The DOI matches its Crossref record; 51 of the 51 references it cites were found in a registry or an index.
Rejecting or Accepting Parameter Values in Bayesian Estimation
Open accessAbstract
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.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The cited source says what the claim attributes to it.
In the citing paper
“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”
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
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
Cited by
Sorted by citations
Items 701–742 of 742
Bergqvist, E. (2026) · Frontiers in Psychology · doi:10.3389/fpsyg.2026.1852588
“ROPE defines a range of values considered practically negligible, and the proportion of the posterior distribution within this range was used to evaluate the practical relevance of effects (Kruschke, 2018).”
Psilocybin’s kinematic effect on manual dexterity
Klintefors, P., Bhagavan, C., Kanaan, R., Bryson, A., Berlowitz, D. J., Attard, Z., & Carter, O. L. (2026) · Psychopharmacology · doi:10.1007/s00213-026-07106-8
Digital N ‐of‐1 trials and their application in experimental physiology
Konigorski, S., Ried‐Larsen, M., & Schmid, C. H. (2026) · Experimental Physiology · doi:10.1113/ep092753
“This is similar to the region of practical equivalence (ROPE) that has been suggested as a way to judge the strength of an effect (Kruschke, 2018).”
Pre-shot strategy selection and scoring performance in golf
Ai, G., Liang, T., Wang, X., Zhou, Z., Tian, H., Zhao, S., Liang, Z., Du, S., & Ning, Z. (2026) · Frontiers in Psychology · doi:10.3389/fpsyg.2026.1838440
“For the between-player effect, a Region of Practical Equivalence (ROPE) analysis was conducted using the interval [ − 0.10, 0.10] (Kruschke, 2018, 2021).”
Influentialda Silva, A. M. P., Santos, D. H., Lima, D. D. S., Cardoso, L. J. C., Moura, C. B., Høilund‐Carlsen, P. F., Perry, G. L., Kishi, T., Barbosa, B. J. A. P., & Anghinah, R. (2026) · American Journal of Geriatric Psychiatry · doi:10.1016/j.jagp.2026.06.014
Xu, Y., Webb, J. A., & Bovill, W. D. (2026) · Population Ecology · doi:10.1002/1438-390x.70026
“We considered populations to have reached a stationary phase when at least 95% of the posterior distribution was within the ROPE (Kruschke 2018).”
Sweetman, J., & McManus, R. M. (2026) · Journal of Experimental Social Psychology · doi:10.1016/j.jesp.2026.104972
WSPsignal: Weibull Shape Parameter Tests for Signal Detection
Dyck, J., & Sauzet, O. (2026) · doi:10.32614/cran.package.wspsignal
Drivers of Attrition in the First Year of College: A Bayesian Modeling Approach
Lauría, E. J. M. (2026) · SN Computer Science · doi:10.1007/s42979-026-05195-y
“The ROPE was set to [−0.2, 0.2], as recommended for binary logistic regression with both binary and z-score scaled numeric predictors [61].”
InfluentialCastro, L. A. V., Castillo-Aguilar, M., Águila, J. A. P., & Núñez-Espinosa, C. A. (2026) · Frontiers in Education · doi:10.3389/feduc.2026.1788944
Torenvliet, C., Bertens, D., Oosterman, J. M., & Wiegand, I. (2026) · Personality and Individual Differences · doi:10.1016/j.paid.2026.114011
Delem, M., Mas, M., Luminet, O., Plancher, G., & Ruby, P. M. (2026) · Peer Community Journal · doi:10.24072/pcjournal.772
“…finding, using a different mechanism: rather than a fixed group boundary at VVIQ = 16, it estimates a single breakpoint freely from the data, seeded (but not fixed) by a fast, frequentist spline search (via the earth package, Milborrow S. Derived from mda:mars by T. Hastie and R. Tibshi-rani., 2018).”
InfluentialNielsen, A. L., Jespersen, L., Bjørndal, J. R., Christiansen, L., Karabanov, A. N., & Lundbye‐Jensen, J. (2026) · The Journal of Physiology · doi:10.1113/jp291217
“…that are practically negligible in this context, that is, clearly smaller than the typical magnitude of tDCS effects reported in meta-analytic work on motor learning ( ≈ 0.2–0.4 SMD) (Nielsen, Gad et al., 2025) and consistent with suggested boundaries for negligible effects (Kruschke, 2018).”
InfluentialKühlwein, F., Merk, S., Schneider, J., & Schmidt, K. (2026) · Learning and Instruction · doi:10.1016/j.learninstruc.2026.102427
KilonovaSCORER : Prior-predictive Scoring of Kilonovae for Real-time Multimessenger Follow-up
Darc, P., & Kilpatrick, C. D. (2026) · Publications of the Astronomical Society of the Pacific · doi:10.1088/1538-3873/ae8e00
Fu, Y., Jan-Cordón, D. E., Margaretto, B. B., Wang, H., & Domı́nguez, A. (2026) · Cortex · doi:10.1016/j.cortex.2026.07.006
Fatty acid composition and climate change: A long-term analysis in Italian extra virgin olive oils
Taiti, C., Chatzievangelou, D., Spinelli, G., Masi, E., Fiorino, P., Marone, E., Costa, C., & Mancuso, S. (2026) · Journal of Food Composition and Analysis · doi:10.1016/j.jfca.2026.109421
van den Dorpel, W. M., Alink, L. R. A., Schuengel, C., Rozema, L. J., Rippe, R. C. A., van der Voort, A., & van der Asdonk, S. (2026) · Infant Mental Health Journal · doi:10.1002/imhj.70114
“To interpret the substantive meaning of the posterior regression coefficient a Region of Practical Equivalence (ROPE) was defined, which ranged from − .10 to .10 (Kruschke, 2018).”
Guerra, E., Semmelhack, E. A., Schacht, A., & Prilla, M. (2026) · Mensch und Computer (MuC) · doi:10.1145/3820253.3820271
“In accordance with the ROPE-only rule [24], conditions were considered practically equivalent if at least 95% of the posterior distribution falls within our predefined ROPE.”
InfluentialGuerra, E., Söhngen, Y. N., & Prilla, M. (2026) · Mensch und Computer (MuC) · doi:10.1145/3820253.3820273
“According to the ROPE-only rule by Kruschke [23], conditions were considered practically equivalent if the at least 95% of that computed posterior distribution falls within our predefined ROPE.”
Habacha, H. (2026) · Current Psychology · doi:10.1007/s12144-026-09956-z
“…posterior distribution falling within a pre-specified range of values considered negli - gible or too small to be of any practical relevance (ROPE; Kruschke, 2018, 2021). the ROPE (full) was used (rather than Bayes factors) because it is preferred with uninforma-tive priors and limited prior…”
Speakers Use Indirect Language to Pursue Their Own Goals While Managing Social Relationships
Gotzner, N., & Scontras, G. (2026) · Open Mind · doi:10.1162/opmi.a.388
“If the 95% credible interval includes zero under the posterior distribution, then we consider zero to be within the range of credible values given the model, the data, and our assumptions (Gelman et al., 1995; Kruschke, 2018).”
Action Framing Modulates the Pavlovian Bias in Go and No-Go Learning
Chen, Z., & Braem, S. (2026) · Psychological Science · doi:10.1177/09567976261471405
“To provide additional insight into practical equivalence, we defined a region of practical equivalence (ROPE) for each outcome measure (Kruschke, 2018).”
Publisher coverage bias in the Stanford/Ioannidis “top 2% of scientists” rankings
Lipo, C. P., DiNapoli, B., & Andrus, B. (2026) · Scientometrics · doi:10.1007/s11192-026-05789-6
“We follow the Bayesian equivalence-testing framework of Kruschke (2018): an effect is judged practically equivalent to zero when at least 95% of its posterior falls within the ROPE.”
InfluentialA Bayesian framework for multivariate differential analysis
Chion, M., & Leroy, A. (2026) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1014637
“Any reporting threshold should therefore be chosen in light of the scientific objective and a practically relevant effect size, in a way that is conceptually related to ROPE-style decision rules [34], although we do not use it here as a strict binary testing device.”
Estimation of fuzzy hazard rates from two exponential populations with an unknown common location
Sahoo, K. S., Mahapatra, A. K., & Sahoo, A. (2026) · Research in Mathematics · doi:10.1080/27684830.2026.2727394
Ogata, K. (2026) · Criminal Psychology Science and Practice · doi:10.65603/cpsp01030003
Is Bad Luck Unfair? Children’s and Adults’ Judgments of Non-Agentic InequalityPreprint
Zeng, N., & Bloom, P. (2026) · SSRN Electronic Journal · doi:10.2139/ssrn.7450760
Gillies, N., Phillips, R. A., Weimerskirch, H., Potts, J. R., Réale, D. J. F., Wilson, A. J., Angelier, F., Barbraud, C., Bennison, A., Delord, K., et al. (2026) · Journal of Animal Ecology · doi:10.1111/1365-2656.70350
Recovering subjective probability distributions: a Bayesian approach
Harrison, G. W., Monroe, B. A., & Ulm, E. R. (2026) · Experimental Economics · doi:10.1017/eec.2026.10057
Blondé, P., Ribeiro, N., Quaglino, V., & Sperduti, M. (2026) · Psychological Research · doi:10.1007/s00426-026-02387-2
“…(i.e. if the effect can be considered negligible or not) by report - ing the percentage of the posterior distribution that is over-lapping with the Region Of Practical Equivalence (ROPE; an interval where values can be considered equal to 0, see Kruschke, 2018; Kruschke & Liddell, 2018).”
InfluentialTu, S.-P., Sewell, D. K., Garcia, B., Stoddard-O'Neill, Q., Hogarth, M. A., Shuffler, M. L., Boussina, A. E., Chew, H. K., Cooke, D. T., Romano, P. S., et al. (2026) · medRxiv · doi:10.64898/2026.09.22.26362777
A beta way: A tutorial on Bayesian beta regression for psychological research
Geller, J., Kubinec, R., Parlett-Pelleriti, C., & Vuorre, M. (2026) · Behavior Research Methods · doi:10.3758/s13428-026-03106-w
“As a rule of thumb (see Kruschke, 2018), an effect may be considered practically equivalent to the negligible range when more than 95% of the posterior distribution lies within the ROPE, whereas it may be considered meaningfully different when less than 5% lies within the ROPE.”
Inferring gene expression profiles of tumor clones
Shafighi, S., Jurzysta, B., & Szczurek, E. (2026) · Bioinformatics · doi:10.1093/bioinformatics/btag717
“For each gene g and each pair of clones ð k 1 ; k 2 Þ , we assess differential expression on the log2 fold-change scale using the Highest Density Interval plus Region of Practical Equivalence (HDI+ROPE) criterion (Kruschke 2018).”
Mirza, A. B., Georgiannakis, A., Rashed, S., Priestley, J., Fayez, F., Lam, P. Y., Vastani, A., Simon, N., Zahid, S., Chowdhury, Y. A., et al. (2026) · Brain and Spine · doi:10.1016/j.bas.2026.107467
Schulze, J. B., Plambeck, M., Staindl, M., von Känel, R., & Euler, S. (2026) · Research Square · doi:10.21203/rs.3.rs-10221296/v1
The Influence of Age and Native Language Prosody on the Perception of Czech Word Stress
Tymbay, A. A. (2026) · Journal of Monolingual and Bilingual Speech · doi:10.3138/jmbs-2025-0016
Aslan, H. (2026) · Behavioral Sciences · doi:10.3390/bs16101904
“We defined a region of practical equivalence of |beta| 0.05 for standardised indirect associations and report the proportion of the posterior falling inside it (Kruschke, 2018).”
InfluentialFrick, A., Blest‐Hopley, G., Grin, M., Erritzøe, D., Nutt, D., & Carhart-Harris, R. L. (2026) · Psychopharmacology · doi:10.21203/rs.3.rs-9880403/v1
Corpuz, R., & Shah, A. (2026) · Psychoneuroendocrinology · doi:10.1016/j.psyneuen.2026.108058
Cognitive dormancy: Supplanting structured learning with AI affordances
Braun, V. (2026) · Computers in Human Behavior Artificial Humans · doi:10.1016/j.chbah.2026.100406
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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
