It is sometimes important to test the hypothesis that a given set ofNunit vectors, representing the directions of a physical quantity, comes from a population of vectors which are randomly oriented in two or three dimensions, as opposed to a population in which the vectors are clustered to some degree. For three dimensions, Watson has proposed the length of the sample resultant as a suitable statistic, and given the appropriate tests. An improved table is given for the application of Watson's tests. The power of the test against a specific alternative distribution, used in geophysical problems, is used to give a table of sample sizes necessary to detect a degree of clustering.