  The direct detection of gravitational waves has provided new opportunities
for studying the universe, but also new challenges, such as the detection and
characterization of stochastic gravitational-wave backgrounds at different
gravitational-wave frequencies. In this paper we examine two different methods
for their description, one based on the amplitude of a gravitational-wave
signal and one on its Stokes parameters. We find that the Stokes parameters are
able to describe anisotropic and correlated backgrounds, whereas the usual
power spectra of the amplitudes cannot -- i.e. the Stokes spectra are sensitive
to properties such as the spatial distribution of the gravitational-wave
sources in a realistic backgrounds.
