Preprint / Version 1

Understanding quantitative analysis in sport and exercise science

concepts, tools and approaches


  • Tony Myers Birmingham Newman University
  • Iain J. Gallagher
  • Jacob Reading



Data Analysis, Bayesian, frequentist, Fisher, Neyman-Pearson, causal effects, sport and exercise science


This chapter provides a comprehensive overview of the concepts, tools, and approaches necessary for effective quantitative analysis in sport and exercise science. It begins with an exploration of inference, detailing how it reduces uncertainty and informs decisions about observations. It contrasts classical probabilities with frequentist probabilities and subjective probabilities. It then critically examines null-hypothesis significance testing (NHST), identifying common misinterpretations of p-values and the 'user interface' problem stemming from the hybrid nature of Fisher's and Neyman-Pearson's approaches.

It goes on to explain Bayesian parameter estimation and hypothesis testing, with discussions on prior knowledge, likelihood, and posterior distribution. The chapter emphasises the importance of quantifying uncertainty through confidence intervals and Bayesian credible intervals, explaining their distinct interpretations.

The chapter then examines different effect sizes and their uses, including raw differences, standardised differences, Common language effect size, Cohen's U3, the proportion of variance explained or shared between variables and different ratios and their practical significance for sport and exercise. The chapter emphasises the importance of understanding causal effects by introducing randomised controlled experiments, longitudinal studies, and quasi-experiments. It also explores causal modelling using Directed Acyclic Graphs (DAGs) to represent and analyze cause-and-effect relationships from observational data.

This chapter advocates the use of plots to uncover underlying data patterns and ensure data quality by highlighting visualisation and exploratory data analysis as crucial steps in any data analysis project. The chapter concludes by stressing the importance of accurate and meaningful data analysis and visualisation in supporting robust decision-making in sport and exercise science.

In summary, the chapter provides a comprehensive overview of the concepts, tools, and approaches necessary for effective quantitative analysis for sport and exercise science. It aims to equip researchers with the knowledge to avoid common pitfalls and make informed decisions based on robust data analysis.


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