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Inference about magnitudes of effects
Richard J Barker1, Matthew R Schofield
1Department of Mathematics and Statistics, University of Otago, Dunedin, New Zealand.
International Journal of Sports Physiology and Performance
|February 19, 2009
Summary
Magnitude-based inference, proposed as an alternative to null hypothesis testing, is not truly Bayesian. Sport scientists should use fully Bayesian methods for accurate parameter uncertainty analysis.
Area of Science:
- Statistics
- Sport Science
- Data Analysis
Background:
- Critique of null hypothesis testing in statistical inference.
- Proposal of magnitude-based inference by Batterham and Hopkins.
- Claim that magnitude-based inference is Bayesian without prior assumptions.
Discussion:
- Batterham and Hopkins' magnitude-based inference is only approximately Bayesian.
- This method incorporates a hidden, specific joint prior on parameters.
- It does not truly assume no prior information.
Key Insights:
- Magnitude-based inference requires a specific, unstated prior.
- The approach is mathematically distinct from standard Bayesian methods.
- Accurate application of magnitude-based inference principles necessitates full Bayesian analysis.
Outlook:
- Sport scientists should adopt fully Bayesian methods for robust statistical inference.
- Understanding the implicit priors in statistical models is crucial.
- Further research into practical Bayesian applications in sports science is warranted.
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