Local G Statistics

Ho	There is no clustering of high or low values around location i, test statistic is close to zero.
Ha	There is clustering of high or low values around location i. A significant positive value implies a clustering of high values, and a significant negative value indicates a clustering of low values.

Statistic

There are two variants of the local G statistic. The Gi statistic excludes the value at i ("ego") from the summation and is used for spread or diffusion studies, while the Gi* includes the value at i in the summation and is most often used for studies of clustering. SpaceStat implements the local G statistics as generalized to more flexible spatial weights in Ord and Getis (1995). In these equations, the xj,t are the values of a variable (x) observed at location j and time t. These values are multiplied by the spatial weights set, wij, that denotes which locations to include in the analysis and how to weight them. The sum of these observed values is subtracted from the expected value, the sample mean (x bar), multiplied by the sum of the weights. Then, this difference is divided by the standard deviation, which includes some weighting factors.

Gi		Gi*
notation		notation
	sample mean excluding location i ("ego")		sample mean including ego
	sum of the weights not including the ego		sum of the weights including ego's weight
	sample standard deviation, excluding ego		sample standard deviation, including ego
	number of objects in the geography at time t		number of objects in the geography at time t
	the sum of the squared weights, not including ego		the sum of the squared weights, including ego

Significance

The significance of each Gi and Gi* value is evaluated using a Monte Carlo randomizations of the dataset.