  One of the difficulties with performing polarization analysis is that the
mean polarization fraction of sub-divided data sets is larger than the
polarization fraction for the integrated measurement. The resulting bias is one
of the properties of the generating distribution discussed in this work. The
limitations of Gaussian approximations in standard analysis based on Stokes
parameters for estimating polarization parameters and their uncertainties are
explored by comparing with a Bayesian analysis. Different signal-to-background
scenarios are considered making the analysis relevant for a large variety of
observations. The effect of uncertainty on the modulation factor is also shown,
since it can have a large impact on the performance of gamma-ray burst
polarimeters. Results are related to the minimum detectable polarization (MDP),
a common figure of merit, making them easily applicable to any X-ray
polarimeter.
