In this paper the authors state the following regarding a null hypothesis significance test:

If P-value < critical value, reject null hypothesis and accept the alternative hypothesis (difference detected). If P-value > critical value, accept null hypothesis (no difference is detected)

Have the authors made a mistake by saying 'accept the null'? I initially thought so but then I noticed in the abstract they state:

P value is condemned by one school of thought who claims that focusing more on P value undermines the generalizability and reproducibility of research.

So they are clearly aware of the issues with p-values. So why do they then say 'accept the null' instead of 'fail to reject the null'? Maybe its just a convention to say 'accept the null' even if one is aware that what we are really doing is failing to reject the null?

  • 1
    $\begingroup$ A possible reason is because they do not know about tests for equivalence, such as TOST. $\endgroup$
    – Alexis
    Jun 3, 2021 at 14:42
  • 1
    $\begingroup$ Some related threads: 1, 2, 3 $\endgroup$
    – user20160
    Jun 3, 2021 at 17:21


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