Decisions about support for predictions of theories in light of data are made using statistical inference. The dominant approach in sport and exercise science is the Neyman-Pearson significance-testing approach. When applied correctly it provides a reliable procedure for making dichotomous decisions for accepting or rejecting zero-effect null hypotheses with known and controlled long-run error rates. Type I and type II error rates must be specified in advance and the latter controlled by conducting an a priori sample size calculation. The Neyman-Pearson approach does not provide the probability of hypotheses or indicate the strength of support for hypotheses in light of data, yet many scientists believe it does. Outcomes of analyses allow conclusions only about the existence of non-zero effects, and provide no information about the likely size of true effects or their practical / clinical value. Bayesian inference can show how much support data provide for different hypotheses, and how personal convictions should be altered in light of data, but the approach is complicated by formulating probability distributions about prior-subjective estimates of population effects. A pragmatic solution is magnitude-based inference, which allows scientists to estimate the true magnitude of population effects and how likely they are to exceed an effect magnitude of practical / clinical importance thereby integrating elements of subjective-Bayesian-style thinking. While this approach is gaining acceptance, progress might be hastened if scientists appreciate the shortcomings of traditional N-P null-hypothesis-significance testing.