A method is provided for automatically characterizing data sets containing data points, which may be produced by measurements such as with sonar arrays, as either random or non-random. The data points for each data are located within a Cartesian space and a polygon envelope is constructed which contains the data points. The polygon is divided into grid cells by constructing a grid over the polygon. A prediction is made as to how many grid cells would be occupied if the data were merely a random process. The prediction takes one of two forms depending on the sample size. For small sample sizes, an exact Poisson probability method is utilized. For large sample sizes an approximation to the exact Poisson probability is utilized. A third test is utilized to test the adequacy of the Poisson based model is adequate to assess the data set as either random or non-random.