  The measurement of radio polarization may be regarded as a three-dimensional
statistical problem because the large photon densities at radio wavelengths
allow the simultaneous detection of the three Stokes parameters which
completely describe the radiation's polarization. The statistical nature of the
problem arises from the fluctuating instrumental noise, and possibly from
fluctuations in the radiation's polarization. A statistical model is used to
derive the general, three-dimensional statistics that govern radio polarization
measurements. The statistics are derived for specific cases of source-intrinsic
polarization, with an emphasis on the orthogonal polarization modes in pulsar
radio emission. The statistics are similar to those commonly found in other
fields of the physical, biological, and Earth sciences. Given the highly
variable linear and circular polarization of pulsar radio emission, an
understanding of the three-dimensional statistics may be an essential
prequisite to a thorough interpretation of pulsar polarization data.
