  Effective field theory methods allow us to modify general relativity through
higher-curvature corrections to the Einstein-Hilbert action, while preserving
Lorentz invariance and the number of gravitational degrees of freedom. We here
construct an approximate inspiral-merger-ringdown waveform model within the
cubic, parity-preserving class of effective-field-theory extensions to
Einstein's theory for the gravitational waves emitted by quasi-circular binary
black holes with aligned/anti-aligned spins. Using this waveform model, we
first explore the detectability of non-Einsteinian effective-field-theory
effects through an extended version of effective cycles to illustrate the need
to include non-Einsteinian amplitude corrections. We then use this model to
analyze the GW170608 event in a full Bayesian framework, and we place new
improved and more robust constraints on the coupling constants of the effective
field theory. Our Bayesian model selection study disfavors the non-Einsteinian
theory with a (log) Bayes factor of $\log \mathcal{B}^{\text{EFT}}_{\text{GR}}
= -2.81$. Our Bayesian parameter estimation study places the constraints
$\bar{\alpha}_1=0.87^{+1.95}_{-1.03}$ and $
\bar{\alpha}_2=-0.35^{+4.12}_{-2.92}$ at $90\%$ confidence on the coupling
parameters of the effective-field theory. These constraints are $3.5$ stronger
than previous constraints, informative relative to the prior, and independent
of the choice of prior on the coupling parameters of the modified theory.
