  In our work on the development of a model-independent data analysis method
for estimating the spin-independent (SI) scalar coupling of Weakly Interacting
Massive Particles (WIMPs) on nucleons by using measured recoil energies from
direct Dark Matter detection experiments directly, it was assumed that the
analyzed data sets are background-free, i.e., all events are WIMP signals. In
this article, as a more realistic study, we take into account a fraction of
possible residue background events, which pass all discrimination criteria and
then mix with other real WIMP-induced events in our data sets. Our simulations
show that, for the estimation of the SI WIMP-nucleon coupling, the maximal
acceptable fraction of residue background events in the analyzed data set of
O(50) total events is ~ 10% - 20%. For a WIMP mass of 100 GeV and 20% residue
background events, the systematic deviation of the reconstructed SI WIMP
coupling (with a reconstructed WIMP mass) would in principle be ~ +13% with a
statistical uncertainty of ~ ^{+21%}_{-14%} (~ -3.3%^{+18%}_{-13%} for
background-free data sets).
