title: Statistical tests, P values, confidence intervals, and power: a guide to misinterpretations.
abstract: 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.
authors.affiliation: Department of Epidemiology and Department of Statistics, University of California, Los Angeles, CA, USA. lesdomes@ucla.edu.
authors.forename: Sander
authors.initials: S
authors.lastname: Greenland
authors.affiliation: Competence Center for Methodology and Statistics, Luxembourg Institute of Health, Strassen, Luxembourg.
authors.forename: Stephen J
authors.initials: SJ
authors.lastname: Senn
authors.affiliation: RTI Health Solutions, Research Triangle Institute, Research Triangle Park, NC, USA.
authors.forename: Kenneth J
authors.initials: KJ
authors.lastname: Rothman
authors.affiliation: Clinical Epidemiology and Biostatistics Unit, Murdoch Children's Research Institute, School of Population Health, University of Melbourne, Melbourne, VIC, Australia.
authors.forename: John B
authors.initials: JB
authors.lastname: Carlin
authors.affiliation: Department of Epidemiology, Gillings School of Global Public Health, University of North Carolina, Chapel Hill, NC, USA.
authors.forename: Charles
authors.initials: C
authors.lastname: Poole
authors.affiliation: Meta-Research Innovation Center, Departments of Medicine and of Health Research and Policy, Stanford University School of Medicine, Stanford, CA, USA.
authors.forename: Steven N
authors.initials: SN
authors.lastname: Goodman
authors.affiliation: Centre for Statistics in Medicine, Nuffield Department of Orthopaedics, Rheumatology and Musculoskeletal Sciences, University of Oxford, Oxford, UK.
authors.forename: Douglas G
authors.initials: DG
authors.lastname: Altman
mesh_terms: D016001:Confidence Intervals; D003627:Data Interpretation, Statistical; D006801:Humans; D011336:Probability
keywords: Confidence intervals; Hypothesis testing; Null testing; P value; Power; Significance tests; Statistical testing