Phase-space transforms describe spatial and angular information about light sources where one example is the Wigner functions in wave optics. Stokes parameters, on the other hand, supply information about the polarization of light beams. The generalized phase space Stokes parameters of 2D stochastic electromagnetic beams are already developed. In this article, the application of anisotropic light sources in generalized phase space Stokes parameters is theoretically investigated and numerically analyzed. There are several different ways of studying electromagnetic light beams depending on the spatial domain. But, most measure of the polarization of random light fields is carried out within the Stokes parameters context. In this account we study the electromagnetism, Stokes parameters, phase space, and the anisotropy properties of random light beams at once. We find here that when an anisotropy introduced in phase space then the cross terms of the Wigner matrix depart from the diagonal terms, which is not the same in configuration space. As a result, anisotropy has a different effect in Phase space, i.e. an anisotropic source introduces a phase and a variance change only in the cross terms of Wigner matrix. This is due to the use of anisotropy in the shifted kernel of Wigner transform.