Consider a set of points, some of which are anomalous (larger than a specified cutoff value), located on a plane. Whether some or all of these points are clustered to form one anomaly or more or, alternatively whether these points are scattered at random, may be investigated by measuring perimeters of convex hulls. A convex hull is the smallest convex polygon that will encompass a group of points. Examples of convex polygons are triangles, rectangles, and all other regular polygons. A set of anomalous points is selected and the perimeters of the convex hulls of this set and all its subsets are measured and compared with tabulated values of perimeters for each subset size. For a given subset size consider those perimeters which are less than the tabulated perimeter. If the number of convex hulls is greater than the maximum number expected by chance, then the chance that any one of the observed hulls is a nonrandom cluster is the ratio of the observed number to the sum of the observed and the maximum number expected by chance. Otherwise, the points are evidently not clustered. If many sample points are anomalous, an alternate model defines various configurations of contiguous points and compares the observed number of configurations per unit area with the expected number. Applications are discussed.