Statistical tests, P values, confidence intervals, and power: a guide to misinterpretations
Open accessAbstract
Misinterpretation and abuse of statistical tests, confidence intervals, and statistical power have been decried for decades, yet remain rampant. A key problem is that there are no interpretations of these concepts that are at once simple, intuitive, correct, and foolproof. Instead, correct use and interpretation of these statistics requires an attention to detail which seems to tax the patience of working scientists. This high cognitive demand has led to an epidemic of shortcut definitions and interpretations that are simply wrong, sometimes disastrously so-and yet these misinterpretations dominate much of the scientific literature. In light of this problem, we provide definitions and a discussion of basic statistics that are more general and critical than typically found in traditional introductory expositions. Our goal is to provide a resource for instructors, researchers, and consumers of statistics whose knowledge of statistical theory and technique may be limited but who wish to avoid and spot misinterpretations. We emphasize how violation of often unstated analysis protocols (such as selecting analyses for presentation based on the P values they produce) can lead to small P values even if the declared test hypothesis is correct, and can lead to large P values even if that hypothesis is incorrect. We then provide an explanatory list of 25 misinterpretations of P values, confidence intervals, and power. We conclude with guidelines for improving statistical interpretation and reporting.
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Misuse and misinterpretation of null-hypothesis testing methods have high prevalence.
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The use of statistical methods has been demonstrated to be suboptimal in some fields.
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To curb research misreporting, replace significance and confidence by compatibility
Greenland, S., Mansournia, M. A., & Joffe, M. (2022) · Preventive Medicine · doi:10.1016/j.ypmed.2022.107127 · Cited by 115 · see citing works
Self-citationon behalf of the Participant Values Work Stream of the Global Alliance for Genomics and Health, Milne, R., Morley, K. I., Howard, H. C., Niemiec, E., Nicol, D., Critchley, C. R., Prainsack, B., Vears, D. F., Smith, J. A., et al. (2019) · Human Genetics · doi:10.1007/s00439-019-02062-0 · Cited by 114 · see citing works
Solari, S., Egüen, M., Polo, M. J., & Losada, M. Á. (2017) · Water Resources Research · doi:10.1002/2016wr019426 · Cited by 114 · see citing works
- Authors
- Greenland, S., Senn, S. J., Rothman, K. J., Carlin, J. B., Poole, C., Goodman, S. N., & Altman, D. G.
- Affiliations
- University of California, Los Angeles (US)
- Luxembourg Institute of Health (LU)
- RTI International (US)
- The University of Melbourne (AU)
- University of North Carolina at Chapel Hill (US)
- Stanford Medicine (US)
- University of Oxford (GB)
- Corresponding author
- Greenland, Sander
- ORCID
- Venue
- European Journal of Epidemiology
- Published
- 2016-04
- Volume
- 31
- Issue
- 4
- Pages
- 337-350
- ISSN
- 0393-2990 (ISSN-L)
- 1573-7284
- PMC
- PMC4877414
- OpenAlex
- W2408017125
- Cited by
- 3,200
- References
- 135
- Citations by year
- 2026: 325 · 2025: 454 · 2024: 407 · 2023: 290 · 2022: 348 · 2021: 392 · 2020: 330 · 2019: 270 · 2018: 201 · 2017: 148 · 2016: 33 · 2015: 1
- FWCI
- 220.87
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Locations
- European Journal of Epidemiology (publishedVersion, cc-by)
- Europe PMC (PubMed Central) (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- eScholarship (California Digital Library) (submittedVersion, cc-by)
- Minerva Access (University of Melbourne) (submittedVersion, cc-by)
- Funders
- Seventh Framework Programme (602552)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistics Education and Methodologies
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
- Keywords
- p-values, confidence intervals, statistical power, statistical misinterpretation, hypothesis testing, selective analysis, analysis protocol, statistical reporting guidelines, statistics education
- MeSH terms
- Data Interpretation, Statistical, Humans, Probability, Confidence Intervals
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 ›
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