Brain and Cognition · doi:10.1016/j.bandc.2019.02.004 · Cited by 12
“Bayes factors express the probability of the data given H0 relative to H1 (Dienes, 2011)).”
Civile, C., Cooke, A., Liu, X., McLaren, R., Elchlepp, H., Lavric, A., Milton, F., & McLaren, I. P. L. (2019) · Journal of Experimental Psychology Animal Learning and Cognition · doi:10.1037/xan0000232 · Cited by 11
“Additional Bayes Factor Analysis Using the procedure outlined by Dienes (2011), we first conducted a Bayes analysis on”
MethodAnodal transcranial direct current stimulation reduces motor slowing in athletes and non-athletes
Seidel-Marzi, O., & Ragert, P. (2020) · BMC Neuroscience · doi:10.1186/s12868-020-00573-5 · Cited by 12
Validation of the International Reading Speed Texts in a Canadian Sample
Morrice, E., Hughes, J., Stark, Z., Wittich, W., & Johnson, A. P. (2020) · Optometry and Vision Science · doi:10.1097/opx.0000000000001538 · Cited by 11
“A Bayesian analysis was used due to known issues with traditional null hypothesis significance testing (NHST; Dienes, 2011; Kline, 2013; Wetzels et al., 2011).”
MethodTo Grasp the World at a Glance: The Role of Attention in Visual and Semantic Associative Processing
Gronau, N. (2021) · Journal of Imaging · doi:10.3390/jimaging7090191 · Cited by 9
Efficient alternatives for Bayesian hypothesis tests in psychology.
Pramanik, S., & Johnson, V. E. (2022) · Psychological Methods · doi:10.1037/met0000482 · Cited by 11
Baker, K. S., Yamamoto, N., Pegna, A. J., & Johnston, P. (2022) · Biological Psychology · doi:10.1016/j.biopsycho.2022.108422 · Cited by 11
Hilgard, J., Engelhardt, C. R., Bartholow, B. D., & Rouder, J. N. (2015) · Psychology of Popular Media Culture · doi:10.1037/ppm0000102 · Cited by 11
“Bayesians, in contrast, are interested in the quantification of evidence, not the control of such error rates, so there is no need for such corrections (Dienes, 2011; Royall, 1997).”
BackgroundMethodInfluentialParker, A., Powell, D., & Dagnall, N. (2017) · Brain and Cognition · doi:10.1016/j.bandc.2017.12.002 · Cited by 12
“Finally, Baysian analyses were used to assess the evidence in favour of the null effects of eye movements being true (Dienes , 2011, 2014).”
MethodThe neural dynamics underlying prioritisation of task-relevant informationPreprint
Grootswagers, T., Robinson, A. K., Shatek, S. M., & Carlson, T. A. (2020) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2020.06.25.172643 · Cited by 10
Nalborczyk, L., Batailler, C., Lœvenbruck, H., Vilain, A., & Bürkner, P. (2019) · doi:10.31234/osf.io/guhsa · Cited by 11
Chikako, T. U., Bacha, R. H., Hagan, J. E., Seidu, A., Kuse, K. A., & Ahinkorah, B. O. (2022) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph19116600 · Cited by 10
Evaluating the Pedagogical Effectiveness of Study Preregistration in the Undergraduate Dissertation
Pownall, M., Pennington, C. R., Norris, E., Juanchich, M., Smailes, D., Russell, P. S., Gooch, D., Evans, T. R., Persson, S., Mak, M. H., et al. (2023) · Advances in Methods and Practices in Psychological Science · doi:10.1177/25152459231202724 · Cited by 16
“Bayes factors were calculated for all analyses to evaluate strength of evidence (Dienes, 2011).”
MethodDynamics of visual object coding within and across the hemispheres: Objects in the periphery
Robinson, A. K., Grootswagers, T., Shatek, S. M., Behrmann, M., & Carlson, T. A. (2025) · Science Advances · doi:10.1126/sciadv.adq0889 · Cited by 10
“RSA allowed a comparison between hemispheres which was abstracted away from specific neural activity patterns and rather focused on the relationships between stimulus representations.”
Rindskopf, D., Shadish, W. R., & Clark, M. H. (2018) · Evaluation Review · doi:10.1177/0193841x18789532 · Cited by 10
“Readers wanting more detail can refer to many excellent introductions (Dienes, 2011; Gelman, Carlin, Stern, & Rubin, 2003; Gill, 2007; Jackman, 2009; Kaplan, 2014; Kruschke, 2015; Lynch, 2007; Masson, 2011; Ntzoufras, 2009; Wetzels et al., 2011; Winkler, 2003; Zyphur & Oswald, 2013), and readers…”
BackgroundNo effect of hippocampal lesions on stimulus-response bindings
Henson, R. N., Horner, A. J., Greve, A., Cooper, E., Gregori, M., Simons, J. S., Erzinçlioğlu, S., Browne, G., & Kapur, N. (2017) · Neuropsychologia · doi:10.1016/j.neuropsychologia.2017.07.024 · Cited by 9
“To provide more evidence for this conclusion, rather than relying on failure to reject the null hypothesis that the two groups differ, we calculated the Bayes Factor for the likelihood of patients showing the same size congruency effect as controls (alternate hypothesis), relative to the likelihood of patients showing…”
Role of prior knowledge in implicit and explicit learning of artificial grammars
Ziori, E., Pothos, E. M., & Dienes, Z. P. (2014) · Consciousness and Cognition · doi:10.1016/j.concog.2014.06.003 · Cited by 10
“…for chance performance; a B between 3 and 1/3 indicates data insensitivity for deciding whether or not there was any learning (see Dienes, 2008, 2011 collapsed together was found in the baseline condition (55%, p < .001, r 2 = .26), but not in the dual task one (51%, p = .176, r 2 = .03), a…”
BackgroundSelf-citationNo Such Thing as Too Much Chocolate
Moser, C., Phelan, C., Resnick, P., Schoenebeck, S. Y., & Reinecke, K. (2017) · CHI Conference on Human Factors in Computing Systems · doi:10.1145/3025453.3025778 · Cited by 13
“Bayes factor, which is the ratio of two models’ average likelihoods [12].”
Background
Metadata
- Authors
- Dienes, Z.
- Affiliations
- University of Sussex (GB)
- Corresponding author
- Dienes, Zoltan
- ORCID
- Dienes, Zoltan
- Venue
- Perspectives on Psychological Science
- Publisher
- SAGE Publications
- Published
- 2011-05
- Volume
- 6
- Issue
- 3
- Pages
- 274-290
- ISSN
- 1745-6916 (ISSN-L)
- 1745-6924
- OpenAlex
- W2055754299
- Cited by
- 938
- References
- 60
- Citations by year
- 2026: 25 · 2025: 35 · 2024: 39 · 2023: 46 · 2022: 64 · 2021: 99 · 2020: 87 · 2019: 84 · 2018: 98 · 2017: 82 · 2016: 76 · 2015: 68 · 2014: 48 · 2013: 42 · 2012: 33
- FWCI
- 6.30
- Type
- journal article
- Language
- en
- Open access
- green
- figshare.com
- Locations
- Perspectives on Psychological Science (publishedVersion)
- PubMed (publishedVersion)
- Figshare (submittedVersion, cc-by)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Keywords
- Bayesian inference, significance testing, null hypothesis significance testing, multiple comparisons, stopping rules
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