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Semantic and cognitive tools to aid statistical science: replace confidence and significance by compatibility and surprise
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BACKGROUND: Researchers often misinterpret and misrepresent statistical outputs. This abuse has led to a large literature on modification or replacement of testing thresholds and P-values with confidence intervals, Bayes factors, and other devices. Because the core problems appear cognitive rather than statistical, we review some simple methods to aid researchers in interpreting statistical outputs. These methods emphasize logical and information concepts over probability, and thus may be more robust to common misinterpretations than are traditional descriptions. METHODS: (p), to provide a measure of the information supplied by the testing procedure, and to help calibrate intuitions against simple physical experiments like coin tossing. We also use tables or graphs of test statistics for alternative hypotheses, and interval estimates for different percentile levels, to thwart fallacies arising from arbitrary dichotomies. Finally, we reinterpret P-values and interval estimates in unconditional terms, which describe compatibility of data with the entire set of analysis assumptions. We illustrate these methods with a reanalysis of data from an existing record-based cohort study. CONCLUSIONS: In line with other recent recommendations, we advise that teaching materials and research reports discuss P-values as measures of compatibility rather than significance, compute P-values for alternative hypotheses whenever they are computed for null hypotheses, and interpret interval estimates as showing values of high compatibility with data, rather than regions of confidence. Our recommendations emphasize cognitive devices for displaying the compatibility of the observed data with various hypotheses of interest, rather than focusing on single hypothesis tests or interval estimates. We believe these simple reforms are well worth the minor effort they require.
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![Fig. 2 P-Values for a range of hazard ratios (HR). A compatibility graph in which P-values are plotted across alternative hazard ratios. Computed from results in Brown et al. [34]. Compatibility intervals (CI) in percents can be read moving from the right-hand axis to the bottom (HR) axis. HR = 1 represents no association](/paper-figures/7a7850289c7f4ae8bd0a22de9b383544/semantic-and-cognitive-tools-to-aid-statistical-science-replace-confidence-and-figure-2.jpg)
![Fig. 3 S-Values (surprisals) for a range of hazard ratios (HR). An information graph in which S-values are plotted across alternative hazard ratios. Computed from results in Brown et al. [34]. HR = 1 represents no association](/paper-figures/485567a53edd49018a56a85dfbf519b6/semantic-and-cognitive-tools-to-aid-statistical-science-replace-confidence-and-figure-3.jpg)
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“The 95 % CIs[13,14] calculated are therefore only approximate because we do not know which patients had multiple events.”
From Serious adverse events of special interest following mRNA COVID-19 vaccination in randomized trials in adults (2022) · cites this paper as [14]
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Metadata
- Authors
- Rafi, Z., & Greenland, S.
- Affiliations
- NYU Langone Health (US)
- University of California, Los Angeles (US)
- Corresponding author
- Rafi, Zad
- Venue
- BMC Medical Research Methodology
- Published
- 2020-09-30
- Volume
- 20
- Issue
- 1
- Pages
- 244-244
- ISSN
- 1471-2288 (ISSN-L)
- PMC
- PMC7528258
- OpenAlex
- W2974063679
- Cited by
- 243
- References
- 97
- Citations by year
- 2026: 14 · 2025: 46 · 2024: 45 · 2023: 51 · 2022: 52 · 2021: 31 · 2020: 3
- FWCI
- 5.56
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- BMC Medical Research Methodology (publishedVersion, cc-by)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- arXiv (Cornell University)
- Zenodo (CERN European Organization for Nuclear Research) (cc-by)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Physical Sciences › Mathematics › Statistics and Probability › Statistics Education and Methodologies
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Keywords
- p-value interpretation, surprise, statistical misinterpretation, confidence intervals, Bayes factor, statistical reporting, cognitive tools, statistics education, hypothesis testing
- MeSH terms
- Bayes Theorem, Cognition, Humans, Probability, Semantics, Cohort Studies, Confidence Intervals
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