Non-QCD like confining gauge theories promise to be potential UV completions for the Standard Model Electroweak sector, which do not suffer from fine tuning problems. In these scenarios, the Higgs boson would be a composite particle, kept lighter than other composites by the dynamics of the gauge theory. To determine the viability of these scenarios, we have developed an effective field theory (EFT) framework to analyze lattice data for gauge theories in which the number of light fermions is near but below the transition from confinement to infrared conformal behavior. Lattice studies of such theories have indicated the presence of a remarkably light singlet scalar particle, which in our framework is interpreted as a dilaton. In this talk, I will describe this framework and recent results obtained applying it to lattice data for the SU(3) gauge theory with 8 fermion flavors in the fundamental representation, and the SU(3) gauge theory with 2 fermion flavors in the sextet representation.