This paper presents the statistical methods used in setting limits
and discovery significances in the search for new particles in the CDF
experiment at the Fermilab Tevatron.  For single-channel counting experiments
the collaboration employs the classical Helene formula, with Bayesian
integration over systematic uncertainties in the signal acceptance and
background.  For more complex cases such as spectral fits and combining
channels, likelihood-based methods are used.  In the discoveries of the top
quark and B(c) meson, the significance was estimated from the probability of
the null hypothesis, using toy Monte Carlo methods.  Lastly, in the recent
SUSY/Higgs Workshop, the Higgs Working Group used a method of combining
channels and experiments based on the calculation of the joint likelihood for
a particular experimental outcome, and averaging over all possible outcomes.