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Cited by 247Statistical Methods in EpidemiologyStatistics Education and MethodologiesStatistical Methods and Bayesian Inference

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Semantic and cognitive tools to aid statistical science: replace confidence and significance by compatibility and surprise

Open access
Rafi, Zad, Greenland, Sander·2020·BMC Medical Research Methodology
DOI 10.1186/s12874-020-01105-9PMC PMC7528258
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Abstract

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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Crossref · 10.1186/s12874-020-01105-9

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Fig. 1 Comparison of P-value and S-value scales. Top labels: Data compatibility with test model as measured by P-values. Bottom labels: Information against test model as measured by S-values
Fig. 1 Comparison of P-value and S-value scales. Top labels: Data compatibility with test model as measured by P-values. Bottom labels: Information against test model as measured by S-valuesCC BY · PubMed Central
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
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 associationCC BY · PubMed Central
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
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 associationCC BY · PubMed Central

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Citations

Cites

Research works printed but not linked: 6

  1. Tyler RW. What is statistical significance? Educ Res Bull. 1931;10:115–42.
  2. Cole SR, Edwards JK, Greenland S. Surprise! Am J Epidemiol. 2020; doi: https://doi.org/10/gg63md.
  3. Stigler SM. Attempts to Revive the Binomial. In: The history of statistics: the measurement of uncertainty before 1900: Harvard University Press; 1986. https://books.google.com/books?id=M7yvkERHIIMC.
  4. Rothman KJ, Greenland S, Lash TL. Precision and statistics in epidemiologic studies. In: Rothman KJ, Greenland S, Lash TL, editors. Modern Epidemiology. 3rd edition: Lippincott Williams & Wilkins; 2008. p. 148–67. https://books.google.com/books/about/Modern_Epidemiology.html?id=Z3vjT9ALxHUC.
  5. Greenland S, Rothman KJ. Fundamentals of epidemiologic data analysis. In: Rothman KJ, Greenland S, Lash TL, editors. Modern Epidemiology. 3rd edition: Lippincott Williams & Wilkins; 2008. p. 213–37. https://books.google.com/books/about/Modern_Epidemiology.html?id=Z3vjT9ALxHUC.
  6. Cox DR, Hinkley DV. Chapter 3, pure significance tests. In: Theoretical Statistics: Chapman and Hall/CRC; 1974. p. 64–87. https://doi.org/10.1201/b14832. · DOI

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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
ORCID
Venue
BMC Medical Research Methodology
Publisher
Springer Science and Business Media LLC
Published
2020-09-30
Volume
20
Issue
1
Pages
244-244
ISSN
1471-2288 (ISSN-L)
DOI
10.1186/s12874-020-01105-9
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
Licence
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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