  One of the assumptions of simplified models is that there are a few new
particles and interactions accessible at the LHC and all other new particles
are heavy and decoupled. The effective field theory (EFT) method provides a
consistent method to test this assumption. Simplified models can be augmented
with higher order operators involving the new particles accessible at the LHC.
Any UV completion of the simplified model will be able to match onto these
beyond the Standard Model EFTs (BSM-EFT). In this paper we study the simplest
simplified model: the Standard Model extended by a real gauge singlet scalar.
In addition to the usual renormalizable interactions, we include dimension-5
interactions of the singlet scalar with Standard Model particles. As we will
show, even when the cutoff scale is 3 TeV, these new effective interactions can
drastically change the interpretation of Higgs precision measurements and
scalar searches. In addition, we discuss how power counting in a BSM-EFT
depends strongly on the processes and parameter space under consideration.
Finally, we propose a $\chi^2$ method to consistently combine the limits from
new particle searches with measurements of the Standard Model. Unlike imposing
a hard cut off on heavy resonance rates, our method allows fluctuations in
individual channels that are consistent with global fits.
