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• Author: Alan M. Batterham
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## An Imaginary Bayesian Monster

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## Making Meaningful Inferences About Magnitudes

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 non significant 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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## A Comment on “Does Mathematical Coupling Matter to the Acute to Chronic Workload Ratio? A Case Study From Elite Sport”

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## Reduction in Physical Match Performance at the Start of the Second Half in Elite Soccer

### Purpose:

Soccer referees’ physical match performances at the start of the second half (46–60 min) were evaluated in relation to both the corresponding phase of the first half (0–15 min) and players’ performances during the same match periods.

### Methods:

Match analysis data were collected (Prozone, UK) from 12 soccer referees on 152 English Premier League matches during the 2008/09 soccer season. Physical match performance categories for referees and players were total distance, high-speed running distance (speed >5.5 m/s), and sprinting distance (>7.0 m/s). The referees’ heart rate was recorded from the start of their warm-up to the end of the match. The referees’ average distances (in meters) from the ball and fouls were also calculated.

### Results:

No substantial differences were observed in duration (16:42 ± 2:35 vs 16:27 ± 1:00 min) or intensity (107 ± 11 vs 106 ± 14 beats/min) of the referees’ preparation periods immediately before each half. Physical match performance was reduced during the initial phase of the second half when compared with the first half in both referees (effect sizes—standardized mean differences—0.19 to 0.73) and players (effect sizes 0.20 to 1.01). The degree of the decreased performance was consistent between referees and players for total distance (4.7 m), high-speed running (1.5 m), and sprinting (1.1 m). The referees were closer to the ball (effect size 0.52) during the opening phase the second half.

### Conclusion:

Given the similarity in the referees’ preparation periods, it may be that the reduced physical match performances observed in soccer referees during the opening stages of the second half are a consequence of a slower tempo of play.

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## The Effect of Structured Exercise Classes and a Lifestyle Intervention on Cardiovascular Risk Factors in Primary Schoolchildren: An Exploratory Trial (The A-CLASS Project)

This exploratory trial evaluates the effect of a structured exercise (STEX) or lifestyle intervention (PASS) program upon cardiovascular (CV) disease risk factors in children. Sixty-one schoolchildren were randomly assigned by school to an intervention or control (CON) condition. The effect of the STEX (compared with CON) was a mean benefit of −0.018 mm for average maximum carotid intimamedia thickness. The PASS intervention did not result in clinically important effects, and no other substantial changes were observed. Relatively high probability of clinically beneficial effects of the STEX intervention suggests that a larger, definitive randomized trial with longer follow-up is warranted.

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## Tracking Within-Athlete Changes in Whole-Body Fat Percentage in Wheelchair Athletes

Purpose: To evaluate the tracking of within-athlete changes in criterion measures of whole-body fat percentage (BF%; dual-energy X-ray absorptiometry) with skinfold thickness (Σ 4, 6, or 8) in wheelchair basketball players. Methods: Dual-energy X-ray absorptiometry-derived whole BF% and Σ 4, 6, or 8 skinfolds were obtained at 5 time points over 15 months (N = 16). A linear mixed model with restricted maximum likelihood (random intercept, with identity covariance structure) to derive the within-athlete prediction error for predicting criterion BF% from Σ skinfolds was used. This prediction error allowed us to evaluate how well a simple measure of the Σ skinfolds could track criterion changes in BF %; that is, the authors derived the change in Σ skinfolds that would have to be observed in an individual athlete to conclude that a substantial change in criterion BF% had occurred. Data were log-transformed prior to analysis. Results: The Σ 8 skinfolds was the most precise practical measure for tracking changes in BF%. For the monitoring of an individual player, a change in Σ 8 skinfolds by a factor of greater than 1.28 (multiply or divide by 1.28) is associated with a practically meaningful change in BF% (≥1 percentage point). Conclusions: The Σ 8 skinfolds can track changes in BF% within individuals with reasonable precision, providing a useful field monitoring tool in the absence of often impractical criterion measures.