Spatial Autocorrelation

Steve Henderson



Moran's I Analysis


The map below shows the a percentile clorpleth of the percentage of Maori population in the City of Aukland by Census Area Units (CAU's).  The Moran's I scatterplot to the right shows that the data does show a tendency towards clustering, with a Moran's I greater than zero.  The map and scatter plot below have the areas which have a lower percentage of Maori population than the whole, mostly the central  and northern parts of the city.


Straight Line Distance


The map below has the area with higher than average Maori population highlighted, two clusters on the east and west sides of the city.  Since most of the points in the scatterplot can be found in the upper right and lower left quadrants, this analysis shows a clear tendency towards clustering.  Most of the Census Area Units (CAU) fell into these quadrants with the exception of some areas on the edges of these two clusters and with the notable exception of the Orakei North area (the orange CAU on the north side of the City..







Local Indicators of Spatial Association (LISA) Analysis


A Local Indicators of Spatial Association (LISA) analysis uses Moran's I and a Monte Carlo simulation to calculate which CAU's have the greatest conribution to the tendency towards clustering.  The map below show the CAU's for the greater Aukland area based on percentage of Pacific Islander population.  The percentile map shows a the CAU with the most Pacific Islanders as a central area of greater Aukland south of the main part of the City.  The Moran's I plot on the right shows strong signs of clustering (Moran's I = .07371, fairly close to 1) with most points falling in the upper right and lower left quadrants.  The Clustering map shows the CAU's with the most positive spatial autocorrellation in red and blue.  The Significance map show the CAU's in dark green which contribute most strongly to the positive autocorrelation, note that both the areas with strong High-High (red) and Low-Low (blue) CAU's contribute strongly to the positive autocorrelation.


Weighted Raster