When a two-dimensional map contains points that appear to be scattered somewhat at random, a question that often arises is whether groups of points that appear to cluster are merely exhibiting ordinary behavior that one can expect with any random distribution of points, or whether the clusters are too pronounced to be attributable to chance alone. In this paper a method for detecting clusters along a straight line.is applied to the two-dimensional map of bismuth-214 anomalies observed as part of the National Uranium Resource Evaluation Program in the Lubbock, Texas region. Some exact probabilities associated with this method are computed and compared with two approximate methods. The two methods for approximating probabilities work well in the cases examined, and can be used when it is prohibitive to obtain the exact probabilities.