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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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      Power failure: why small sample size undermines the reliability of neuroscience.

      A study with low statistical power has a reduced chance of detecting a true effect, but it is less well appreciated that low power also reduces the likelihood that a statistically significant result reflects a true effect. Here, we show that the average statistical power of studies in the neurosciences is very low. The consequences of this include overestimates of effect size and low reproducibility of results. There are also ethical dimensions to this problem, as unreliable research is inefficient and wasteful. Improving reproducibility in neuroscience is a key priority and requires attention to well-established but often ignored methodological principles.
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        THE ENVIRONMENT AND DISEASE: ASSOCIATION OR CAUSATION?

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          The earth is round (p < .05).

           Jacob Cohen V (1994)
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            Author and article information

            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
            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
            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 ( 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.

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

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