An error in the significance test associated with a rotational vector procedure for analysis of axial orientation data is pointed out and explained. An alternative approach already well established in the geologic literature, which does not require that sense be assigned to the axial data, is discussed; the results of the application of both methods to 36 till fabrics are compared. It is concluded that the alternative approach is superior because it is statistically sound and more efficient with regard to computer time required; it also provides more information about the fabric than does the rotational vector procedure.