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Statistical tests, P values, confidence intervals, and power: a guide to misinterpretations

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      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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      Most cited references 130

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          The earth is round (p < .05).

           Jacob Cohen V (1994)

            Author and article information

            [ ]Department of Epidemiology and Department of Statistics, University of California, Los Angeles, CA USA
            [ ]Competence Center for Methodology and Statistics, Luxembourg Institute of Health, Strassen, Luxembourg
            [ ]RTI Health Solutions, Research Triangle Institute, Research Triangle Park, NC USA
            [ ]Clinical Epidemiology and Biostatistics Unit, Murdoch Children’s Research Institute, School of Population Health, University of Melbourne, Melbourne, VIC Australia
            [ ]Department of Epidemiology, Gillings School of Global Public Health, University of North Carolina, Chapel Hill, NC USA
            [ ]Meta-Research Innovation Center, Departments of Medicine and of Health Research and Policy, Stanford University School of Medicine, Stanford, CA USA
            [ ]Centre for Statistics in Medicine, Nuffield Department of Orthopaedics, Rheumatology and Musculoskeletal Sciences, University of Oxford, Oxford, UK
            Eur J Epidemiol
            Eur. J. Epidemiol
            European Journal of Epidemiology
            Springer Netherlands (Dordrecht )
            21 May 2016
            21 May 2016
            : 31
            : 337-350
            27209009 4877414 149 10.1007/s10654-016-0149-3
            © The Author(s) 2016

            Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

            Funded by: FundRef, Seventh Framework Programme;
            Award ID: 602552
            Custom metadata
            © Springer Science+Business Media Dordrecht 2016


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