We study the most general contributions due to scalar field perturbations, vector field perturbations, and anisotropic expansion to the generation of statistical anisotropy in the primordial curvature perturbation \zeta. Such a study is done using the \delta N formalism where only linear terms are considered. Here, we consider two specific cases that lead to determine the power spectrum P_\zeta(k) of the primordial curvature perturbation. In the first one, we consider the possibility that the n-point correlators of the field perturbations in real space are invariant under rotations in space (statistical isotropy); as a result, we obtain as many levels of statistical anisotropy as vector fields present and, therefore, several preferred directions. The second possibility arises when we consider anisotropic expansion, which leads us to obtain I+a additional contributions to the generation of statistical anisotropy of \zeta compared with the former case, being I and a the number of scalar and vector fields involved respectively.