Inference About Magnitudes of Effects

In a recent commentary on statistical inference, Batterham and Hopkins advocated an approach to statistical inference centered on expressions of uncertainty in parameters. After criticizing an approach to statistical inference driven by null hypothesis testing, they proposed a method of "magnitude-based" inference and then claimed that this approach is essentially Bayesian but with no prior assumption about the true value of the parameter. In this commentary, after we address the issues raised by Batterham and Hopkins, we show that their method is "approximately" Bayesian and rather than assuming no prior information their approach has a very specific, but hidden, joint prior on parameters. To correctly adopt the type of inference advocated by Batterham and Hopkins, sport scientists need to use fully Bayesian methods of analysis.