Scattering anisotropy is often taken into account, in an isotropic formalism, by a transport correction. This correction, which, even in a homogeneous medium, is known to be false in a multigroup theory, is always incorrect for the calculation of neutron leakages in a lattice. The method presented here allows calculation of the buckling-independent diffusion coefficients in a Wigner-Seitz cell, for a linearly anisotropic scattering law. It allows testing of the degree of approximation of the transport correction in various types of lattices, and shows that the axial coefficient may be strongly underestimated in certain cases. This method also allows testing of the simple formulas presented in the past for diffusion coefficients, which lead to good results. The problem of the coupling between energy groups, which appears in the calculation of diffusion coefficients, is also analyzed by the present method; it usually appears to be weak.