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Magnitude based inference (MBI) is a statistical procedure that successfully introduced researchers to statistical tools other than null hypothesis significance tests. However, it has been criticised for mixing Bayesian and frequentist thinking and for encouraging researchers to run small studies with high Type 1 error rates. We formally describe MBI as a decision procedure that combines one-sided hypotheses tested at multiple alpha levels. The hypotheses concern the presence or absence of meaningful effects. When testing is limited to a single alpha level, this formalisation of MBI reduces to a well-known multiple decision procedure that combines minimal effects tests and equivalence testing. To put MBI on a formal frequentist footing with transparent error control, we recommend replacing mechanistic (non-clinical) MBI with these established tests, and replacing clinical MBI with a pair of one-sided tests at asymmetric alpha levels. These tests can be run using standard statistical software, or the p-values required can be obtained from the spreadsheets that implement MBI. We recommend dropping other MBI outputs, including Bayesian interpretations and testing at multiple alpha levels. New sample size calculators are also required. Researchers should pre-specify their hypotheses and alpha levels, perform a priori sample size calculations, and justify all assumptions. With our recommended changes, researchers can make statistical inferences about their data in relation to meaningful effect sizes while controlling error rates.