I contend that there is a better way to correct the misuse of tests for statistical significance than by dispensing with them altogether (see V. Amrhein et al. Nature 567, 305–307; 2019).
The ‘error-statistical perspective’ described by Deborah Mayo provides valuable insight into tests of significance and other frequentist concepts (see Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars; 2018). It stringently evaluates statistical hypotheses by using different statistical methods and their error probabilities, and by ruling out erroneous interpretations of data.
This approach is principled, whereas that of Amrhein et al. is pragmatic — in that it recommends a linguistic reform. In my view, the error-statistical perspective better advances the discussion and application of statistical significance testing than debating whether we should curtail application of a popular statistical expression.
Nature 569, 487 (2019)