Question about equivalence test

[hiswy]

This is about Chap 2, Part4.2.
When discusssing the results of TOST, the conclusion about Equivalence is a bit strange. The Non-Superiority failed to reject that coef difference is within the upper boundary of interests but equivalence tests proves that the difference is practically zero. Moreover there appeared some typing errors which is confusing....

""
Equivalence: The value associated to the TOST of equivalence corresponds to the maximum of the ### non-superiority and non-superiority values: 0.479. Again, we cannot reject the null hypothesis that the two coefficients are practically equivalent to each other.
""

non-superiority is typed twice....

My question is if non-superiority test failed to reject tha the difference is larger than the predined margin, how is it possible that the equivalence test could not reject the null that the difference is zero?

[vincentarelbundock]

Thanks a lot for reading the text so carefully, and reporting this. I really appreciate it!

It's a typo. Here's the corrected text. I will update the website in the coming days.

[hiswy]

thank you for reply! but maybe i was wrong.
As far as I understood
The null for noninferiority is that the difference is below than predefined margin

the null for non superiority would be the difference is also below the upper margin.

thus to prove equivalence the null hpothesis for:

the non inferiority is to be rejected and the nonsuperiority is to be accepted..

But i am not sure if this was the case..

Apology if I misunderstood...

[vincentarelbundock]

No, because (a) we never accept a hypothesis, so we can't "accept non-superiority", and (b) TOST is obtained by taking the maximum of the two p values associated to the non-sup and non-inf tests. Thus, we reject the TOST null of meaningful effect when both p values are small.

Fig 1.C of this paper may be helpful: https://journals.sagepub.com/doi/10.1177/2515245918770963