Null hypothesis significance testing remains popular despite decades of concern about misuse and misinterpretation. We believe that much of the problem is due to language: significance testing has little to do with other meanings of the word ‘significance’. Despite the limitations of null-hypothesis tests, we argue here that they remain useful in many contexts as a guide to whether a certain effect can be seen clearly in that context (e.g. whether we can clearly see that a correlation or between-group difference is positive or negative). We therefore suggest that researchers describe the conclusions of null-hypothesis tests in terms of statistical ‘clarity’ rather than statistical ‘significance’. This simple semantic change could substantially enhance clarity in statistical communication. I can see clearly now: reinterpreting statistical significance