A general expression allowing the calculation of the influence on cell factors of an anisotropic component of the scattering law in a given medium is established in the framework of the integral transport theory. This expression is applied to the calculations of the thermal utilization, fast fission factor, and diffusion coefficients. In the case of the thermal utilization, the effect of the anisotropic scattering in the moderator can be taken into account by a rigorous correction whatever the cell; this correction coincides with the classical transport correction only for widely spaced lattices, and still with some restrictions; for closely packed lattices the transport correction has no theoretical justification, and seriously underestimates the effect. In the fuel, the transport correction is no more theoretically justified, although it leads to good results for rather large rods; a very simple formula is established from the general expression, allowing the calculation of the correction tof, without using the transport cross section. This formula leads, for all the rod diameters considered, to results in very good agreement with referenced values obtained by theS8method. An analogous formula for the fast-fission factor is established.