statistical vs set/category theoretic "equivalence"? Equivalence is basic to mathematics, e.g. https://en.wikipedia.org/wiki/Equivalence_relation.
"Equivalence tests" are common in statistics, e.g. https://en.wikipedia.org/wiki/Equivalence_test.
Is the name "statistical equivalence" used intentionally to reflect a particular set-theoretic equivalence (and where is this best explained)?
Any views/references welcome.
Thanks!

I do not think statistical equivalence would count as an equivalence relation, as it seems to lacks transitivity.
Let’s say that equivalence is the means being within $2$ of each other.
$$
\bar x_A =0.0\\
\bar x_B =1.5\\
\bar x_C =3.0
$$
$A$ is equivalent to $B$, and $B$ is equivalent to $C$, but $A$ is not equivalent to $C$.
