Copyright @ 200 by the American College of Sports Medicine. Unauthorized reproduction of this article is prohibited. 8 Progressive Statistics for Studies in Sports Medicine and Exercise Science WILLIAM G. HOPKINS1, STEPHEN W. MARSHALL2, ALAN M. BATTERHAM3, and JURI HANIN4 1 Institute of Sport and Recreation Research, AUT University, Auckland, NEW ZEALAND 2 Departments of Epidemiology, Orthopedics, and Exercise & Sport Science, University of North Carolina at Chapel Hill, Chapel Hill, NC 3 School of Health and Social Care, University of Teesside, Middlesbrough, UNITED KINGDOM and 4 KIHU-Research Institute for Olympic Sports, Jyvaskyla, FINLAND ABSTRACT HOPKINS, W. G., S. W. MARSHALL, A. M. BATTERHAM, and J. HANIN. Progressive Statistics for Studies in Sports Medicine and Exercise Science. Med. Sci. Sports Exerc., Vol. 41, No. 1, pp. 3���12, 2009. Statistical guidelines and expert statements are now available to assist in the analysis and reporting of studies in some biomedical disciplines. We present here a more progressive resource for sample-based studies, meta-analyses, and case studies in sports medicine and exercise science. We offer forthright advice on the following controversial or novel issues: using precision of estimation for inferences about population effects in preference to null- hypothesis testing, which is inadequate for assessing clinical or practical importance justifying sample size via acceptable precision or confidence for clinical decisions rather than via adequate power for statistical significance showing SD rather than SEM, to better communicate the magnitude of differences in means and nonuniformity of error avoiding purely nonparametric analyses, which cannot provide inferences about magnitude and are unnecessary using regression statistics in validity studies, in preference to the impractical and biased limits of agreement making greater use of qualitative methods to enrich sample-based quantitative projects and seeking ethics approval for public access to the depersonalized raw data of a study, to address the need for more scrutiny of research and better meta-analyses. Advice on less contentious issues includes the following: using covariates in linear models to adjust for confounders, to account for individual differences, and to identify potential mechanisms of an effect using log transformation to deal with nonuni- formity of effects and error identifying and deleting outliers presenting descriptive, effect, and inferential statistics in appropriate formats and contending with bias arising from problems with sampling, assignment, blinding, measurement error, and researchers��� prejudices. This article should advance the field by stimulating debate, promoting innovative approaches, and serving as a useful checklist for authors, reviewers, and editors. Key Words: ANALYSIS, CASE, DESIGN, INFERENCE, QUALITATIVE, QUANTITATIVE, SAMPLE Istatistical n response to the widespread misuse of statistics in re- search, several biomedical organizations have published guidelines in their journals, including the In- ternational Committee of Medical Journal Editors (www. icmje.org), the American Psychological Association (2), and the American Physiological Society (8). Expert groups have also produced statements about how to publish reports of various kinds of medical research (Table 1). Some medi- cal journals now include links to these statements as part of their instructions to authors. In this article, we provide our view of best practice for the use of statistics in sports medicine and the exercise sciences. The article is similar to those referenced in Table 1 but includes more practical and original material. It should achieve three useful outcomes. First, it should stimulate interest and debate about constructive change in the use of statistics in our disciplines. Secondly, it should help legi- timize the innovative or controversial approaches that we and others sometimes have difficulty including in publica- tions. Finally, it should serve as a statistical checklist for Address for correspondence: Will G. Hopkins, Ph.D., FACSM, Institute of Sport and Recreation Research, AUT University, Akoranga Drive, Private Bag 92006, Auckland 0627, New Zealand E-mail: will@clear.net.nz. Submitted for publication July 2008. Accepted for publication September 2008. 0195-9131/09/4101-0003/0 MEDICINE & SCIENCE IN SPORTS & EXERCISE�� Copyright �� 2008 by the American College of Sports Medicine DOI: 10.1249/MSS.0b013e31818cb278 TABLE 1. Recent statements of best practice for reporting various kinds of biomedical research. Interventions (experiments) CONSORT: Consolidated Standards of Reporting Trials (1,22). See consort-statement.org for statements, explanations, and extensions to abstracts and to studies involving equivalence or noninferiority, clustered randomization, harmful outcomes, nonrandomized designs, and various kinds of intervention. Observational (nonexperimental) studies STROBE: Strengthening the Reporting of Observational Studies in Epidemiology (27,28). See strobe-statement.org for statements and explanations, and see HuGeNet.ca for extension to gene-association studies. Diagnostic tests STARD: Standards for Reporting Diagnostic Accuracy (5,6). Meta-analyses QUOROM: Quality of Reporting of Meta-analyses (21). MOOSE: Meta-analysis of Observational Studies in Epidemiology (25). See also the Cochrane Handbook (at cochrane.org) and guidelines for meta-analysis of diagnostic tests (19) and of gene-association studies (at HuGeNet.ca). 3

Copyright @ 200 by the American College of Sports Medicine. Unauthorized reproduction of this article is prohibited. 8 TABLE 2. Generic statistical advice for sample-based studies. ABSTRACT State why you studied the effect(s). State the design, including any randomizing and blinding. Characterize the subjects who contributed to the estimate of the effect(s) (final sample size, sex, skill, status, I). Ensure all numbers are either in numeric or graphical form in the Results section of the manuscript. Show magnitudes and confidence intervals or limits of the most important effect(s). Avoid P values. [Note 1] Make a probabilistic statement about clinical, practical, or mechanistic importance of the effect(s). The conclusion must not be simply a restatement of results. INTRODUCTION Explain the need for the study. ��� Justify choice of a particular population of subjects. ��� Justify choice of design here, if it is one of the reasons for doing the study. State an achievable aim or resolvable question about the magnitude of the effect(s). Avoid hypotheses. [Note 1] METHODS Subjects Explain the recruitment process and eligibility criteria for acquiring the sample from a population. ��� Justify any stratification aimed at proportions of subjects with certain characteristics in the sample. Include permission for public access to depersonalized raw data in your application for ethics approval. [Note 2] Design Describe any pilot study aimed at measurement properties of the variables and feasibility of the design. To justify sample size, avoid adequate power for statistical significance. Instead, estimate or reference the smallest important values for the most important effects and use with one or more of the following approaches, taking into account any multiple inferences and quantification of individual differences or responses [Notes 3 and 4]: ��� adequate precision for a trivial outcome, smallest expected outcome, or comparison with a published outcome ��� acceptably low rates of wrong clinical decisions ��� adequacy of sample size in similar published studies ��� limited availability of subjects or resources (in which case state the smallest magnitude of effect your study could estimate adequately). Detail the timings of all assessments and interventions. See also Table 3 for advice on design of specific kinds of study. Measures Justify choice of dependent and predictor variables in terms of practicality and measurement properties specific to the subjects and conditions of the study. Use variables with the smallest errors. Justify choice of potential moderator variables: subject characteristics or differences/changes in conditions or protocols that could affect the outcome and that are included in the analysis as predictors to reduce confounding and account for individual differences. Justify choice of potential mediator variables: measures that could be associated with the dependent variable because of a causal link from a predictor and that are included in an analysis of the mechanism of the effect of the predictor. [Note 5] Consider including open-ended interviews or other qualitative methods, which afford serendipity and flexibility in data acquisition. ��� Use in a pilot phase aimed at defining purpose and methods, during data gathering in the project itself, and in a follow-up assessment of the project with stakeholders. Analysis Describe any initial screening for miscodings, e.g., using stem-and-leaf plots or frequency tables. Justify any imputation of missing values and associated adjustment to analyses. Describe the model used to derive the effect. [Note 6] ��� Justify inclusion or exclusion of main effects, polynomial terms, and interactions in a linear model. ��� Explain the theoretical basis for use of any nonlinear model. ��� Provide citations or evidence from simulations that any unusual or innovative data-mining technique you used to derive effects (neural nets, genetic algorithms, decision trees, rule induction) should give trustworthy estimates with your data. ��� Explain how you dealt with repeated measures or other clustering of observations. Avoid purely nonparametric analyses. [Note 7] If the dependent variable is continuous, indicate whether you dealt with nonuniformity of effects and/or error by transforming the dependent variable, by modeling different errors in a single analysis, and/or by performing and combining separate analyses for independent groups. [Note 8] Explain how you identified and dealt with outliers and give a plausible reason for their presence. [Note 9] Indicate how you dealt with the magnitude of the effect of linear continuous predictors or moderators, either as the effect of 2 SD, or as a partial correlation, or by parsing into independent subgroups. [Note 10] Indicate how you performed any subsidiary mechanisms analysis with potential mediator variables, either using linear modeling or (for interventions) an analysis of change scores. [Note 5] Describe how you performed any sensitivity analysis, in which you investigated quantitatively, either by simulation or by simple calculation, the effect of error of measurement and other potential sources of bias on the magnitude and uncertainty of the effect statistic(s). Explain how you made inferences about the true (infinite-sample) value of each effect. [Note 1] ��� Show confidence intervals or limits. ��� Justify a value for the smallest important magnitude, then base the inference on the disposition of the confidence interval relative to substantial magnitudes. ��� For effects with clinical or practical application, make a decision about utility by estimating chances of benefit and harm. ��� Avoid the traditional approach of statistical significance based on a null-hypothesis test using a P value. ��� Explain any adjustment for multiple inferences. [Note 3] Include this statement, when appropriate: measures of centrality and dispersion are mean T SD. ��� Add the following statement, when appropriate: for variables that were log transformed before modeling, the mean shown is the back-transformed mean of the log transform, and the dispersion is a coefficient of variation (%) or / factor SD. ��� The range (minimum���maximum) is sometimes informative, but beware that it is strongly biased by sample size. ��� Avoid medians and other quantiles, except when parsing into subgroups. ��� Never show SEM. [Note 11] See also Table 3 for advice on analysis of specific kinds of study. RESULTS Subject Characteristics Describe the flow of number of subjects from those who were first approached about participation through those who ended up providing data for the effects. Show a table of descriptive statistics of variables in important groups of the subjects included in the final analysis, not the subjects you first recruited. ��� For numeric variables, show mean T SD. [Note 11] ��� For nominal variables, show percent of subjects. ��� Summarize the characteristics of dropouts (subjects lost to follow-up) if they represent a substantial proportion (910%) of the original sample or if their loss is likely to substantially bias the outcome. Be precise about which groups they were in when they dropped out and why they dropped out. See also Table 3 for advice on reporting subject characteristics in specific kinds of study. Outcome Statistics Avoid all exact duplication of data among tables, figures, and text. When adjustment for subject characteristics and other potential confounders is substantial, show unadjusted and adjusted outcomes. Use standardized differences or changes in means to assess qualitative magnitudes of the differences, but there is generally no need to show the standardized values. [Note 1] If the most important effect is unclear, provide a qualitative interpretation of its uncertainty. (For example, it is unlikely to have a small beneficial effect and very unlikely to be moderately beneficial.) State the approximate sample size that would be needed to make it clear. See also Table 3 for advice on outcome statistics in specific kinds of study. Numbers Insert a space between numbers and units, with the exception of % and -. Examples: 70 mLIminj1Ikgj1 90%. Insert a hyphen between numbers and units only when grammatically necessary: the test lasted 4 min it was a 4-min test. (continued on next page) TABLE 2. (Continued) http://www.acsm-msse.org 4 Official Journal of the American College of Sports Medicine