  A four-dimensional statistical description of electromagnetic radiation is
developed and applied to the analysis of radio pulsar polarization. The new
formalism provides an elementary statistical explanation of the modal
broadening phenomenon in single pulse observations. It is also used to argue
that the degree of polarization of giant pulses has been poorly defined in past
studies. Single and giant pulse polarimetry typically involves sources with
large flux densities and observations with high time resolution, factors that
necessitate consideration of source-intrinsic noise and small-number
statistics. Self noise is shown to fully explain the excess polarization
dispersion previously noted in single pulse observations of bright pulsars,
obviating the need for additional randomly polarized radiation. Rather, these
observations are more simply interpreted as an incoherent sum of covariant,
orthogonal, partially polarized modes. Based on this premise, the
four-dimensional covariance matrix of the Stokes parameters may be used to
derive mode-separated pulse profiles without any assumptions about the
intrinsic degrees of mode polarization. Finally, utilizing the small-number
statistics of the Stokes parameters, it is established that the degree of
polarization of an unresolved pulse is fundamentally undefined; therefore,
previous claims of highly polarized giant pulses are unsubstantiated.
Unpublished supplementary material is appended after the bibliography.
