Significance criteria for variance matrix applications

The variance matrix technique for determining preference or avoidance directions in space of a group of vectors is used frequently in the analysis of satellite data, especially in the analysis of magnetic-field and solar-wind velocity data. The method gives automatically a parameter that indicates the strength of the preference or avoidance. However, no significance criterion has yet been given that compares the strength parameter against the parameter expected from a random group of vectors. This note gives such a criterion.