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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“The ± 0.18 ROPE range is appropriate for logistic models, as it corresponds to an odds ratio of approximately 1.20, equivalent to a negligible effect size (Kruschke, 2018; Kruschke & Liddell, 2018).”
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“If an effect falls within the range [–γ; γ] (region of practical equivalence (ROPE)) with a probability higher than 95%, the null hypothesis that the effect is absent is accepted [9, 22], suggesting practical equivalence of local neuronal activity for the samples compared.”
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“The model also confirmed that there was no effect of experiment, since all 95% credible intervals included 0, and all effect sizes were small (Cohen’s d minimally 0.061, maximally 0.168), and all 95% credible intervals overlapped with a ROPE (region of practical equivalence; Kruschke, 2018) defined to include all effe…”
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“Within the current study, this was set as ± 5% of the standard deviation (SD)(Kruschke 2018).”
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“We tested the ROPE for each parameter separately using the formula (Kruschke, 2018): ROPE = ±0.1�(𝜎𝜎 + 𝜎𝜎 )/2 in which and are the variances of the posterior distributions of the two groups.”
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“…of such a statistical estimate: whether a p-value is smaller than 5% or a 95% confidence/credible interval does not include zero to reject the null hypothesis; and whether the size of a causal effect is substantively significant to indicate practical relevance (Gross 2015; Kruschke 2018).”
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“In instances with more than 5% of the 95% HDI within the ROPE, we accepted the alternative hypothesis if the 95% HDI did not contain the null value (center of the ROPE or zero) (Kruschke, 2018).”
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“Kruschke (2018) recommended the following heuristics for interpreting the ROPE: Accept the null hypothesis when the posterior proportions are 1, reject it when the proportions are 0, and refrain from making a decision for practical purposes (because of the uncertainty in the data) when the…”
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“The ROPE region of (0.”
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“In interpreting the effects, we established a region of practical equivalence (ROPE) of ± 0.05 around the point null value 0, which is a region/interval that is practically equivalent to zero (Kruschke, 2018).”
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“…the region of practical equivalence (ROPE), set to [−0.1, 0.1], where values were interpreted as >99% negligible (null hypothesis acceptance), >97.5% probably negligible, 2.5%-97.5% undecided significance, 2.5% probably significant, and 1% significant (null hypothesis rejection) (Kruschke, 2018).”
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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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