  The coming flood of CMB polarization experiments, spurred by the recent
detection of CMB polarization by DASI and WMAP, will be confronted by many new
analysis tasks specific to polarization. For the analysis of CMB polarization
data sets, the devil is truly in the details. With this in mind, we present the
details of the data analysis for the POLAR experiment, which recently led to
the tightest upper limits on the polarization of the Cosmic Microwave
Background Radiation at large angular scales. We discuss the data selection
process, mapmaking algorithms, offset removal, and the likelihood analysis
which were used to find upper limits on the polarization. Stated using the
modern convention for reporting CMB Stokes parameters, these limits are 5.0 \uK
on both E-type and B-type polarization at 95% confidence. Finally, we discuss
simulations used to test our analysis techniques and to probe the fundamental
limitations of the experiment.
