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Revisiting the first implementation ofSpatial Analysis with the
Spatial Statistics
Toolbox
Joshua [email protected]
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On August 31, 1854 after several
outbreaks had already occurredelsewhere in the city a
majoroutbreak of cholera struck Soho.
Over the next ten days, over 500people on or near Broad Street
died.
Dr. John Snow wanted to prove hishypothesis that the cause of
thedisease was contaminated water
sources. He created a map, plottingrelated deaths and water
pumps toillustrate how cases of cholera were
centered around the Broad Streetwater pump.
Snows map was unique as it was the first to use cartographic
methods not only to depict a geographic area, but to also
analyze clusters of geographically dependent phenomena .
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Spatial statistics are tools that help analyze thedistribution
and relationship of features spatially.
Differing from traditional statistics, spatial
statisticsimplement distance, area and space as an integral
part of the analysis.
As Dr. Snows GIS Analyst, we are hoping to spatiallyidentify the
cause of the cholera outbreak
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Measuring GeographicDistributions
Mean Center
Directional Distribution
Analyzing Patterns
Average Nearest Neighbor
Spatial Autocorrelation
High/Low Clustering tool
Mapping Clusters
Cluster and Outlier Analysis
Hot Spot Analysis
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The first step in our analysis is todetermine the center of
ourcholera deaths. This will be a clueas to the location of
thecontaminated water source. We will weight the features sothe
mean center is more a measureof concentration than a measure
ofpurely geographic distribution. In
this case, we want to use thenumber of deaths at each point
asthe weight. We will also create a standarddistance circle, a
circle with a radiusequal to one standard deviation,with the mean
center also thecenter of the standard distancecircle.
What the mean center doesnttell us is whether the data
isconcentrated or dispersed orwhether it has a directional
trend.
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The High/Low Clustering tool measures concentrations of high or
low
values for an entire study area.
We will use this tool to see if buildings with numerous cholera
relateddeaths are clustered. If so, the location of the
contaminated water
source could be within that cluster.
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Legend
!( < -2.0
!(!( -2.0 to -1.
!(!(!( -1.0 to 1.0
!(!(!(!( 1.0 to 2.0
!(!(!(!(!( > 2.0
Looking for hot and cool spots in the data will help determine
where there is a high
concentration of cholera related deaths.
In other words, we want to look for clusters of features with
high values and clusters of featureswith low values.
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Legend
!( < -2.0
!(!( -2.0 to -1.
!(!(!( -1.0 to 1.0
!(!(!(!( 1.0 to 2.0
!(!(!(!(!( > 2.0
We can also determine which clusters are statistically
significant.
Statistically speaking, that is a confidence of greater than 95%
that it the cluster of high (or low)
values is not a random occurrence.
High Value Clusters
Outlier
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0
50
100
150
200
250
300
Deaths Per Water Pump
Broad Street Little Marlborough Rupert
Bridle Newman Warwick
Beamers Marlborough Vigo
Piccadilly Dean
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