  With reference to the equivalence theorem, we discuss the selection of basis
operators for effective field theories in general. The equivalence relation can
be used to partition operators into equivalence classes, from which
inequivalent basis operators are selected. These classes can also be identified
as containing Potential-Tree-Generated (PTG) operators, Loop-Generated (LG)
operators, or both, independently of the specific dynamics of the underlying
extended models, so long as it is perturbatively decoupling. For an equivalence
class containing both, we argue that the basis operator should be chosen from
among the PTG operators, because they may have the largest coefficients. We
apply this classification scheme to dimension-six operators in an illustrative
Yukawa model as well in the Standard Model (SM). We show that the basis chosen
by Grzadkowski {\it et. al.} \cite{Grzadkowski:2010es} for the SM satisfies
this criterion. In this light, we also revisit and verify our earlier result
\cite{Arzt:1994gp} that the dimension-six corrections to the triple-gauge-boson
couplings only arise from LG operators, so the magnitude of the coefficients
should only be a few parts per thousand of the SM gauge coupling if BSM
dynamics respects decoupling. The same is true of the quartic-gauge-boson
couplings.
