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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.
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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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Cited by
Sorted by citations
Lakens, D. (2022) · Collabra Psychology · doi:10.1525/collabra.33267 · Cited by 1,962
Makowski, D., Ben-Shachar, M., & Lüdecke, D. (2019) · Journal of Open Source Software · doi:10.21105/joss.01541 · Cited by 1,483
“Such a Test for Practical Equivalence , implemented via equivalence_test() , is based on the “HDI+ROPE decision rule” (Kruschke, 2018) to check whether parameter values should be accepted or rejected against an explicitly formulated “null hypothesis” (i.e., a ROPE).”
BackgroundMethodBayesian Analysis Reporting Guidelines
Kruschke, J. K. (2021) · Nature Human Behaviour · doi:10.1038/s41562-021-01177-7 · Cited by 525
Self-citationWhy Hypothesis Testers Should Spend Less Time Testing Hypotheses
Scheel, A. M., Tiokhin, L., Isager, P. M., & Lakens, D. (2021) · Perspectives on Psychological Science · doi:10.1177/1745691620966795 · Cited by 382
“This problem is not solved with mere practice—forcing researchers to specify what would falsify their hypotheses when they have no theoretical basis for doing so can lead to testing against arbitrary values (Kruschke, 2018) and runs the risk of replacing one mindless ritual with another.”
BackgroundImproving inferences about null effects with Bayes factors and equivalence tests.
Lakens, D., McLatchie, N., Isager, P. M., Scheel, A. M., & Dienes, Z. (2020) · The Journals of Gerontology: Series B · doi:10.1093/geronb/gby065 · Cited by 279
“The TOST approach is equivalent to examining whether a 90% CI (for alpha = 0.05) around the effect falls between ΔL and ΔU, and concluding equivalence if the 90% CI does not contain either equivalence bound (Westlake, 1972; for a related Bayesian procedure, see Kruschke, 2011, 2018).”
BackgroundMethodInfluentialggdist: Visualizations of Distributions and Uncertainty in the Grammar of Graphics
Kay, M. (2023) · IEEE Transactions on Visualization and Computer Graphics · doi:10.1109/tvcg.2023.3327195 · Cited by 185
“A common procedure in Bayesian estimation is to use regions of practical equivalence ( ROPE s) [32].”
MethodDecomposing age effects in EEG alpha power
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Quittkat, H. L., Düsing, R., Holtmann, F., Buhlmann, U., Svaldi, J., & Vocks, S. (2020) · Frontiers in Psychology · doi:10.3389/fpsyg.2020.586246 · Cited by 120
GABA and glutamate deficits from frontotemporal lobar degeneration are associated with disinhibition
Murley, A. G., Rouse, M. A., Jones, P. S., Ye, R., Hezemans, F. H., O’Callaghan, C., Frangou, P., Kourtzi, Z., Rua, C., Carpenter, T. A., et al. (2020) · Brain · doi:10.1093/brain/awaa305 · Cited by 104
“The null hypotheses was rejected if the 95% highest density interval (HDI) of the ‘R’ correlation values did not overlap with the region of practical equivalence (Kruschke, 2018).”
BackgroundMethodInfluentialRousselet, G. A., Pernet, C. R., & Wilcox, R. R. (2023) · Meta-Psychology · doi:10.15626/mp.2019.2058 · Cited by 110
“…not require the bootstrap: for instance diffusion models of reaction times (Matzke & Wagenmakers, 2009; Voss et al., 2013), beta-binomial models of accuracy scores (Kr-uschke, 2014), and ordinal models of Likert scale results (Bürkner & Vuorre, 2019; Liddell & Kruschke, 2018; Taylor et al., 2022).”
MethodA Specificity Principle of Memory: Evidence From Aging and Associative Memory
Greene, N. R., & Naveh‐Benjamin, M. (2020) · Psychological Science · doi:10.1177/0956797620901760 · Cited by 96
“Because analyses were based on Bayesian posterior estimation, a formal power analysis, which is non-Bayesian by nature, was not conducted, given that evidence for a null effect is equally informative in the Bayesian framework (e.g., Kruschke, 2011, 2018).”
BackgroundMethodInfluentialGrieder, S., & Steiner, M. D. (2021) · Behavior Research Methods · doi:10.3758/s13428-021-01581-x · Cited by 111
“We defined the ROPE to be [−0.1 ∗ SDdv, 0.1 ∗ SDdv] for linear regression models and [−0.18, 0.18] for logistic regression models (in line with Makowski et al., 2019; Kruschke, 2018).”
MethodInfluentialReilly, S. K., Gosai, S. J., Gutierrez, A., Mackay-Smith, A., Ulirsch, J. C., Kanai, M., Mouri, K., Berenzy, D., Kales, S., Butler, G. M., et al. (2021) · Nature Genetics · doi:10.1038/s41588-021-00900-4 · Cited by 86
Signing at the beginning versus at the end does not decrease dishonesty
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Kelter, R. (2020) · BMC Medical Research Methodology · doi:10.1186/s12874-020-00968-2 · Cited by 100
“Kruschke JK. Bayesian estimation supersedes the t-test,.”
BackgroundInfluentialOliver, M., & Adkins, M. J. (2020) · Energy Research & Social Science · doi:10.1016/j.erss.2020.101641 · Cited by 90
Sadness, but not all negative emotions, heightens addictive substance use
Dorison, C. A., Wang, K., Rees, V. W., Kawachi, I. I., Ericson, K. M. M., & Lerner, J. S. (2019) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1909888116 · Cited by 74
“‡ We used Bayesian parameter estimation to assess whether data from study 4 strengthened the evidence from prior studies (45, 46).”
MethodEstimating the impacts of habitat loss induced by urbanization on bird local extinctions
Dri, G. F., Fontana, C. S., & Dambros, C. (2021) · Biological Conservation · doi:10.1016/j.biocon.2021.109064 · Cited by 73
Long term structural and functional neural changes following a single infusion of Ketamine in PTSD
Duek, O. A., Korem, N., Li, Y., Kelmendi, B., Amen, S. L., Gordon, C., Milne, M., Krystal, J. H., Levy, I., & Harpaz‐Rotem, I. (2023) · Neuropsychopharmacology · doi:10.1038/s41386-023-01606-3 · Cited by 75
“A difference was considered robust (i.e., signi fi cant) when the 95% High Density Interval (HDI) was excluding zero (i.e. either the interval is completely below or above zero) [65].”
BackgroundBayesian reassessment of the epigenetic architecture of complex traits
Baños, D. T., McCartney, D. L., Patxot, M., Anchieri, L., Battram, T., Christiansen, C., Costeira, R., Walker, R. M., Morris, S. W., Campbell, A., et al. (2020) · Nature Communications · doi:10.1038/s41467-020-16520-1 · Cited by 62
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“2] was selected as the region of practical equivalence (ROPE; Kruschke, 2018), as it contains all effect sizes that we deemed a priori to be practically equivalent to zero.”
MethodInfluentialEvaluating Performance and Agreement of Coronary Heart Disease Polygenic Risk Scores
Abramowitz, S. A., Boulier, K. M., Keat, K., Cardone, K. M., Shivakumar, M., DePaolo, J. S., Judy, R., Bermudez, F., Mimouni, N., Neylan, C. J., et al. (2024) · JAMA · doi:10.1001/jama.2024.23784 · Cited by 69
How to use and report Bayesian hypothesis tests.
Dienes, Z. P. (2020) · Psychology of Consciousness Theory Research and Practice · doi:10.1037/cns0000258 · Cited by 77
“The other choice is in specifying the predictions of one’s theory: What counts as a minimally interesting effect size (Kruschke, 2018)?”
BackgroundMethodInfluentialRemote Blood Oxygen Estimation From Videos Using Neural Networks
Mathew, J., Tian, X., Wong, C.-W., Ho, S., Milton, D. K., & Wu, M. H. (2023) · IEEE Journal of Biomedical and Health Informatics · doi:10.1109/jbhi.2023.3236631 · Cited by 66
“assessment of whether the results from two groups being compared have the same mean [37]–[41].”
BackgroundWilliams, Z. J., Suzman, E., Bordman, S. L., Markfeld, J. E., Kaiser, S., Dunham, K., Zoltowski, A. R., Failla, M. D., Cascio, C. J., & Woynaroski, T. G. (2022) · Journal of Autism and Developmental Disorders · doi:10.1007/s10803-022-05656-2 · Cited by 69
“We also used Bayesian inference to evaluate the interval null hypothesis that the overall summary effect was too small to be practically significant, falling within a region of practical equivalence (ROPE; Kruschke, 2018).”
MethodLionetti, F., Klein, D. N., Pastore, M., Aron, E. N., Aron, A. P., & Pluess, M. (2021) · European Child & Adolescent Psychiatry · doi:10.1007/s00787-021-01830-6 · Cited by 62
“Rumination at age 9 was associated with depression at both age 9 and 12 [B = 0.39, (0.31, 0.47), I = 1, and B = 0.22, 90% HPDI (0.13, 0.31), I = 1.00.”
MethodInfluentialKoehn, J. Z., Allison, E. H., Villeda, K. T., Chen, Z., Nixon, M., Crigler, E., Zhao, L. Z., Chow, M. I., Vaitla, B., Thilsted, S. H., et al. (2021) · Fish and Fisheries · doi:10.1111/faf.12603 · Cited by 67
Machado, A. V., Volchan, E., Figueira, I. L. D. V., Aguiar, C., Xavier, M., Souza, G. G. L., Sobral, A. P. B., Oliveira, L., & Mocaiber, I. (2020) · PLoS ONE · doi:10.1371/journal.pone.0228661 · Cited by 60
“However, the Bayesian approach used in the present study is less dependent on sample size when compared to classical tests that use p-values from null hypothesis tests [49,55].”
BackgroundMethodGiudice, N. A., Guenther, B. A., Jensen, N. A., & Haase, K. N. (2020) · Frontiers in Human Neuroscience · doi:10.3389/fnhum.2020.00087 · Cited by 60
“For noninferiority testing, only one side of the ROPE is emphasized (Kruschke, 2018).”
MethodDo voices carry valid information about a speaker’s personality?
Stern, J., Schild, C., Jones, B. C., DeBruine, L. M., Hahn, A. C., Puts, D. A., Zettler, I., Kordsmeyer, T. L., Feinberg, D. R., Zamfir, D., et al. (2021) · Journal of Research in Personality · doi:10.1016/j.jrp.2021.104092 · Cited by 59
“According to recommendations by Kruschke (2018), we focused on estimating the strength of associations between voice parameters and personality traits.”
MethodDecisions about equivalence: A comparison of TOST, HDI-ROPE, and the Bayes factor.
Linde, M., Tendeiro, J. N., Selker, R., Wagenmakers, E., & van Ravenzwaaij, D. (2021) · Psychological Methods · doi:10.1037/met0000402 · Cited by 63
effectsize: Indices of Effect Size
Ben‐Shachar, M. S., Makowski, D., Lüdecke, D., Patil, I., Wiernik, B. M., Thériault, R., & Waggoner, P. (2019) · doi:10.32614/cran.package.effectsize · Cited by 56
Maturana, F. M., Schellhorn, P., Erz, G., Burgstahler, C., Widmann, M., Munz, B., Soares, R. N., Murias, J. M., Thiel, A., & Niess, A. M. (2021) · European Journal of Applied Physiology · doi:10.1007/s00421-021-04676-7 · Cited by 56
“…of them (calculated from simulated 100 measures that spanned across all the possible ranges): where is the ∆V ̇O2max, and µ is the ∆sd. Step 3—calculate the HDI and ROPE The HDI was retrieved from each individual normal distribution, calculated as 89% of the credible interval (Kruschke 2015, 2018).”
BackgroundMethodInfluentialMahmoud, R., Casadebaig, P., Hilgert, N., Alletto, L., Freschet, G. T., de Mazancourt, C., & Gaudio, N. (2022) · Agronomy for Sustainable Development · doi:10.1007/s13593-022-00754-y · Cited by 52
“Bayesian estimation for the difference in group means (Kruschke 2018) is an alternative to the classic Student’s t test to compare the means of two groups.”
MethodMaking 'Null Effects' Informative: Statistical Techniques and Inferential Frameworks
Harms, C., & Lakens, D. (2018) · Europe PMC (PubMed Central) · doi:10.17605/osf.io/48zca · Cited by 52
Kuper, N., Kroencke, L., Harari, G. M., & Denissen, J. J. A. (2022) · Journal of Personality and Social Psychology · doi:10.1037/pspp0000438 · Cited by 55
Covariate modeling in pharmacometrics: General points for consideration
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“75,76 This convention has been borrowed from the bioequivalence context, but alternative heuristics have been proposed for establishing regions of practical equivalence that are appropriate to a given context.”
BackgroundPre‐diagnostic cognitive and functional impairment in multiple sporadic neurodegenerative diseases
Swaddiwudhipong, N., Whiteside, D. J., Hezemans, F. H., Street, D., Rowe, J. B., & Rittman, T. (2023) · Alzheimer's & Dementia · doi:10.1002/alz.12802 · Cited by 48
Drivers’ and cyclists’ safety perceptions in overtaking maneuvers
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“However, any such inferences about parameter influences need to be carefully motivated (Kruschke, 2018).”
BackgroundPerception of affect in unfamiliar musical chords
Smit, E. A., Milne, A. J., Dean, R. T., & Weidemann, G. (2019) · PLoS ONE · doi:10.1371/journal.pone.0218570 · Cited by 51
Obtaining Evidence for No Effect
Dienes, Z. P. (2021) · Collabra Psychology · doi:10.1525/collabra.28202 · Cited by 54
Casillas, J. V. (2021) · Languages · doi:10.3390/languages6010009 · Cited by 45
Kück, K., Naik, B. I., Domino, K. B., Posner, K. L., Saager, L., Stuart, A. R., Johnson, K. B., Alpert, S. B., Durieux, M. E., Sinha, A. K., et al. (2023) · Anesthesiology · doi:10.1097/aln.0000000000004510 · Cited by 45
Reconsidering the Duchenne Smile: Indicator of Positive Emotion or Artifact of Smile Intensity?
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“If desired, we can also use the HDI+ROPE decision rule to make discrete interpretations of the results [42].”
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“Here, we demonstrate Bayesian inference using an approach that combines the approach combining highest density interval (HDI) and the region of practical equivalence (ROPE; Kruschke, 2018; see Box 1).”
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Samaš, P., Hauber, M. E., & Honza, M. (2021) · Frontiers in Ecology and Evolution · doi:10.3389/fevo.2021.703208 · Cited by 43
Pick, J. L., Kasper, C., Allegue, H., Dingemanse, N. J., Dochtermann, N. A., Laskowski, K. L., Lima, M. R., Schielzeth, H., Westneat, D. F., WRIGHT, J. M., et al. (2023) · Methods in Ecology and Evolution · doi:10.1111/2041-210x.14200 · Cited by 43
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“We used methodology outlined by Kruschke (2018) and Makowski et al. (2019) to develop decision rules using Bayesian posterior probabilities as a basis to determine the statistical significance of covariates on period survival rates.”
MethodFour principles for improved statistical ecology
Popovic, G. C., Mason, T. J., Drobniak, S. M., Marques, T. A., Potts, J., Joo, R., Altwegg, R., Burns, C. C. I., Mccarthy, M. A., Johnston, A., et al. (2024) · Methods in Ecology and Evolution · doi:10.1111/2041-210x.14270 · Cited by 59
“…is the quantity of interest and must be pri - oritised in analysis and reporting, along with a discussion on how ecologically relevant the measured effect size is, which must be based on knowledge of the system (see Kruschke, 2018 , for review on meaningful effect sizes in different fields).”
BackgroundGlobal Well-Being and Mental Health in the Internet Age
Vuorre, M., & Przybylski, A. K. (2023) · Clinical Psychological Science · doi:10.1177/21677026231207791 · Cited by 39
“To determine the practical significance of the standardized associations, we report posterior probabilities that their magnitudes exceed the region of practical equivalence (ROPE) to zero ( p ROPE ; Kruschke, 2018) as defined by [ − 0.1, 0.1] (Ferguson & Heene, 2021).”
InfluentialA Bayesian Theory of Mind Approach to Nonverbal Communication
Lee, J. J., Sha, F., & Breazeal, C. (2019) · ACM/IEEE International Conference on Human-Robot Interaction (HRI) · doi:10.1109/hri.2019.8673023 · Cited by 39
“1 around the null value of zero [43].”
BackgroundNeural dynamics differentially encode phrases and sentences during spoken language comprehension
Bai, F., Meyer, A., & Martin, A. E. (2022) · PLoS Biology · doi:10.1371/journal.pbio.3001713 · Cited by 40
German Vargas, G., Kunert, N., Hammond, W. M., Berry, Z. C., Werden, L. K., Smith‐Martin, C. M., Wolfe, B. T., Toro, L., Mondragón‐Botero, A., Pinto‐Ledezma, J. N., et al. (2022) · Ecology Letters · doi:10.1111/ele.14128 · Cited by 38
“We defined the ROPE based on the variability of the response variable in question as [−0.1 * SDy, 0.1 * SDy] (Kruschke, 2018), where SDy is the standard deviation of either Ks, ΨTLP or ΨP50.”
MethodInfluentialKelter, R. (2020) · Wiley Interdisciplinary Reviews Computational Statistics · doi:10.1002/wics.1523 · Cited by 46
“Future research should consider developing new indices or investigating indices of significance or effect size already proposed in the literature, like the region of practical equivalence (ROPE) as proposed by Kruschke (2013) and Kruschke and Liddell (2018), the MAP-based p-value (Mills, 2017) and the probability of d…”
BackgroundMethodInfluentialHow do oncoming traffic and cyclist lane position influence cyclist overtaking by drivers?
Rasch, A., Boda, C.-N., Thalya, P., Aderum, T., Knauss, A., & Dozza, M. (2020) · Accident Analysis and Prevention · doi:10.1016/j.aap.2020.105569 · Cited by 34
“These differences, or contrasts, offer a way to determine the effect size and significance of a factor in a model: the 95 % highest-density interval (HDI) can be compared to a use-case-specific region of practical equivalence, typically centred around zero (Kruschke, 2018).”
BackgroundKelter, R. (2020) · Computational Statistics · doi:10.1007/s00180-020-01034-7 · Cited by 38
“A different widely used approach is based on the region of practical equivalence (ROPE), see Kruschke (2013, 2015, 2018) and also Lakens (2017) and Lakens et al. (2018).”
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Gehmacher, Q., Schubert, J., Schmidt, F., Hartmann, T., Reisinger, P., Rösch, S., Schwarz, K., Popov, T. G., Maria Chait, A., & Weisz, N. (2024) · Nature Communications · doi:10.1038/s41467-024-48126-2 · Cited by 34
“Future studies should take advantage of the fi ndings presented here and de fi ne a region of practical equivalence (ROPE) to further infer support for any potential null-hypothesis testing 48 .”
BackgroundThe effects of psychosocial stress on intergroup resource allocation
Schweda, A., Faber, N. S., Crockett, M. J., & Kalenscher, T. (2019) · Scientific Reports · doi:10.1038/s41598-019-54954-w · Cited by 39
Porumbescu, G. A., Piotrowski, S. J., & Mabillard, V. (2020) · Journal of Public Administration Research and Theory · doi:10.1093/jopart/muaa049 · Cited by 36
“Acknowledging calls to avoid discrete accept or reject decisions (Kruschke 2018) we also examine the strength of our parameter estimates (difference in means and effect size) related to these hypotheses using a Bayesian estimation strategy (Kruschke 2018).”
MethodDeterminants of Effect of Extracorporeal CO 2 Removal in Hypoxemic Respiratory Failure
Dianti, J., McNamee, J. J., Slutsky, A. S., Fan, E., Ferguson, N. D., McAuley, D. F., & Goligher, E. C. (2023) · NEJM Evidence · doi:10.1056/evidoa2200295 · Cited by 33
Dopamine regulates decision thresholds in human reinforcement learning in males
Chakroun, K., Wiehler, A., Wagner, B., Mathar, D., Ganzer, F., van Eimeren, T., Sommer, T., & Peters, J. (2023) · Nature Communications · doi:10.1038/s41467-023-41130-y · Cited by 36
Tschötschel, R., Schuck, A. R. T., Schwinges, A., & Wonneberger, A. (2021) · Journal of Environmental Psychology · doi:10.1016/j.jenvp.2021.101655 · Cited by 33
Disrupted state transition learning as a computational marker of compulsivity
Sharp, P. B., Dolan, R. J., & Eldar, E. (2021) · Psychological Medicine · doi:10.1017/s0033291721003846 · Cited by 30
“For hypothesis testing, we defined a Region Of Practical Equivalence (ROPE; Kruschke, 2018) representing the range of insignificant effect sizes, and compared it to the 95% most credible parameter values (i.e. the 95% Highest Density Intervals; HDI).”
ResultEliasen, A. U., Pedersen, C. E. T., Rasmussen, M. A., Wang, N., Soverini, M., Fritz, A., Stokholm, J., Chawes, B., Morin, A., Bork‐Jensen, J., et al. (2022) · Journal of Allergy and Clinical Immunology · doi:10.1016/j.jaci.2022.03.019 · Cited by 32
“To focus on interactions with larger effect sizes, we defined a region of practical equivalence (ROPE) to no effect between 0.91 and 1.10 on the odds ratio scale (24), and estimate the posterior probability that interactions have an effect outside this region (see supplementary methods).”
BackgroundInfluentialClaesdotter‐Knutsson, E., André, F., Fridh, M., Delfin, C., Håkansson, A., & Lindström, M. (2021) · JMIR Pediatrics and Parenting · doi:10.2196/30889 · Cited by 43
“Furthermore, the region of practical equivalence (ROPE) approach was used to determine whether an estimated difference was of practical and/or clinical importance [26].”
Projecting Flood Risk Dynamics for Effective Long‐Term Adaptation
Schoppa, L., Barendrecht, M. H., Paprotny, D., Sairam, N., Sieg, T., & Kreibich, H. (2024) · Earth s Future · doi:10.1029/2022ef003258 · Cited by 31
Unsupervised learning reveals interpretable latent representations for translucency perception
Liao, C., Sawayama, M., & Xiao, B. (2023) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1010878 · Cited by 28
Williams, Z. J., Schaaf, R. C., Ausderau, K., Baranek, G. T., Barrett, D. J., Cascio, C. J., Dumont, R. L., Eyoh, E. E., Failla, M. D., Feldman, J. I., et al. (2023) · Molecular Autism · doi:10.1186/s13229-023-00563-4 · Cited by 35
“These interval null hypotheses were assessed using a Bayesian hypothesis testing procedure based on the region of practical equivalence (ROPE [136]) and the ROPE Bayes factor ( BF ROPE [141–143]).”
MethodExploration of a novel virtual environment improves memory consolidation in ADHD
Baumann, V., Birnbaum, T., Breitling-Ziegler, C., Tegelbeckers, J., Dambacher, J., Edelmann, E., Bergado-Acosta, J. R., Flechtner, H., & Krauel, K. (2020) · Scientific Reports · doi:10.1038/s41598-020-78222-4 · Cited by 33
Exploring the relationship between anthropomorphism and theory‐of‐mind in brain and behaviour
Hortensius, R., Kent, M., Darda, K. M., Jastrzab, L. E., Koldewyn, K., Ramsey, R., & Cross, E. S. (2021) · Human Brain Mapping · doi:10.1002/hbm.25542 · Cited by 34
“In addition, similar to Experiment 1, we used the HDI of the posterior distribution and a ROPE around the null decision rule (Kruschke, 2018).”
BackgroundMethodInfluentialTsirgiotis, J. M., Young, R. L., & Weber, N. (2021) · Journal of Autism and Developmental Disorders · doi:10.1007/s10803-021-05300-5 · Cited by 22
“For differences between two proportions, log odds ratios (LORs) are reported.”
MethodInfluentialWiebels, K., Addis, D. R., Moreau, D., van Mulukom, V., Onderdijk, K. E., & Roberts, R. P. (2020) · Journal of Experimental Psychology Learning Memory and Cognition · doi:10.1037/xlm0000831 · Cited by 29
Angelakis, S., Weber, N., & Nixon, R. D. V. (2020) · Journal of Anxiety Disorders · doi:10.1016/j.janxdis.2020.102324 · Cited by 30
The effects of divided attention at encoding on specific and gist-based associative episodic memory
Greene, N. R., & Naveh‐Benjamin, M. (2021) · Memory & Cognition · doi:10.3758/s13421-021-01196-9 · Cited by 29
“Following the approach to parameter interpretation advocated by Kruschke (2011, 2018), we specified a region of practical equivalence (ROPE) around 0.”
BackgroundMethodInfluentialDynamic associations between glucose and ecological momentary cognition in Type 1 Diabetes
Hawks, Z., Beck, E. D., Jung, L., Fonseca, L. M., Sliwinski, M. J., Weinstock, R. S., Grinspoon, E. A., Xu, I., Strong, R. W., Singh, S. M., et al. (2024) · npj Digital Medicine · doi:10.1038/s41746-024-01036-5 · Cited by 27
“Variation was operationalized with respect to the tau matrix and quanti fi ed using the test for practical equivalence with region bounds 0 ; 0 : 2 (cid:2) SD y h i 91,92 .”
Widespread cryptic variation in genetic architecture between the sexes
van der Bijl, W., & Mank, J. E. (2021) · Evolution Letters · doi:10.1002/evl3.245 · Cited by 28
Han, H. (2022) · Epidemiology and Infection · doi:10.1017/s0950268822000255 · Cited by 26
“In this context, a ROPE means a range of a parameter of interest that shall be considered practically near-zero or trivial [34].”
BackgroundResultInfluentialG-matrix stability in clinally diverging populations of an annual weed
Henry, G. A., & Stinchcombe, J. R. (2022) · Evolution · doi:10.1093/evolut/qpac005 · Cited by 27
Svärd, M., Bärgman, J., & Victor, T. (2020) · Accident Analysis & Prevention · doi:10.1016/j.aap.2020.105853 · Cited by 32
“The ROPE is a range of values that can be considered equivalent for practical purposes (Kruschke, 2018) and was here ́a priori set to +/- 100 ms (for this type of analysis – decided in workshop with experts not having seen the study results before the decision of ROPE).”
BackgroundThe impact of biological sex on alternative splicingPreprint
Karlebach, G., Veiga, D. F. T., Mays, A. D., Chatzipantsiou, C., Barja, P. P., Chatzou, M., Kesarwani, A. K., Daniš, D., Kararigas, G., Zhang, X., et al. (2018) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/490904 · Cited by 28
How do drivers overtake pedestrians? Evidence from field test and naturalistic driving data
Rasch, A., Panero, G., Boda, C.-N., & Dozza, M. (2020) · Accident Analysis & Prevention · doi:10.1016/j.aap.2020.105494 · Cited by 26
“According to the methods for Bayesian hypothesis testing proposed by Kruschke (2018), only if the HDI falls completely outside of the ROPE can the null hypothesis be rejected, and only if the HDI falls completely inside the ROPE can the null hypothesis be accepted.”
MethodResultOberleitner, F., Hartmann, H., Hasibeder, R., Huang, J., Losso, A., Mayr, S., Oberhuber, W., Wieser, G., & Bahn, M. (2022) · Plant Cell & Environment · doi:10.1111/pce.14369 · Cited by 26
Improving Inferences about Null Effects with Bayes Factors and Equivalence TestsPreprint
Lakens, D., McLatchie, N. M., Isager, P. M., Scheel, A. M., & Dienes, Z. P. (2018) · doi:10.31234/osf.io/qtzwr · Cited by 35
Sokolovič, L., Hofmann, M., Mohammad, N., & Kukolja, J. (2023) · Frontiers in Aging Neuroscience · doi:10.3389/fnagi.2023.1267434 · Cited by 33
“Since we want to formulate suggestions for clinical practice, we also define the region of practical equivalence (Kruschke, 2018) as the interval between − 1.7 and 1.7 Hedges’ g .”
MethodInfluentialLiao, J., Midya, V., & Berg, A. S. (2019) · The American Statistician · doi:10.1080/00031305.2019.1701550 · Cited by 25
“Alternatively, Krushke and others (Freedman, Lowe, and Macaskill 1984; Hobbs and Carlin 2007; Carlin and Louis 2008; Edwards and Berry 2010; Kruschke 2011, 2013, 2014, 2018) have championed a procedure called region of practical equivalence (ROPE), in which 0 = {θ : ‖θ − θ0‖ ≤ δ} is treated as a…”
BackgroundMethodFacial first impressions form two clusters representing approach-avoidance
Jones, A. L., & Kramer, R. S. S. (2021) · Cognitive Psychology · doi:10.1016/j.cogpsych.2021.101387 · Cited by 26
The effect of sleep deprivation on objective and subjective measures of facial appearance
Holding, B. C., Sundelin, T., Cairns, P., Perrett, D. I., & Axelsson, J. (2019) · Journal of Sleep Research · doi:10.1111/jsr.12860 · Cited by 25
“When analysing subjective ratings of health, fatigue and paleness of the images as the response variables, ordinal models were used because Likert‐type scales cannot be assumed to be interval data (Liddell & Kruschke, 2018).”
MethodInfluentialSelective and deferred treatment of clinical mastitis in seven New Zealand dairy herds
Bates, A., Laven, R. A., Bork, O., Hay, M., McDowell, J., & Saldias, B. (2020) · Preventive Veterinary Medicine · doi:10.1016/j.prevetmed.2020.104915 · Cited by 25
Perceived Emotions of Harmonic Cadences
Smit, E. A., Dobrowohl, F. A., Schaal, N. K., Milne, A. J., & Herff, S. A. (2020) · Music & Science · doi:10.1177/2059204320938635 · Cited by 26
“Evidence for the tested hypotheses will be qualified by the guidelines proposed by Jeffreys (1998) as cited by Kruschke (2018): 1.”
Social norms in adolescent risk engagement and recommendation
Ciranka, S., & van den Bos, W. (2021) · British Journal of Developmental Psychology · doi:10.1111/bjdp.12369 · Cited by 24
The human factor: Weather bias in manual lake water quality monitoring
Rand, J. M., Nanko, M. O., Lykkegaard, M. B., Wain, D., King, D. W., Bryant, L. D., & Hunter, A. J. (2022) · Limnology and Oceanography Methods · doi:10.1002/lom3.10488 · Cited by 24
“To evaluate the significance of the Bayesian results, we report the Region of Practical Equivalence (ROPE), which is broadly the Bayesian equivalent of a p-value (Kruschke 2018).”
MethodKelter, R. (2021) · BMC Medical Research Methodology · doi:10.1186/s12874-021-01341-7 · Cited by 25
“Second, the proposals based on the region of practical equivalence (ROPE) made by Kruschke [36, 58], Kruschke and Liddell [22] and Kelter [32] are outlined.”
BackgroundMethodInfluentialPuri, R., & Hinder, M. R. (2021) · Neuropsychologia · doi:10.1016/j.neuropsychologia.2021.108120 · Cited by 23
Early nest initiation and vegetation density enhance nest survival in Wild Turkeys
Keever, A. C., Collier, B. A., Chamberlain, M. J., & Cohen, B. S. (2022) · The Auk · doi:10.1093/ornithology/ukac050 · Cited by 23
Insect community structure covaries with host plant chemistry but is not affected by prior herbivory
Visakorpi, K., Riutta, T., Martínez-Bauer, A. E., Salminen, J., & Gripenberg, S. (2019) · Ecology · doi:10.1002/ecy.2739 · Cited by 23
Richter, T., Geres, L. S., König, S., Braziunas, K. H., Senf, C., Thom, D., Bässler, C., Müller, J. C., Seidl, R., & Seibold, S. (2024) · Communications Biology · doi:10.1038/s42003-024-07239-6 · Cited by 22
“The ROPE percentage indicates the proportion of the 95% HDI within this area, which here is de fi ned as a range from – 0.1 * SD y to 0.1 * SD y 90 .”
InfluentialHuang, X., & Xu, S. (2025) · NeuroImage · doi:10.1016/j.neuroimage.2025.121542 · Cited by 25
Williams, Z. J., Barnett, H., & Szigeti, B. (2026) · JAMA Psychiatry · doi:10.1001/jamapsychiatry.2025.4809 · Cited by 24
New relevance and significance measures to replace p-values
Stahel, W. A. (2021) · PLoS ONE · doi:10.1371/journal.pone.0252991 · Cited by 24
“” [7] I come back to these concepts in Section 2.”
BackgroundMethodResultInfluentialNishihama, Y., Nakayama, S. F., & Tabuchi, T. (2022) · Environment International · doi:10.1016/j.envint.2022.107560 · Cited by 22
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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