  Following an extensive simulation study comparing the operating
characteristics of three different procedures used for establishing equivalence
(the frequentist "TOST", the Bayesian "HDI-ROPE", and the Bayes factor interval
null procedure), Linde et al. (2021) conclude with the recommendation that
"researchers rely more on the Bayes factor interval null approach for
quantifying evidence for equivalence." We redo the simulation study of Linde et
al. (2021) in its entirety but with the different procedures calibrated to have
the same predetermined maximum type 1 error rate. Our results suggest that,
when calibrated in this way, the Bayes Factor, HDI-ROPE, and frequentist
equivalence tests all have similar -- almost exactly -- type 2 error rates. In
general any advocating for frequentist testing as better or worse than Bayesian
testing in terms of empirical findings seems dubious at best. If one decides on
which underlying principle to subscribe to in tackling a given problem, then
the method follows naturally. Bearing in mind that each procedure can be
reverse-engineered from the others (at least approximately), trying to use
empirical performance to argue for one approach over another seems like tilting
at windmills.
