Survey on cluster tests for spatial area data

Geographical data usually exhibit some amount of spatial dependency, a correlation between the values of neighbouring districts. Thus one wants to have measures for the strength of this dependency and tests for the deviation from randomly distributed values. There exist several tests. In this survey, they are collected and compared. This is done separately for binary variables assuming only two values and for real-valued variables. Among the tests are the black-black count, the black-white count, Moran's I, Geary's c and the Getis-Ord statistics. Some new statistics are proposed, a variant to the black-black count and statistics based on clusters composed of triplets of districts. Included are also new results on the distribution of Moran's I and its local version, based on simulations using several areas with 37 to 327 districts. Roughly speaking, the distribution of I is fairly close to a normal distribution and surprisingly independent of the underlying distribution of the district values while the local I's are extremely far from normal and highly dependent on the underlying distribution