The day-to-day variations of the total vector anisotropy observed by neutron monitors are discussed. A model is developed to explain these variations in terms of counting-statistics noise, convection in the solar wind, scattering of cosmic rays in the interplanetary magnetic field, and particle drifts. Both the amplitude and the phase variations of the Deep River neutron monitor diurnal anisotropy are shown to agree with the model's predictions. A novel prediction, confirmed by the observations, is the tendency for afternoon hour anisotropies to be larger than evening hour anisotropies.