  We show that naive dimensional analysis (NDA) is equivalent to the result
that L-loop scattering amplitudes have perturbative order N=L+Delta, with a
shift Delta that depends on the NDA-weight of operator insertions. The NDA
weight of an operator is defined in this paper, and the general NDA formula for
perturbative order N is derived. The formula is used to explain why the
one-loop anomalous dimension matrix for dimension-six operators in the Standard
Model effective field theory has entries with perturbative order ranging from 0
to 4. The results in this paper are valid for an arbitrary effective field
theory, and they constrain the coupling constant dependence of anomalous
dimensions and scattering amplitudes in a general effective field theory.
