Analysis of object clustering

Objects of a given type lie on a plane or in a thin layer. In the analysis of the arrangement of such objects, the question may arise as to whether these objects form clusters or whether they are randomly distributed. This question can be answered by the calculation of the coefficient of dispersion (CD) of the objects. Some statistical properties of this coefficient, i.e., its sensitivity and its chi-square approximation, are analyzed in this paper. The proposed approach for calculating sensitivity is a mathematical simulation that is not generally applicable but is valid in various biologic applications. Assuming that the objects are much smaller than the expected clusters and that no knowledge exists about interactions among the objects or between the objects and their surroundings, the objects can be assumed to be distributed randomly on the plane. Such situations may occur in various fields, i.e., biology, sociology, archaeology and ecology. The authors have applied this approach successfully in investigating the densities of T-cell lymphocytes in renal transplants treated with Cyclosporin A or conventional immunosuppressive therapy.