Existing methods for the analysis of the shape of directional data sets, primarily paleosccular variation data, tend to have serious inconsistencies in their application and in general are difficult to apply. The question of whether or not a given data set is distributed in a circular manner about its mean is important in many types of analysis, particularly so, since circularity is a necessary condition for the application of the statistical techniques of Fisher (1953). A new statistic, called the eccentricity, is developed and shown to offer information as to the shape of a distribution of directions. The eccentricity statistic does not depend on choice of classes or intervals, is invariant to rotations of the distribution about the mean directions, is simple to apply, and is easily understood in trms of a simple physical analogy. The mothod is applied to 112 Hawaiian lavas (Doell and Cox, 1965). The analysis shows good agreement with a model in which magnetic variations in Hawaii are a consequence of dipole wobble only, with no significant contributions from the nondipole field.