"Magnitude-based Inference" : a statistical review

Abstract

PURPOSE: 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. RESULTS AND 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.