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Statistical significance provides evidence for or against an explanation of a population of interest, not a description of data sampled from the population. This simple distinction gets ignored in hundreds of thousands of research publications yearly, which confuse statistical with biological significance by referring to hypothesis-testing analyses as demonstrating significant results. Here we identify three key steps to objective reporting of evidence-based analyses. Firstly, by interpreting P -values correctly as explanation not description, authors set their inferences in the context of the design of the study and its purpose to test for effects of biologically relevant size; nowhere in this process is it informative to use the word ‘significant’. Secondly, empirical effect sizes demand interpretation with respect to a size of relevance to the test hypothesis. Thirdly, even without an a priori expectation of biological relevance, authors can and should interpret significance tests with respect to effects of reliably detectable size.