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

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          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.

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          The Abuse of Power

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            Toward evidence-based medical statistics. 1: The P value fallacy.

            An important problem exists in the interpretation of modern medical research data: Biological understanding and previous research play little formal role in the interpretation of quantitative results. This phenomenon is manifest in the discussion sections of research articles and ultimately can affect the reliability of conclusions. The standard statistical approach has created this situation by promoting the illusion that conclusions can be produced with certain "error rates," without consideration of information from outside the experiment. This statistical approach, the key components of which are P values and hypothesis tests, is widely perceived as a mathematically coherent approach to inference. There is little appreciation in the medical community that the methodology is an amalgam of incompatible elements, whose utility for scientific inference has been the subject of intense debate among statisticians for almost 70 years. This article introduces some of the key elements of that debate and traces the appeal and adverse impact of this methodology to the P value fallacy, the mistaken idea that a single number can capture both the long-run outcomes of an experiment and the evidential meaning of a single result. This argument is made as a prelude to the suggestion that another measure of evidence should be used--the Bayes factor, which properly separates issues of long-run behavior from evidential strength and allows the integration of background knowledge with statistical findings.
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              Sifting the evidence-what's wrong with significance tests?

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                Author and article information

                Contributors
                lesdomes@ucla.edu
                stephen.senn@lih.lu
                john.carlin@mcri.edu.au
                cpoole@unc.edu
                steve.goodman@stanford.edu
                doug.altman@csm.ox.ac.uk
                Journal
                Eur J Epidemiol
                Eur. J. Epidemiol
                European Journal of Epidemiology
                Springer Netherlands (Dordrecht )
                0393-2990
                1573-7284
                21 May 2016
                21 May 2016
                2016
                : 31
                : 337-350
                Affiliations
                [ ]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
                Article
                149
                10.1007/s10654-016-0149-3
                4877414
                27209009
                12657c37-7667-4264-ad0a-59f9ecb8cc52
                © The Author(s) 2016

                Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License ( http://creativecommons.org/licenses/by/4.0/), 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.

                History
                : 9 April 2016
                : 9 April 2016
                Funding
                Funded by: FundRef http://dx.doi.org/10.13039/501100004963, Seventh Framework Programme;
                Award ID: 602552
                Categories
                Essay
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                © Springer Science+Business Media Dordrecht 2016

                Public health
                confidence intervals,hypothesis testing,null testing,p value,power,significance tests,statistical testing

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