We discuss in detail the extraction of hadronic mixing strengths from latti
ce studies. We apply this to the mixing of a scalar glueball and a scalar m
eson in the quenched approximation. We also measure correlations appropriat
e for flavor-singlet scalar mesons using dynamical quark configurations fro
m UKQCD. This enables us to compare the results from the quenched study of
the mixing with the direct determination of the mixed spectrum. Improved me
thods of evaluating the disconnected quark diagrams are also presented.