Spatial statistics Lecture 3 2/4/2008

Spatial statistics
Lecture 3
What are spatial statistics
Not like traditional, a-spatial or non-spatial statistics
But specific methods that use distance, space, and
spatial relationships as part of the math for their
It is a spatial distribution and pattern analysis tool
– Identifying characteristics of a distribution; tools
used to answer questions like where is the
center, or how are feature distributed around the
center? (Measuring Geographic Distributions)
– Quantifying or describing spatial pattern; are our
features random, clustered, or evenly dispersed
across our study area? (Analyzing Patterns)
– Mainly deal with point, line, polygon (vector)
Why use spatial statistics?
– To help assess patterns, trends, and
• Better understanding of geographic
• Pinpoint causes of specific geographic
• Make decision with high level of confidence
• Summarize the distribution in a single
1. Measuring geographic (spatial)
– Not only crime analysts but
also GIS practitioners in
many research areas, such
as epidemiology,
archaeology, wildlife biology,
and retail analysis, will
benefit from the spatial
statistics tools in ArcGIS 9.
These tools can be easily
modified or extended
because most were written
using the Python scripting
language. The source code
for the statistical tools can be
accessed from ArcToolbox
and serve as samples and
templates for further
Mean center of
distribution and
Track changes
in the
Average of x, y
Mean center and central feature tools tell about the center of a distribution
But do not tell the overall distribution.
Standard distance tool tells how dispersed our features are around that center
Analyzing spatial patterns
• Give us ways to measure the degree to which our
features are clustered, dispersed, or randomly
distributed across the study area
• Analyzing Patterns
– Global calculations
– Identifies the patterns/overall trends of data
• Are features clustered and what is the overall pattern?
– Spatial Autocorrelation tool
• Mapping Cluster
– Local calculations
– Identifies the extent and location of clustering or dispersion
• Where are the clusters (or where are the hot spots)?
– Hot Spot Analysis tool
Meaning the clustering in 2003 is more intense than it was in 1994
Z score is a measure of standard
deviation. If you have σ is (-1.96,
1.96), z score is falling between
them, you are seeing a pattern of
random pattern. If z score falls
outside, like -2.5 or 5.4, then you
have a pattern that’s too unusual
to be a pattern of random
If there is any place
in the USA where
people either dying
earlier, or living
longer, than the
average American?
Blue living longer
than normal, red
living shorter than
• In the global analysis previously, we ask: is there clustering?
• In the local analysis, we ask: where are the clusters, or where
do features with similar attribute values cluster spatially
– Hot spots tool
• “understanding Spatial Statistics in ArcGIS
9” by Sandi Schaefer and Lauren Scott.