| Abstract: | Several procedures, based upon cell count analysis, have been proposed for classifying spatial distributions, or maps, associated with some region R. Such procedures are rather imprecise and are known to depend upon the sixes and shapes of the cells in the particular partition of R under consideration. In this paper, the problem is considered from the point of view of hypothesis testing. A test of randomness based upon an arbitrary number of partitions of R is giuen. If the hypothesis of randomness is rejected, additional tests may be performed to classify the map into one of two categories, clustered or regular. These tests provide a number of advantages over existing procedures. Based upon multiple partitions of R, they decrease the dependence upon any particular partition, and the colresponding classification is precise since the null hypothesis distribution of the test statistic is (asymptotically) known. Finally, they allow a great deal of flexibility in testing for certain alternatives to randomness, and are applicable to one-, two-, and three- dimensional maps. |
