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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?

sonicboom
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    A possible reason is because they do not know about tests for equivalence, such as [TOST](https://stats.stackexchange.com/tags/tost/info). – Alexis Jun 03 '21 at 14:42
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    Some related threads: [1](https://stats.stackexchange.com/questions/60670/accept-null-hypothesis-or-fail-to-reject-the-null-hypothesis), [2](https://stats.stackexchange.com/questions/85903/why-do-statisticians-say-a-non-significant-result-means-you-cant-reject-the-nu), [3](https://stats.stackexchange.com/questions/125541/does-failure-to-reject-the-null-in-neyman-pearson-approach-mean-that-one-should) – user20160 Jun 03 '21 at 17:21

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