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]
Citations
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“…when researchers work with quantitatively instantiated theories – which MPT models undoubtedly are – prior distributions along with model equations, are an opportunity to fully describe all aspects captured by theory (e.g., Dienes, 2011; Rouder et al., 2016; Vanpaemel, 2010; Vanpaemel & Lee, 2012).”
BackgroundLinde, M., Tendeiro, J. N., & van Ravenzwaaij, D. (2025) · Journal of Applied Statistics · doi:10.1080/02664763.2025.2472150 · Cited by 3
“The use of NHST in biomedical research is ubiquitous [16] even though it has been criticized repeatedly (e.g.[ 8,9,21,26,31,33–35, 56 , 73, 76– 78 ]).”
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“many situations the p values are calculated using the wrong sampling distribution (Dienes, 2011).”
MethodSchut, M. J., Fabius, J. H., & der Stigchel, S. V. (2016) · Visual Cognition · doi:10.1080/13506285.2016.1206050 · Cited by 3
“We choose a Bayesian approach since it allowed us to further examine whether the null hypothesis (i.e., crowding does not affect accuracy on the transsaccadic memory paradigm) was rightly rejected or that our test was inconclusive (Dienes, 2011).”
BackgroundGeorge, D. N., & Oltean, B. P. (2019) · Journal of Experimental Psychology Learning Memory and Cognition · doi:10.1037/xlm0000773 · Cited by 3
“Values close to 1 provide no clear support in either direction, those above 3 provide substantial support for the experimental hypothesis, and those below 1/3 provide substantial support for the null hypothesis (Jeffreys, 1961; Dienes, 2011).”
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Does Motor Memory Reactivation through Practice and Post-Learning Sleep Modulate Consolidation?
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“33 < BF < 3 are deemed inconclusive [75].”
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“BFs >1 indicate that there is more evidence for the alternative hypothesis than the null hypothesis (Dienes, 2011) with a BF >3 considered as “ substantial ” evidence for the alternative hypothesis, i.e., decoding above-chance level.”
Expectation dynamically modulates the representational time course of objects and locations
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“While the frequentist approach provides a p -value indicating the probability of the data under the null hypothesis (H₀), it cannot quantify evidence for H₀ or directly state the probability of the hypotheses themselves (Dienes, 2011).”
Civile, C., & Wang, G. (2026) · Social Cognitive and Affective Neuroscience · doi:10.1093/scan/nsag001 · Cited by 3
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“The final sample size employed was guided via the Bayesian Stopping Rule (Dienes, 2011) which was applied to the Bayesian analyses with a first look conducted at 24 participants, and in this case data collection was terminated at the pre-determined maximum of 32 (cf. Campbell, Chambers, Allen,…”
InfluentialBayesian Inference: Understanding Experimental Data With Informative Hypotheses
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“An advantage of a Bayesian approach is that it allows combining of evidence without type-1 error inflation (Dienes, 2011).”
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Pinto, R., & Albuquerque, P. B. (2024) · Memory · doi:10.1080/09658211.2024.2304771 · Cited by 2
“Considering the limitations of null hypothesis signi fi cance testing (Dienes, 2011), Bayesian analyses were conducted to examine the evidence in favour of the null hypothesis (H0: no di ff erences in destination memory when proverbs were transmitted aloud compared with when proverbs were transmitted…”
MethodFluent Processing Amplifies Affective Judgments
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“BFs larger than 1 indicate that there is more evidence for the alternative hypothesis than the null hypothesis (Dienes, 2011) with a BF greater than 3 considered as “ substantial ” evidence for the alternative hypothesis i.e. decoding above-or below-chance level.”
Data-driven prior elicitation for Bayes factors in Cox regression for nine subfields in biomedicine
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“According to them, the prior allows the incorporation of domain knowledge and results from prior studies into Bayesian analyses and therefore permits tests of theories [32,76].”
King, K. M., Dora, J., Schultz, M. E., McCabe, C. J., Lee, C. M., Shoda, Y., Fairlie, A. M., Litt, D., Lewis, M. A., Patrick, M. E., et al. (2025) · Psychology of Addictive Behaviors · doi:10.1037/adb0001074 · Cited by 2
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It's all about the transient: Intra-saccadic onset stimuli do not capture attention
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“Using these parameters, and assuming a uniform prior distribution, we determined the Bayes factor (cf. Dienes, 2011), Bf = 0.15.”
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“However, from this non-significant result we are unable to determine whether this implies that there is evidence for the null hypothesis or that there is no evidence for any conclusion (Dienes, 2011; Rouder, Speckman, Sun, Morey, & Iverson, 2009).”
BackgroundReduced effects of pictorial distinctiveness on false memory following dynamic visual noise
Parker, A., Kember, T., & Dagnall, N. (2016) · Memory · doi:10.1080/09658211.2016.1229793 · Cited by 2
Song, M., Shinomori, K., & Qian, Q. (2018) · Japanese Psychological Research · doi:10.1111/jpr.12198 · Cited by 2
Saint‐Mont, U. (2018) · Advances in Social Sciences Research Journal · doi:10.14738/assrj.58.4867 · Cited by 2
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“A full discussion of this is beyond the scope of this article but see Dienes (2011); Ioannidis (2019); Kruschke and Liddell (2018); Szucs and Ioannidis (2017); and Wagenmakers et al. (2018).”
BackgroundExploring the ventral white matter language network in bimodal and unimodal bilinguals
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“This has the advantage to quantify the evidence in favor of the alternative hypothesis and to overcome the problem of multiple testing (Dienes, 2011).”
The Impact of Sleep Quality on Mood in Beach Volleyball Athletes: A Cross-Sectional Study
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“For a more appropriate use and advantages of Bayesian statistics, readers are directed to the reference literature or textbooks (Dienes, 2011; Howard et al., 2000; Kruschke, 2010).”
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“Theory rejection represents the logic substratum of hypothesis testing as implemented in classical ‘frequentist’ statistics 12,14 .”
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“B10 values between 1 and 3 (as well as between 1 and 1/3 accordingly) would only yield ‘anecdotal evidence’ for an hypothesis (e.g. Dienes, 2011; Wagenmakers et al., 2011).”
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“adre of methodologists has recently advocated the use of Bayesian statistical methods as a superior alternative to the messy frequentist practice that dominates psychology’s research landscape (e.g., Dienes, 2011, Wagenmakers, 2007). These Bayesians criticize NHST, often advocate the use of Bayes factors for hypothesi…”
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“…statistics (like p-values and confidence intervals) are often attributable to the wrong interpretation of these statistics as resulting from a Bayesian analysis (e.g., Dienes, 2011; Gigerenzer, 2004; Hoekstra, Morey, Rouder, & Wagenmakers, 2014; Kruschke & Liddell, 2018a; Morey et al., 2015).”
Perski, O., Herbeć, A., Shahab, L., & Brown, J. (2020) · doi:10.2196/preprints.19392 · Cited by 2
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“Bayes factors greater than 6 were interpreted as substantial evidence for the hypotheses and Bayes factors less than 1/6 were interpreted as substantial evidence for the null (Dienes, 2011; Jeffreys, 1998).”
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Knott, L. M., Litchfield, D., Donovan, T., & Marsh, J. E. (2024) · Memory · doi:10.1080/09658211.2024.2307921 · Cited by 1
“Software described in Dienes (2008, 2011, 2014) was used to under-take the Bayes factor calculation.”
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“30 We denoted force onset as the first instance of sustained divergence using a conservative threshold of BF > 10, indicating a strong likelihood of a difference.”
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“Bayes factors (BFs) were computed following the convention adopted in previous works with this protocol [45], using a half-normal prior whose standard deviation was set from the relevant earlier finding.”
Civile, C., & Stephens, A. (2026) · Social Neuroscience · doi:10.1080/17470919.2026.2751696 · Cited by 1
“To evaluate the non-significant Orientation × Target interaction in the anodal group, we computed a Bayes factor (B; Dienes, 2011, 2014) for the objectification index, defined as the inversion effect (upright − inverted d’) for male targets minus that for female targets, so that positive values…”
Suggestions and Recommendations on Statistical Analysis and Research Methodology
Voidăzan, S. T., Moldovan, C., & Dobreanu, M. (2014) · Revista română de medicină de laborator · doi:10.2478/rrlm-2014-0046 · Cited by 1
“This ensures that the results yielded by that representative sample are not produced by chance and can be extrapolated to the target population [5, 6].”
BackgroundStructural equation modelling for studying intended game processes
Svahn, M., & Wahlund, R. (2015) · ETC Press eBooks · Cited by 1
Beliefs about a speaker affect feeling of another's knowing
Mol, L., Kuhlen, A. K., der Steen, R. V., & Obbens, M. (2013) · eScholarship (California Digital Library) · Cited by 1
Parris, B. A., Dienes, Z. P., & Hodgson, T. L. (2012) · Cited by 1
Self-citationOdours reduce the magnitude of object substitution masking for matching visual targets in females
Robinson, A. K., Laning, J., Reinhard, J., & Mattingley, J. B. (2016) · Attention Perception & Psychophysics · doi:10.3758/s13414-016-1157-9 · Cited by 1
“…the strength of support for the alternative hypothesis (H1) relative to the null; values of B > 3 suggest substantial evidence in favour of H1, whereas values smaller than one third are regarded as providing substantial evidence in favour of the null hypothesis (Dienes, 2011; Jeffreys, 1961).”
BackgroundShi, D. (2016) · SHAREOK (University of Oklahoma; Oklahoma State University; Central Oklahoma University) · Cited by 1
Anticipatory access to group-level information in working memory
Farrell, S. (2018) · Quarterly Journal of Experimental Psychology · doi:10.1177/1747021817744428 · Cited by 1
“, Botvinick & Plaut, 2006; Brown, Neath, & Chater, 2007; Brown, Preece, & Hulme, 2000; Burgess & Hitch, 1999; Estes, 1972; Farrell, 2012; Farrell & Lewandowsky, 2002; Henson, 1998; Lewandowsky & Murdock, 1989; Page & Norris, 1998); for a review, see Lewandowsky and Farrell (2008). Despite their differing assumptions,…”
BackgroundMethodBayesian Inference: Parameter Estimation for Inference in Small Samples
Baig, S. A. (2021) · Nicotine & Tobacco Research · doi:10.1093/ntr/ntab221 · Cited by 1
“Bayesian methods permit researchers to conduct as many statistical tests as desired so long as their total evidential value is taken into account in the process of inference.(17)”
Let’s Talk about Stats: Revising Our Approach to Teaching Statistics in Psychology
Reynolds, J. J. (2021) · Psychological Reports · doi:10.1177/00332941211043447 · Cited by 2
“Dienes (2011) provides a comparison of the two approaches and where they may result in different conclusions. Kruschke and Liddell (2018b) present an excellent overview of Bayesian data analysis for individuals starting out on the topic, as does Etz and Vandekerckhove (2018). van de Schoot and Depaoli (2014), as well…”
BackgroundResultInfluentialInternal and External Validity
Kazdin, A. E. (2021) · Cambridge University Press eBooks · doi:10.1017/9781108993647.003 · Cited by 1
Mistakes strengthen the temporal binding effect in the context of goal-directed actions
Jenkins, M. A., & Obhi, S. S. (2022) · Experimental Brain Research · doi:10.1007/s00221-022-06407-6 · Cited by 1
“Using Bayes Factors (BF), it is possible to assess the relative likelihood of the null hypothesis and the alternative hypothesis (see Dienes, 2011; 2014).”
MethodRabeyron, T. (2022) · In Analysis · doi:10.1016/j.inan.2022.10.016 · Cited by 1
Likelihoodism and Guidance for Belief
Tokhadze, T. (2022) · Journal for General Philosophy of Science · doi:10.1007/s10838-022-09608-3 · Cited by 1
“Many critics of frequentism see Bayesianism as providing superior methods of dataanalysis (Dienes 2011; Wetzels et al. 2011; Kruschke 2013).”
MethodBayesian analysis for nurse and midwifery research: statistical, practical and ethical benefits
Malone, H., & Coyne, I. (2023) · Nurse Researcher · doi:10.7748/nr.2023.e1852 · Cited by 1
Pérez-Salas, C., Parra, V. S., Ortega, A., Sáez-Delgado, F., Ramírez-Peña, P. F., & Zañartu, I. (2023) · International Journal of Developmental Disabilities · doi:10.1080/20473869.2023.2243414 · Cited by 1
“Building on this idea, Bayesian analysis allows us to compare two (or more) competing models (e.g. null vs alternative) in light of the existent data and not only based on theoretical probability distributions, as in the Frequentist approach to hypothesis testing (Dienes 2011).”
Baranes, L., Shimoni, H., & Axelrod, V. (2024) · Current Psychology · doi:10.1007/s12144-024-06541-0 · Cited by 1
“Bayes factor (BF 10 ) below 0.33 was taken as support for H 0 (Dienes, 2011).”
InfluentialBiased competition between action representations
Kyllingsbæk, S., Larsen, L. B., Pedersen, J. K., Sangoi, L., & Grünbaum, T. (2025) · Neuropsychologia · doi:10.1016/j.neuropsychologia.2025.109149 · Cited by 1
“As Dienes (2011, 2024) and others (Etz et al., 2018; Rouder, 2014) have convincingly argued, Bayesian statistical analyses do not rely on any specification of the data collection in advance.”
Woo, H. S., Willems, B. F., Harrison, J., İzzetoğlu, K., Hah, S., & Ayaz, H. (2013) · Journal of Bioresource Management · Cited by 1
Feldman, K., Solymos, G. M. B., de Albuquerque, M. P., & Chawla, N. V. (2019) · Scientific Reports · doi:10.1038/s41598-019-55260-1 · Cited by 1
Overlapping Mechanisms in Implying and Inferring
Rees, A., & Bott, L. A. (2019) · Cognitive Science · doi:10.1111/cogs.12808 · Cited by 1
Labalestra, M., Stefaniak, N., Lefèbvre, L., & Besche‐Richard, C. (2021) · Frontiers in Psychology · doi:10.3389/fpsyg.2021.598114 · Cited by 2
“33 < BF < 3 is considered to lack sensitivity (Dienes, 2011).”
BackgroundInfluentialPerski, O., Stevens, C., West, R., & Shahab, L. (2021) · PLoS ONE · doi:10.1371/journal.pone.0259949 · Cited by 1
“Values greater than 3 or smaller than 1/3 are typically regarded as providing substantial evidence for the alternative or null hypothesis, respectively, with intermediate values indicating that data are insensitive to distinguish between the two [20].”
BackgroundCase-Control and Cohort Designs
Kazdin, A. E. (2021) · Cambridge University Press eBooks · doi:10.1017/9781108993647.008 · Cited by 1
Null Hypothesis Significance Testing
Kazdin, A. E. (2021) · Cambridge University Press eBooks · doi:10.1017/9781108993647.014 · Cited by 1
Does transliminality predict subperceptual information processing?
Polito, V., Howarth, S., Roberts, A., & Arbige, S. (2025) · Neuroscience of Consciousness · doi:10.1093/nc/niaf044 · Cited by 1
Good science, bad science: Questioning research practices in psychological research
Bakker, M. (2014) · UvA-DARE (University of Amsterdam) · Cited by 1
Acute effects of alcohol on inhibition
Campbell, A. (2016) · ORCA Online Research @Cardiff (Cardiff University) · Cited by 1
Fast fronto-parietal cortical dynamics of conflict detection and context updating in a flanker taskPreprint
Brydges, C. R., Barceló, F., Nguyen, A. T., & Fox, A. M. (2018) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/336958 · Cited by 1
“allows a hypothesis to be accepted or rejected by gathering evidence in favor of it (Dienes, 2011; Kruschke, 2013).”
In pursuit of visual attention: SSVEP frequency-tagging moving targetsPreprint
de Lissa, P., Caldara, R., Nicholls, V. I., & Miellet, S. (2019) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/804708 · Cited by 1
Decoding Predictions and Violations of Object Position and Category in Time-resolved EEGPreprint
Whyte, C. J., Robinson, A. K., Grootswagers, T., Hogendoorn, H., & Carlson, T. A. (2020) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2020.04.08.032888 · Cited by 1
“Using these distributions, we computed Bayes factors (Dienes, 2011; Jeffreys, 1998; Rouder, Speckman, Sun, Morey, & Iverson, 2009; Wagenmakers, 2007) which, being a ratio of marginal likelihoods, measures the evidence for the alternative hypothesis relative to the null.”
MethodPerski, O., Stevens, C., West, R., & Shahab, L. (2020) · doi:10.32388/7idpz6 · Cited by 1
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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