A second-rank tensor (e.g. anisotropy of magnetic susceptibility) has six independent elements, whereas a tensor normalized by the mean of its trace elements has five. For a sample of measurements of anisotropic magnetic susceptibility Jelinek's (1978) sixfold multivariate statistical analysis is applicable to unnormalized data, but it is widely applied to normalized data only, though more powerful than it need be for this task. The equivalent fivefold analysis, appropriate to normalized measurements, is developed here and its relationship to the sixfold analysis is demonstrated. Since the normalized and unnormalized analyses weight specimen contributions differently, comparison of the two can give an indication of magnetic fabric homogeneity. ¿ 2000 American Geophysical Union