  Detection thresholds in polarized intensity and polarization bias correction
are investigated for surveys where the polarization information is obtained
from RM synthesis. Considering unresolved sources with a single rotation
measure, a detection threshold of $8 \sigma_{QU}$ applied to the Faraday
spectrum will retrieve the RM with a false detection rate less than $10^{-4}$,
but polarized intensity is more strongly biased than Ricean statistics suggest.
For a detection threshold of $5 \sigma_{QU}$, the false detection rate
increases to ~4%, depending also on $\lambda^2$ coverage and the extent of the
Faraday spectrum. Non-Gaussian noise in Stokes Q and U due to imperfect imaging
and calibration can be represented by a distribution that is the sum of a
Gaussian and an exponential. The non-Gaussian wings of the noise distribution
increase the false detection rate in polarized intensity by orders of
magnitude. Monte-Carlo simulations assuming non-Gaussian noise in Q and U, give
false detection rates at $8 \sigma_{QU}$ similar to Ricean false detection
rates at $4.9 \sigma_{QU}$.
