Magnitude based inference (MBI) was widely adopted by sport science researchers as an alternative to null hypothesis significance tests. It has been criticized for lacking a theoretical framework, mixing Bayesian and frequentist thinking, and encouraging researchers to run small studies with high Type 1 error rates. MBI terminology describes the position of confidence intervals in relation to smallest meaningful effect sizes. We show these positions correspond to combinations of one-sided tests of hypotheses about the presence or absence of meaningful effects, and formally describe MBI as a multiple decision procedure. MBI terminology operates as if tests are conducted at multiple alpha levels. We illustrate how error rates can be controlled by limiting each one-sided hypothesis test to a single alpha level. To provide transparent error control in a Neyman-Pearson framework and encourage the use of standard statistical software, we recommend replacing MBI with one-sided tests against smallest meaningful effects, or pairs of such tests as in equivalence testing. Researchers should pre-specify their hypotheses and alpha levels, perform a priori sample size calculations, and justify all assumptions. Our recommendations show researchers what tests to use and how to design and report their statistical analyses to accord with standard frequentist practice.
