The article by Batterham and Hopkins critiques the traditional approach of using null-hypothesis testing to infer statistical significance, arguing that it is confusing and can be misleading. They propose a more intuitive and practical approach based on uncertainty in the true value of the statistic, using confidence intervals to define the likely range of the true value. The authors then refine this approach by considering the real-world relevance of the uncertainty, taking into account values that are substantial in positive and negative senses, such as beneficial and harmful. They suggest that if the likely range of values overlaps substantially, the outcome is unclear; otherwise, the true value is inferred to be substantially positive, trivial, or substantially negative. The article also discusses other approaches to inferences, including Bayesian statistics and meta-analysis, and emphasizes the importance of making meaningful inferences about magnitudes rather than just statistical significance. The authors conclude by advocating for a shift towards magnitude-based inferences in scientific reporting.The article by Batterham and Hopkins critiques the traditional approach of using null-hypothesis testing to infer statistical significance, arguing that it is confusing and can be misleading. They propose a more intuitive and practical approach based on uncertainty in the true value of the statistic, using confidence intervals to define the likely range of the true value. The authors then refine this approach by considering the real-world relevance of the uncertainty, taking into account values that are substantial in positive and negative senses, such as beneficial and harmful. They suggest that if the likely range of values overlaps substantially, the outcome is unclear; otherwise, the true value is inferred to be substantially positive, trivial, or substantially negative. The article also discusses other approaches to inferences, including Bayesian statistics and meta-analysis, and emphasizes the importance of making meaningful inferences about magnitudes rather than just statistical significance. The authors conclude by advocating for a shift towards magnitude-based inferences in scientific reporting.