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Using Multivariate Statistics

A Guideline of Selecting and Reporting Intraclass Correlation Coefficients for Reliability Research

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 nonuniformity 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.

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Progressive Statistics for Studies in Sports Medicine and Exercise Science

Prospective Cohort Study

Reliability refers to the reproducibility of values of a test, assay or other measurement in repeated trials on the same individuals. Better reliability implies better precision of single measurements and better tracking of changes in measurements in research or practical settings. The main measures of reliability are within-subject random variation, systematic change in the mean, and retest correlation. A simple, adaptable form of within-subject variation is the typical (standard) error of measurement: the standard deviation of an individual’s repeated measurements. For many measurements in sports medicine and science, the typical error is best expressed as a coefficient of variation (percentage of the mean). A biased, more limited form of within-subject variation is the limits of agreement: the 95% likely range of change of an individual’s measurements between 2 trials. Systematic changes in the mean of a measure between consecutive trials represent such effects as learning, motivation or fatigue; these changes need to be eliminated from estimates of within-subject variation. Retest correlation is difficult to interpret, mainly because its value is sensitive to the heterogeneity of the sample of participants. Uses of reliability include decision-making when monitoring individuals, comparison of tests or equipment, estimation of sample size in experiments and estimation of the magnitude of individual differences in the response to a treatment. Reasonable precision for estimates of reliability requires approximately 50 study participants and at least 3 trials. Studies aimed at assessing variation in reliability between tests or equipment require complex designs and analyses that researchers seldom perform correctly. A wider understanding of reliability and adoption of the typical error as the standard measure of reliability would improve the assessment of tests and equipment in our disciplines. CURRENT OPINION

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Measures of reliability in sports medicine and science.

A study of a sample provides only an estimate of the true (population) value of an outcome statistic. A report of the study therefore usually includes an inference about the true value. Traditionally, a researcher makes an inference by declaring the value of the statistic statistically significant or nonsignificant on the basis of a P value derived from a null-hypothesis test. This approach is confusing and can be misleading, depending on the magnitude of the statistic, error of measurement, and sample size. The authors use a more intuitive and practical approach based directly on uncertainty in the true value of the statistic. First they express the uncertainty as confidence limits, which define the likely range of the true value. They then deal with the real-world relevance of this uncertainty by taking into account values of the statistic that are substantial in some positive and negative sense, such as beneficial or harmful. If the likely range overlaps substantially positive and negative values, they infer that the outcome is unclear; otherwise, they infer that the true value has the magnitude of the observed value: substantially positive, trivial, or substantially negative. They refine this crude inference by stating qualitatively the likelihood that the true value will have the observed magnitude (eg, very likely beneficial). Quantitative or qualitative probabilities that the true value has the other 2 magnitudes or more finely graded magnitudes (such as trivial, small, moderate, and large) can also be estimated to guide a decision about the utility of the outcome.

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Making meaningful inferences about magnitudes.

The reliability of power in tests of physical performance affects the precision of assessment of athletes, patients, clients and study participants. In this meta-analytic review we identify the most reliable measures of power and the factors affecting reliability. Our measures of reliability were the typical (standard) error of measurement expressed as a coefficient of variation (CV) and the percent change in the mean between trials. We meta-analysed these measures for power or work from 101 studies of healthy adults. Measures and tests with the smallest CV in exercise of a given duration include field tests of sprint running (∼0.9%), peak power in an incremental test on a treadmill or cycle ergometer (∼0.9%), equivalent mean power in a constant-power test lasting 1 minute to 3 hours on a treadmill or cycle ergometer (0.9 to 2.0%), lactate-threshold power (∼1.5%), and jump height or distance (∼2.0%). The CV for mean power on isokinetic ergometers was relatively large (>4%). CV were larger for nonathletes versus athletes (1.3 ×), female versus male nonathletes (1.4 ×), shorter (∼1-second) and longer (∼1-hour) versus 1-minute tests (≤1.6 ×), and respiratory- versus ergometer-based measures of power (1.4 to 1.6 ×). There was no clear-cut effect of time between trials. The importance of a practice trial was evident in studies with >2 trials: the CV between the first 2 trials was 1.3 times the CV between subsequent trials; performance also improved by 1.2% between the first 2 trials but by only 0.2% between subsequent trials. These findings should help exercise practitioners and researchers select or design good measures and protocols for tests of physical performance.

Reliability of Power in Physical Performance Tests

Design and analysis of research on sport performance enhancement. Med. Sci. Sports Exerc., Vol. 31, No. 3, pp. 472-485, 1999.Purpose:The purpose of this study was to assess research aimed at measuring performance enhancements that affect success of individual elite athletes in competitive ev

Will G. Hopkins

Papers

Progressive Statistics for Studies in Sports Medicine and Exercise Science

Measures of reliability in sports medicine and science.

Making meaningful inferences about magnitudes.

Reliability of Power in Physical Performance Tests

Design and analysis of research on sport performance enhancement.