title: "Magnitude-based inference": a statistical review.
abstract: OBJECTIVE
  We consider "magnitude-based inference" and its interpretation by examining in detail its use in the problem of comparing two means.
  
  
  METHODS
  We extract from the spreadsheets, which are provided to users of the analysis (http://www.sportsci.org/), a precise description of how "magnitude-based inference" is implemented. We compare the implemented version of the method with general descriptions of it and interpret the method in familiar statistical terms.
  
  
  CONCLUSIONS
  We show that "magnitude-based inference" is not a progressive improvement on modern statistics. The additional probabilities introduced are not directly related to the confidence interval but, rather, are interpretable either as P values for two different nonstandard tests (for different null hypotheses) or as approximate Bayesian calculations, which also lead to a type of test. We also discuss sample size calculations associated with "magnitude-based inference" and show that the substantial reduction in sample sizes claimed for the method (30% of the sample size obtained from standard frequentist calculations) is not justifiable so the sample size calculations should not be used. Rather than using "magnitude-based inference," a better solution is to be realistic about the limitations of the data and use either confidence intervals or a fully Bayesian analysis.
authors: 1Mathematical Sciences Institute, Australian National University, Canberra, Australian Capital Territory, AUSTRALIA; and 2Performance Research, Australian Institute of Sport, Belconnen, Australian Capital Territory, AUSTRALIA.
authors: Alan H
authors: AH
authors: Welsh
authors: Emma J
authors: EJ
authors: Knight
mesh_terms: D001499:Bayes Theorem; D003627:Data Interpretation, Statistical; D006801:Humans; D013178:Sports Medicine / Q000706:statistics & numerical data*