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Rejecting or Accepting Parameter Values in Bayesian Estimation
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This article explains a decision rule that uses Bayesian posterior distributions as the basis for accepting or rejecting null values of parameters. This decision rule focuses on the range of plausible values indicated by the highest density interval of the posterior distribution and the relation between this range and a region of practical equivalence (ROPE) around the null value. The article also discusses considerations for setting the limits of a ROPE and emphasizes that analogous considerations apply to setting the decision thresholds for p values and Bayes factors.
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“There is no uniquely correct ROPE; however, by convention, the ROPE range is often set at half the size of Cohen’s definition of small effect size (i.e. 0.2 [306];) resulting in ROPE values of ±0.1 and ±0.05 for standardized mean differences (e.g. Cohen’s d = group 1 mean – group 2 mean/pooled standard deviation) and standardized regression coefficients (i.e. sβ = coefficient from a regression on”
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Citations
Cites
Statistical Power Analysis for the Behavioral Sciences
Muller, K. E., & Cohen, J. (1989) · Technometrics · doi:10.2307/1270020 · Cited by 99,603
Statistical Power Analysis for the Behavioral Sciences (2nd ed.).
Lachenbruch, P. A., & Cohen, J. (1989) · Journal of the American Statistical Association · doi:10.2307/2290095 · Cited by 37,421
Kass, R. E., & Raftery, A. E. (1995) · Journal of the American Statistical Association · doi:10.1080/01621459.1995.10476572 · Cited by 12,558
The ASA Statement on p -Values: Context, Process, and Purpose
Wasserstein, R. L., & Lazar, N. A. (2016) · The American Statistician · doi:10.1080/00031305.2016.1154108 · Cited by 6,306 · cited 1×
“Discrete decisions should be avoided if possible, because such decisions encourage people to ignore the magnitude of the parameter value and its uncertainty (e.g., Cumming, 2014; Kruschke & Liddell, 2018b; Wasserstein & Lazar, 2016, and many references cited therein).”
BackgroundJAGS: A program for analysis of Bayesian graphical models using Gibbs sampling
Plummer, M. (2003) · Cited by 4,720
The Confrontation between General Relativity and Experiment
Will, C. M. (2014) · Living Reviews in Relativity · doi:10.12942/lrr-2014-4 · Cited by 3,996
The New Statistics: Why and How
Cumming, G. (2014) · Psychological Science · doi:10.1177/0956797613504966 · Cited by 3,200
Bayes, T. (1763) · Philosophical Transactions of the Royal Society of London · doi:10.1098/rstl.1763.0053 · Cited by 3,023
AN ESSAY TOWARDS SOLVING A PROBLEM IN THE DOCTRINE OF CHANCES
BAYES (1958) · Biometrika · doi:10.1093/biomet/45.3-4.296 · Cited by 2,939
Redefine statistical significance
Benjamin, D. J., Berger, J. O., Johannesson, M., Nosek, B. A., Wagenmakers, E.-J., Berk, R., Bollen, K. A., Brembs, B., Brown, L., Camerer, C., et al. (2017) · Nature Human Behaviour · doi:10.1038/s41562-017-0189-z · Cited by 2,772
Research works printed but not linked: 5
- Jeffreys H., 1961, Theory of probability
- Lakens D., 2017, t, 8, 355
- Lesaffre E., 2008, Bulletin of the NYU Hospital for Joint Diseases, 66, 150
- Little T. A., 2015, BioPharm International, 28, 45
- Westlake W. J., 1981, Biometrics, 37, 591
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“…density interval (HDI) of the posterior for a given standardized β -coefficient or (partial) correlation coefficient was not overlapping with a region of practical equivalence between –0.1 and 0.1 as suggested by Kruschke, 2018 based on negligible effect sizes according to Cohen, 1988 .”
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“We follow Kruschke (2018), who recommends that scholars use a standardized negligible effect size (0 : 1 � SD Y ) as their region of practical equivalence (ROPE).”
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“Indeed, inference using the Region of Practical Equivalence (ROPE) 30 showed 100% of the posterior estimates for the aggregate slope fell within a region that would be reasonably said to be a “null” effect.”
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“As per our expectation, both scores have a practically negligible effect with the 95% HPDIs overlapping with the ±0.05 ROPEs: β o Mµr = 0.04 [−0.13,0.20] and β o Mµf = 0.07 [−0.14,0.29], β a Mµr = 0.15 [−0.02,0.33] and β a Mµf = 0.21 [−0.03,0.44], for rates of obesity o and physical activity a, respectively.”
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Morimoto, N., Nishihama, Y., Onishi, K., & Nakayama, S. F. (2024) · Environment International · doi:10.1016/j.envint.2024.108932 · Cited by 7
Malone, C., Ryan, S. M., Nicholson, J., McArdle, O., Brennan, S., McCavana, P., McClean, B., & Duane, F. K. (2024) · Practical Radiation Oncology · doi:10.1016/j.prro.2024.06.017 · Cited by 7
Abadie, M., & Guette, C. (2024) · Memory & Cognition · doi:10.3758/s13421-024-01620-w · Cited by 7
“Nevertheless, we performed Bayesian analyses in which evidence of a null effect is equally informative (Kruschke, 2011, 2018), and Type I error does not increase with optional stopping (Rouder, 2014).”
Toffoli, L., Zdorovtsova, N., Epihova, G., Duma, G. M., Cristaldi, F. D. P., Pastore, M., Astle, D. E., & Mento, G. (2024) · Human Brain Mapping · doi:10.1002/hbm.70011 · Cited by 7
“For hypothesis testing, we used the region of practical equivalence (ROPE; Kruschke, 2018; R package: “ bayestestR, ” Makowski et al., 2019).”
MethodStereotypes disrupt probabilistic category learning.
Derreumaux, Y., Elder, J., Suri, G., Ben-Zeev, A., Quimby, T., & Hughes, B. (2023) · Journal of Experimental Psychology General · doi:10.1037/xge0001335 · Cited by 5
Improving estimates of waning immunity rates in stochastic SIRS models with a hierarchical framework
Alahakoon, P., McCaw, J. M., & Taylor, P. (2023) · Infectious Disease Modelling · doi:10.1016/j.idm.2023.10.002 · Cited by 8
Winders, S., Lyon, D., Kelly, D. L., Weaver, M. T., Yi, F., de Carvalho, M. R., & Stechmiller, J. K. (2023) · Advances in Wound Care · doi:10.1089/wound.2023.0124 · Cited by 11
Navarro, V. M., Dwyer, D. M., & Honey, R. C. (2024) · Neurobiology of Learning and Memory · doi:10.1016/j.nlm.2024.107915 · Cited by 7
“After a final model was selected, statistical inference was performed using an HDI + ROPE criterion on median posterior differences (Kruschke, 2018, 2021).”
MethodProbabilistic Estimation of Cadence and Walking Speed From Floor Vibrations
MejiaCruz, Y., Caicedo, J. M., Jiang, Z., & Franco, J. M. (2024) · IEEE Journal of Translational Engineering in Health and Medicine · doi:10.1109/jtehm.2024.3415412 · Cited by 7
“Employing ROPE as a decision rule requires the most credible values of the marker to be sufficiently close to the null value to accept it or sufficiently far to reject it [37].”
BackgroundMethodInfluentialKeating, G. D. (2024) · Language Learning · doi:10.1111/lang.12662 · Cited by 7
Climatic Predictors of Long‐Distance Migratory Birds Breeding Productivity Across Europe
Hanzelka, J., Telenský, T., Koleček, J., Procházka, P., Robinson, R. A., Baltà, O., Cepák, J., Gargallo, G., Henry, P., Henshaw, I., et al. (2024) · Global Ecology and Biogeography · doi:10.1111/geb.13901 · Cited by 7
MejiaCruz, Y., Caicedo, J. M., & Matta, F. (2024) · Journal of Structural Engineering · doi:10.1061/jsendh.steng-13641 · Cited by 7
Acute isolation is associated with increased reward seeking and reward learning in human adolescents
Tomova, L., Towner, E., Thomas, K., Zhang, L., Palminteri, S., & Blakemore, S. (2025) · Communications Psychology · doi:10.1038/s44271-025-00306-6 · Cited by 6
“Parameters are considered well recovered if the ground truth is within the 95% HDI of the posterior distribution 69 , which was the case for all parameters.”
Evaluative conditioning of responses to unfamiliar chords by exposure to valenced images
Smit, E. A., Milne, A. J., Dean, R. T., & Weidemann, G. (2021) · Psychology of Music · doi:10.1177/03057356211008972 · Cited by 6
“To qualify the evidence for hypotheses, we follow the guidelines proposed by Jeffreys (1998, as cited by Kruschke, 2018): Condition name refers to the two pairings of stimuli in the conditioning phase.”
MethodShalfawi, S. A. I., & Kailani, G. E. (2021) · Sports · doi:10.3390/sports9090130 · Cited by 7
“Sports 2021, 9, 130 6 of 13 Sports 2021, 9, x FOR PEER REVIEW 6 of 13 Kruschke [34] (i.e., “standard deviation of the prior on µ were set to 1000 times the standard deviation of the pooled data and the mean M of the prior on µ is arbitrarily set to the mean of the pooled data”).”
BackgroundInfluentialSmith, E. S., & Peters, J. (2022) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1010096 · Cited by 6
Change of Variable-Foreperiod Effects within an Experiment: A Bayesian Modeling Approach
Han, T., & Proctor, R. W. (2022) · Journal of Cognition · doi:10.5334/joc.235 · Cited by 7
Model-averaged Bayesian t tests
Maier, M., Bartos̆, F., Quintana, D. S., Dablander, F., van den Bergh, D., Marsman, M., Ly, A., & Wagenmakers, E. (2024) · Psychonomic Bulletin & Review · doi:10.3758/s13423-024-02590-5 · Cited by 8
“…simultaneously taking the normal likelihood under consideration (e.g., Bayarri and Mayoral, 2002; Gelman and Hill, 2006, p. 124; Kruschke, 2013; Kruschke, 2018; O’Hagan and Forster, 2004, pp. 223-231; Western, 1995) In practice, it can be difficult to ascertain whether or not outliers are…”
BayesPostEst: An R Package to Generate Postestimation Quantities for Bayesian MCMC Estimation
Scogin, S., Karreth, J., Beger, A., & Williams, R. (2019) · The Journal of Open Source Software · doi:10.21105/joss.01722 · Cited by 7
“Users can also define a “region of practical equivalence” (ROPE, see Kruschke, 2013, 2018).”
BackgroundMethodAge-related changes in “cortical” 1/f dynamics are linked to cardiac activityPreprint
Schmidt, F., Danböck, S. K., Trinka, E., Klein, D. P., Demarchi, G., & Weisz, N. (2024) · eLife · doi:10.7554/elife.100605.1 · Cited by 7
Age-related changes in “cortical” 1/f dynamics are linked to cardiac activityPreprint
Schmidt, F., Danböck, S. K., Trinka, E., Klein, D. P., Demarchi, G., & Weisz, N. (2025) · eLife · doi:10.7554/elife.100605.2 · Cited by 7
Verb Vocabulary Supports Event Probability Use in Developmental Language Disorder
Kueser, J. B., Borovsky, A., Deevy, P., Muezzinoglu, M., Outzen, C., & Leonard, L. B. (2024) · Journal of Speech Language and Hearing Research · doi:10.1044/2024_jslhr-23-00600 · Cited by 6
“We defined the ROPE for post hoc contrasts based on the range recommended in Kruschke (2018) for a negligible effect size in logistic regression models.”
MethodTranscutaneous Vagus Nerve Stimulation Enhances Probabilistic Learning
Çakır, R., Büyükgüdük, İ., Bilim, P., Erdinç, A., & Veldhuizen, M. G. (2025) · Psychophysiology · doi:10.1111/psyp.70037 · Cited by 8
An Integrated 3D Eye-Gaze Tracking Framework for Assessing Trust in Human–Robot Interaction
Quesada, R. C., Casado, F. E., & Demiris, Y. (2025) · ACM Transactions on Human-Robot Interaction · doi:10.1145/3725861 · Cited by 6
“This suggests An Integrated 3D Eye-Gaze Tracking Framework for Assessing Trust in HRI 57:19 ap[25] ap[23] ap[22] ap[19] ap[17] ap[14] ap[13] ap[9] ap[8] ap[6] ap[4] ap[3] ap[2] −4 −2 0 2 4 Value (a) Posterior - Muir’s: 1 sigmap ap[24] ap[21] ap[20] ap[18] ap[16] ap[15] ap[12] ap[11] ap[10] ap[7] ap[5] ap[1 (5) to the…”
InfluentialRising from the ashes: treatments stabilize carbon storage in California’s frequent-fire forests
Yackulic, E. O., Elias, M., Shannon, J., Gilbert, S. L., Koontz, M. J., Plumb, S. T., Sloggy, M. R., & Duffy, K. A. (2025) · Frontiers in Forests and Global Change · doi:10.3389/ffgc.2025.1498430 · Cited by 7
“We followed standard procedures and set our ROPE range to equal ± 1 standard deviation of the 89% Highest Density Interval (Kruschke, 2018).”
Modelradar: aspect-based forecast evaluation
Cerqueira, V., Roque, L., & Soares, C. (2025) · Machine Learning · doi:10.1007/s10994-025-06877-z · Cited by 6
“Figure 4 shows that, while AutoNHITS exhibits the overall best performance, there is a reasonable chance that it is outperformed by any other method.”
Weak global trade‐off between frost and drought resistance in trees
Larter, M., Charrier, G., Delzon, S., Hammond, W. M., Baranger, A., Bertrand, C., Martin-StPaul, N. K., & Künstler, G. (2025) · New Phytologist · doi:10.1111/nph.70718 · Cited by 6
“We fit both phylogenetic and nonphylogenetic Bayesian mixed effects quantile regressions implemented in the Stan probabilistic programming language (Carpenter et al ., 2017), thanks to the brms package in R (B € urkner, 2017, 2018).”
Borszcz, F. K., Vieira, M. T., Tramontin, A. F., Visentainer, L. H., & Costa, V. P. (2022) · The Journal of Strength and Conditioning Research · doi:10.1519/jsc.0000000000004231 · Cited by 6
Bayesian Bootstrapped Correlation Coefficients
Rodriguez, J. E., & Williams, D. R. (2022) · The Quantitative Methods for Psychology · doi:10.20982/tqmp.18.1.p039 · Cited by 5
“The benefits of adopting Bayesian approaches have been written about extensively in the psychological sciences (see e.g., Vandekerckhove, Rouder, & Kruschke, 2018, and other articles in that special issue).”
BackgroundMethodInfluentialMedvedev, S. V., Masharipov, R. S., Korotkov, A. D., & Kireev, M. V. (2023) · Human Physiology · doi:10.1134/s0362119722700141 · Cited by 6
“If this effect fell in the range [–γ; γ] (region of practical equivalence, ROPE) with a likelihood above 95%, the zero hypothesis on the absence of effect was accepted [11, 29, 31], suggesting a practical equivalence of the BOLD-signal in studied samples.”
BackgroundDouven, I. (2023) · Journal of Mathematical Psychology · doi:10.1016/j.jmp.2023.102794 · Cited by 7
Fuhrmeister, P., Elbuy, S., & Bürki, A. (2024) · Journal of Cognition · doi:10.5334/joc.337 · Cited by 6
“To determine whether our estimates fall within or above the pre-defined ranges in Table 2, we used the region of practical equivalence (ROPE) procedure, as explained in Kruschke (2018).”
MethodOpie, G. M., Hughes, J. M., & Puri, R. (2024) · Neurobiology of Aging · doi:10.1016/j.neurobiolaging.2024.08.001 · Cited by 6
“Within the current study, this was set as ± 5 % of the standard deviation (SD)(Kruschke, 2018).”
BackgroundSugiura‐Ogasawara, M., Suwannarin, N., Tamada, H., Ebara, T., Ito, Y., Nakayama, S. F., Takagi, M., Saitoh, S., & Kamijima, M. (2025) · Environment International · doi:10.1016/j.envint.2025.109663 · Cited by 7
Metadata
- Authors
- Kruschke, J. K.
- Affiliations
- Indiana University Bloomington (US)
- Corresponding author
- Kruschke, John K.
- ORCID
- Kruschke, John K.
- Venue
- Advances in Methods and Practices in Psychological Science
- Publisher
- SAGE Publications
- Published
- 2018-05-08
- Volume
- 1
- Issue
- 2
- Pages
- 270-280
- ISSN
- 2515-2459 (ISSN-L)
- 2515-2467
- OpenAlex
- W2801776818
- Cited by
- 734
- References
- 51
- Citations by year
- 2026: 99 · 2025: 128 · 2024: 128 · 2023: 98 · 2022: 85 · 2021: 93 · 2020: 67 · 2019: 25 · 2018: 10
- FWCI
- 41.08
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Advances in Methods and Practices in Psychological Science (publishedVersion)
- IUScholarWorks Open (Indiana University) (submittedVersion)
- OSF Preprints (OSF Preprints) (submittedVersion)
- Funders
- U.S. Food and Drug Administration
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
- Social Sciences › Decision Sciences › General Decision Sciences › Decision-Making and Behavioral Economics
- Keywords
- Bayesian hypothesis testing, null hypothesis rejection, highest density interval, region of practical equivalence, posterior distribution, decision threshold, p-values, Bayes factor, parameter values
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