In this study the noise sensitivity of various anisotropy indices has been investigated by Monte-Carlo computer simulations and magnetic resonance imaging (MRI) measurements in a phantom and 5 healthy volunteers. Particularly, we compared the noise performance of indices defined solely in terms of eigenvalues and those based on both the eigenvalues and eigenvectors. It is found that anisotropy indices based on both eigenvalues and eigenvectors are less sensitive to noise, and spatial averaging with neighboring pixels can further reduce the standard deviation. To reduce the partial volume effect caused by the spatial averaging with neighboring voxels, an averaging method in the time domain based on the orientation coherence of eigenvectors in repeated experiments has been proposed.