Moran's I Statistic

Ho	Values in different regions are spatially independent, the observed values are assigned at random among locations.  I is close to zero, depending on sample size.
Ha	Values are not spatially independent.  I is not zero.

Test Statistic

Moran's I (Moran 1950) is a weighted correlation coefficient used to detect departures from spatial randomness. Moran's I is used to determine whether neighboring areas are more similar than would be expected under the null hypothesis. Moran's I is:

where N equals the number of regions, wij is an spatial weight set denoting the strength of the connection between areas i and j, zi,t and zj,t are the z-scores of the variable(s) tested (for a bivariate Moran, the zj,t are from the other "neighbor" variable); and W is the sum of the weights

SpaceStat calculates the significance of Moran's I using Monte Carlo randomizations of the dataset.