Cited by 742Statistical Methods and Bayesian InferenceStatistical Distribution Estimation and ApplicationsDecision-Making and Behavioral Economics

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Rejecting or Accepting Parameter Values in Bayesian Estimation

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Kruschke, John K.·2018·Advances in Methods and Practices in Psychological Science

DOI 10.1177/2515245918771304

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Abstract

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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Method
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Diveica, V., Muraki, E. J., Binney, R. J., & Pexman, P. M. (2024) · Journal of Experimental Psychology Learning Memory and Cognition · doi:10.1037/xlm0001328 · Cited by 18
Multi-Dimensional Evaluation of an Augmented Reality Head-Mounted Display User Interface for Controlling Legged Manipulators
Quesada, R. C., & Demiris, Y. (2024) · ACM Transactions on Human-Robot Interaction · doi:10.1145/3660649 · Cited by 14
“The default ROPE range suggested by [48] is − 0.1 to 0.1 for a standardised parameter.”
BackgroundInfluential
Practical Bayesian Inference in Neuroscience: Or How I Learned to Stop Worrying and Embrace the Distribution
Coventry, B. S., & Bartlett, E. L. (2024) · eNeuro · doi:10.1523/eneuro.0484-23.2024 · Cited by 16
“…(ROPEs) may be included in the posterior distribution that explicitly de ﬁ ne a range of values that are effectively equivalent to a null value, with parameters considered signi ﬁ cant if 95% of the posterior distribution (95% HDI) does not contain 0 or any values in the ROPE (Kruschke, 2018).”
Scientific self-correction: the Bayesian way
Romero, F., & Sprenger, J. (2020) · Synthese · doi:10.1007/s11229-020-02697-x · Cited by 16
“…on fat-tailed Cauchy priors in statistical packages), bias in favor of the null hypothesis, and potential mismatch between inference with Bayes factors and estimation based on the posterior distribution (e.g., Sprenger 2013; Kruschke 2018; Lakens et al. 2018a; Mayo 2018; Ten-deiro and Kiers 2019).”
Background
The choice of musical instrument matters: Effect of pitched but not unpitched musicianship on tone identification and word learning
Choi, W., To, C. Y., & Cheng, R. (2023) · Applied Psycholinguistics · doi:10.1017/s0142716423000358 · Cited by 13
“, unpitched musicians and nonmusicians are expected to perform similarly), where appropriate, we would supplement any null hypothesis significance testing with Bayesian hypothesis testing (Kruschke, 2018).”
Method
Causal roles of prefrontal and temporo-parietal theta oscillations for inequity aversion
Christian, P., Kapetaniou, G. E., & Soutschek, A. (2023) · Social Cognitive and Affective Neuroscience · doi:10.1093/scan/nsad061 · Cited by 14
“Re-computing this GLMM revealed that, contrary to the original GLMM results, the effect of tACS theta-sham on inequity aversion no longer passed the statistical threshold, tACS theta-sham ×Inequity absolute : HDI mean = −0,89, HDI 95% = [−1.95, 0.08].”
Influential
Accurate digital quantification of tau pathology in progressive supranuclear palsy
Pansuwan, T., Quaegebeur, A., Kaalund, S. S., Hidari, E., Briggs, M., Rowe, J. B., & Rittman, T. (2023) · Acta Neuropathologica Communications · doi:10.1186/s40478-023-01674-y · Cited by 13
“…of the balanced random forest were tuned using a random-search with the following parameter space: n_features_to_select = [28, 30, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54] (number of features to select) , n_estimators = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000] (number…”
MethodInfluential
Equilibrium Mechanical Properties of the Nonhuman Primate Cervix
Fang, S., Shi, L. T., Vink, J., Feltovich, H. M., Hall, T. J., & Myers, K. M. (2024) · Journal of Biomechanical Engineering · doi:10.1115/1.4064558 · Cited by 13
Replication of null results: Absence of evidence or evidence of absence?
Pawel, S., Heyard, R., Micheloud, C., & Held, L. (2024) · eLife · doi:10.7554/elife.92311.3 · Cited by 13
Timbre Preferences in the Context of Mixing Music
Dobrowohl, F. A., Milne, A. J., & Dean, R. T. (2019) · Applied Sciences · doi:10.3390/app9081695 · Cited by 13
“An Evidence Ratio of 3–10 indicates “substantial” evidence for the reported observation; Evidence Ratios of 10+ indicate strong evidence for the observation [27].”
Background
Fire-mediated germination syndromes in Leucadendron (Proteaceae) and their functional correlates
Newton, R. J., Mackenzie, B. D. E., Lamont, B. B., Barreiro, P. G., Cowling, R. M., & He, T. (2021) · Oecologia · doi:10.1007/s00442-021-04947-2 · Cited by 13
“Adapting the HDI + ROPE (Region of Practical Equivalence) decision rule (Kruschke 2018), treatment effects with 95% HDIs completely contained within the interval [-10%–10”
Method
Memory precision for salient distractors decreases with learned suppression
Won, B.-Y., Venkatesh, A., Witkowski, P. P., Banh, T., & Geng, J. J. (2021) · Psychonomic Bulletin & Review · doi:10.3758/s13423-021-01968-z · Cited by 13
“Figure 8 shows the distribution and marks the Highest Density Interval (HDI) for each group, which describes the 95%most credible values for the parameter (Kruschke, 2018).”
Background
Factors Associated With Telemedicine Use Among Patients With Rheumatic and Musculoskeletal Disease: Secondary Analysis of Data From a German Nationwide Survey
Muehlensiepen, F., Petit, P., Knitza, J., Welcker, M., & Vuillerme, N. (2023) · Journal of Medical Internet Research · doi:10.2196/40912 · Cited by 13
“This variable selection was based on the region of practical equivalence (ROPE) percentage (ROPE% ≤ 5) [18-20], and a subsequent selection was based first on the variance inflation factor (VIF) [21].”
Salmonella Prevalence Is Strongly Associated with Spatial Factors while Listeria monocytogenes Prevalence Is Strongly Associated with Temporal Factors on Virginia Produce Farms
Murphy, C. M., Weller, D. L., & Strawn, L. K. (2023) · Applied and Environmental Microbiology · doi:10.1128/aem.01529-22 · Cited by 13
“5% indicate a nonnegligible effect and values of,1% indicate a substantial effect, and Kruschke (73) states that values of,5% indicate a nonnegligible effect.”
BackgroundInfluential
Mediation analysis of conspiratorial thinking and anti-expert sentiments on vaccine willingness.
Blackburn, A. M., Han, H., Gelpí, R., Stöckli, S., Jeftić, A., Ch’ng, B., Koszałkowska, K., Lacko, D., Milfont, T. L., Lee, Y., et al. (2023) · Health Psychology · doi:10.1037/hea0001268 · Cited by 13
IQ After Pediatric Concussion
Ware, A. L., McLarnon, M. J. W., Lapointe, A. P., Brooks, B. L., Bacevice, A. M., Bangert, B. A., Beauchamp, M. H., Bigler, E. D., Björnson, B., Cohen, D. M., et al. (2023) · PEDIATRICS · doi:10.1542/peds.2022-060515 · Cited by 15
Testing the automaticity features of the affect misattribution procedure: The roles of awareness and intentionality
Kurdi, B., Melnikoff, D. E., Hannay, J. W., Korkmaz, A., Lee, K. M., Ritchie, E. G., Surdel, N., Vuletich, H. A., Xin, Y., Payne, B. K., et al. (2023) · Behavior Research Methods · doi:10.3758/s13428-023-02291-2 · Cited by 14
“Specifically, it is not statistically warranted to conclude that the null hypothesis is true (i.e., that the two versions of the AMP do not differ from each other) from a nonsignificant statistical test (Dienes, 2014; Kruschke, 2018).”
Background
Video-or text-based rubrics: What is most effective for mental model growth of complex skills within formative assessment in secondary schools?
Ackermans, K., Rusman, E., Nadolski, R. J., Specht, M. M., & Brand‐Gruwel, S. (2019) · Computers in Human Behavior · doi:10.1016/j.chb.2019.07.011 · Cited by 13
Two-Stage Collaborative Exams have Little Impact on Subsequent Exam Performance in Undergraduate Mathematics
Kinnear, G. (2021) · International Journal of Research in Undergraduate Mathematics Education · doi:10.1007/s40753-020-00121-w · Cited by 16
“Every parameter in the model has an exact credible interval” (Liddell and Kruschke 2018, p339); this enables us to look at the strength of evidence for differences between different groups of students, without needing to worry about corrections for multiple comparisons.”
BackgroundInfluential
Estimation of the sensitivity and specificity of four serum ELISA and one fecal PCR for diagnosis of paratuberculosis in adult dairy cattle in New Zealand using Bayesian latent class analysis
Bates, A., Laven, R. A., O’Brien, R., Liggett, S., & Griffin, F. (2020) · Preventive Veterinary Medicine · doi:10.1016/j.prevetmed.2020.105199 · Cited by 12
Age Differences in Everyday Emotional Experience: Testing Core Predictions of Socioemotional Selectivity Theory With the MIVA Model
Wirth, M., Voß, A., & Rothermund, K. (2023) · The Journals of Gerontology Series B · doi:10.1093/geronb/gbad033 · Cited by 13
Can low-cost, scalable, online interventions increase youth informed political participation in electoral authoritarian contexts?
Ferrali, R., Grossman, G., & Larreguy, H. (2023) · Science Advances · doi:10.1126/sciadv.adf1222 · Cited by 14
A Tutorial for Deception Detection Analysis or: How I Learned to Stop Aggregating Veracity Judgments and Embraced Signal Detection Theory Mixed Models
Zloteanu, M., & Vuorre, M. (2024) · Journal of Nonverbal Behavior · doi:10.1007/s10919-024-00456-x · Cited by 15
“Decisions about negligible effects can made on the basis of the 95% CI falling entirely within the ROPE, known as the HDI + ROPE decision rule (Kruschke, 2018), or by using the entire posterior density, known as the ROPE(100”
The political (a)symmetry of metacognitive insight into detecting misinformation.
Geers, M., Fischer, H., Lewandowsky, S., & Herzog, S. M. (2024) · Journal of Experimental Psychology General · doi:10.1037/xge0001600 · Cited by 11
Predicting Thoracic Aortic Dissection in a Diverse Biobank Using a Polygenic Risk Score
DePaolo, J. S., Zamirpour, S., Abramowitz, S. A., Biagetti, G. M., Judy, R., Beeche, C., Duda, J., Gee, J. C., Witschey, W. R. T., Chirinos, J. A., et al. (2025) · JACC Advances · doi:10.1016/j.jacadv.2025.101743 · Cited by 14
bayest: An R Package for Effect-Size Targeted Bayesian Two-Sample t-Tests
Kelter, R. (2020) · Journal of Open Research Software · doi:10.5334/jors.290 · Cited by 12
Does insufficient sleep affect how you learn from reward or punishment? Reinforcement learning after 2 nights of sleep restriction
Gerhardsson, A., Porada, D. K., Lundström, J. N., Axelsson, J., & Schwarz, J. (2020) · Journal of Sleep Research · doi:10.1111/jsr.13236 · Cited by 12
“A region of practical equivalence (ROPE) was used as proxy for the null hypothesis, with limits set to reflect half of a small effect size (Kruschke, 2018).”
Variation in Female Leverage: The Influence of Kinship and Market Effects on the Extent of Female Power Over Males in Verreaux’s Sifaka
Lewis, R. J., Bueno, G. L., & Fiore, A. D. (2022) · Frontiers in Ecology and Evolution · doi:10.3389/fevo.2022.851880 · Cited by 12
“Finally, we used an HDI + ROPE approach (Kruschke, 2015, 2018; Kruschke and Liddell, 2018) to evaluate which of our variables of interest might be considered important predictors in all of our models.”
BackgroundMethod
Simulation data for the analysis of Bayesian posterior significance and effect size indices for the two-sample t-test to support reproducible medical research
Kelter, R. (2020) · BMC Research Notes · doi:10.1186/s13104-020-05291-z · Cited by 11
Absolute ethanol intake predicts ethanol preference inDrosophila
Park, S. J., & Ja, W. W. (2020) · Journal of Experimental Biology · doi:10.1242/jeb.224121 · Cited by 12
“testing: reject H 0 if the 95% high density interval (HDI) falls completely outside the ROPE; accept H 0 “for practical purposes” if the HDI falls fully inside the ROPE; remain “undecided” otherwise (Kruschke, 2018). When there was more than an anecdotal evidence for the existence of an association (BF < 1/3 or &gt…”
Method
The Role of Sleep in the Relationship Between ADHD Symptoms and Stop Signal Task Performance
Wolff, B., Sciberras, E., He, J. L., Youssef, G. J., Anderson, V. A., & Silk, T. J. (2020) · Journal of Attention Disorders · doi:10.1177/1087054720943290 · Cited by 13
“Corrections were not made for multiple comparisons, as Bayesian analyses do not correct for other tests conducted and do not use sampling distributions; the posterior distribution is a fixed entity based on the data at hand (Kruschke, 2018).”
BackgroundMethod
Equivalence Testing and the Second Generation P-Value
Lakens, D., & Delacre, M. (2020) · Meta-Psychology · doi:10.15626/mp.2018.933 · Cited by 12
The Role of Emotion Projection, Sexual Desire, and Self-Rated Attractiveness in the Sexual Overperception Bias
Samara, I., Roth, T. S., & Kret, M. E. (2021) · Archives of Sexual Behavior · doi:10.1007/s10508-021-02017-5 · Cited by 12
“Effects were interpreted using the OR 95% highest density intervals (HDI), which summarize 95% of the posterior parameter distribution (Kruschke, 2018).”
Method
Early-Stage Alzheimer's Disease Affects Fast But Not Slow Adaptive Processes in Motor Learning
Sutter, K., Wijdenes, L. O., van Beers, R. J., Claassen, J. A. H. R., Kessels, R. P. C., & Medendorp, W. P. (2024) · eNeuro · doi:10.1523/eneuro.0108-24.2024 · Cited by 11
“We tested the ROPE for each parameter separately using the following formula (Kruschke, 2018): in which s 21 and s 22 are the variances of the posterior distributions of the two groups.”
Method
Bayesian regression modeling and inference of energy efficiency data: the effect of collinearity and sensitivity analysis
Al‐Essa, L. A., Ebrahim, E. A., & Mergiaw, Y. A. (2024) · Frontiers in Energy Research · doi:10.3389/fenrg.2024.1416126 · Cited by 11
Consonant lengthening marks the beginning of words across a diverse sample of languages
Blum, F., Paschen, L., Forkel, R., Fuchs, S. I., & Seifart, F. (2024) · Nature Human Behaviour · doi:10.1038/s41562-024-01988-4 · Cited by 11
“In the complete absence of an effect, the posterior distribution would be fully within the ROPE 37 .”
Influential
An In-Class Demonstration of Bayesian Inference
van Doorn, J. B., Matzke, D., & Wagenmakers, E. (2019) · Psychology Learning & Teaching · doi:10.1177/1475725719848574 · Cited by 11
Hormonal Contraception and Sexuality: Causal Effects, Unobserved Selection, or Reverse Causality?
Botzet, L. J., Gerlach, T. M., Driebe, J. C., Penke, L., & Arslan, R. C. (2021) · Collabra Psychology · doi:10.1525/collabra.29039 · Cited by 11

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
DOI: 10.1177/2515245918771304
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
Licence: journals.sagepub.com/page/policies/text-and-data-mining-license (tdm)
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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Rejecting or Accepting Parameter Values in Bayesian Estimation

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