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?