Diffusion tensor imaging (DTI) provides a powerful tool for identifying white matter (WM) alterations in clinical populations. The prevalent method for group-level analysis of DTI is statistical comparison of the diffusion tensor fractional anisotropy (FA) metric. The FA metric, however, does not capture the full orientational information contained in the diffusion tensor. For example, the FA test is incapable of detecting group-level differences in diffusion orientation when the level of anisotropy is unaffected. Here, we apply multivariate hypothesis testing procedures to the elements of the diffusion tensor as an alternative to univariate testing using FA. Both parametric and nonparametric tests are proposed with each choice carrying specific assumptions about the diffusion tensor model. Of particular interest is the Cramér test, which works on Euclidean interpoint distances and can be readily adapted to a specific non-Euclidean framework by applying matrix logarithms to the diffusion tensors. Using Monte Carlo simulations, we show that multivariate tests can detect diffusion tensor principal eigenvector differences of 15 degrees with up to 80–90% power under typical design conditions. We also show that some multivariate tests are more sensitive to FA differences, when compared to a univariate test on FA, even if there is no principal eigenvector difference. The Cramér test, using the Euclidean interpoint distances, performed best under both simulation scenarios. When applying the Cramér test of the diffusion tensor in a clinical population with a history of migraine, a 169% increase was observed in the volume of a significant cluster compared to the univariate FA test.