Transcript Chapter 4 – Descriptive Spat

Chapter 4 – Descriptive Spatial
Statistics
Scott Kilker
Geog 3000- Advanced
Geographic Statistics
Learning Objectives
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Explain central tendency as applied in a
spatial context
Define spatial measures of dispersion and
recognize possible applications
Identify potential limitations and locational
issues associated with applied descriptive
spatial statistics
21 July 2015
From 'An Introduction to Statistical Problem Solving in Geography'
by McGrew & Monroe
Descriptive Spatial Statistics
Descriptive Spatial Statistics, also referred
to as Geostatistics, are the spatial
equivalent to the basic descriptive statistics.
They can be used to summarize point
patterns and the dispersion of some
phenomena.
21 July 2015
From 'An Introduction to Statistical Problem Solving in Geography'
by McGrew & Monroe
Central Tendency in a Spatial Context
Mean Center
Mean center represents
an average center of a
number of coordinates.
This is calculated by averaging the
X coordinates and Y coordinates
separately and using the average
for the Mean Center coordinate.
21 July 2015
From 'An Introduction to Statistical Problem Solving in Geography'
by McGrew & Monroe
Central Tendency in a Spatial Context
Mean Center
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Considered the Center of
Gravity
Can be strongly affected by
outliers
Most well know use is the U.S.
Bureau of Census geographic
“center of population”
calculation that shows the
mean center of the U.S.
population
21 July 2015
From 'An Introduction to Statistical Problem Solving in Geography'
by McGrew & Monroe
Central Tendency in a Spatial Context
Mean Center in Action
21 July 2015
From 'An Introduction to Statistical Problem Solving in Geography'
by McGrew & Monroe
Central Tendency in a Spatial Context
Weighted Mean Center
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Points can be weighted meaning
they can be given more or less
influence on the calculation of the
mean center
Points could represent cities,
frequencies, volume of sales or
some other value that will affect the
points influence.
Analogous to frequencies in the
calculation of grouped statistics like
the weighted mean
Influenced by large frequencies of a
point
21 July 2015
From 'An Introduction to Statistical Problem Solving in Geography'
by McGrew & Monroe
Central Tendency in a Spatial Context
Least Squares Property
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Analogous to the least squares
for a mean
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Sum of squared deviations
about mean is zero
Sum of squared deviations
about a mean is less than the
sum of squared deviations
about any other number
Deviations are distances
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Calculated as the Euclidean
distance
21 July 2015
From 'An Introduction to Statistical Problem Solving in Geography'
by McGrew & Monroe
Central Tendency in a Spatial Context
Euclidean Median
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Considered the Median
Center
Often more useful than the
Mean Center.
Used when determining the
central location that
minimizes the unsquared
rather than the squared
Can be weighted
21 July 2015
From 'An Introduction to Statistical Problem Solving in Geography'
by McGrew & Monroe
Central Tendency in a Spatial Context
Euclidean Median
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Used in economic geography to solve the “Weber” problem which
searches for the “best” location for an industry.
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The best location will result in
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Minimized transportation costs of raw material to factory
Minimized transportation costs of finished products to the market
21 July 2015
From 'An Introduction to Statistical Problem Solving in Geography'
by McGrew & Monroe
Central Tendency in a Spatial Context
Euclidean Median
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Heavily used in public and private facility location
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Used to minimize the average distance a person must travel to
reach a destination.
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Useful in location of fire stations, police stations, hospitals and care centers
Used in conjunction with demographics to select store locations that will
target the desired consumers
21 July 2015
From 'An Introduction to Statistical Problem Solving in Geography'
by McGrew & Monroe
Spatial measures of dispersion
Standard Distance
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Analogous to the Standard
Deviation in descriptive
statistics
Measures the amount of
absolute dispersion in a
point pattern
Uses the straight-line
Euclidean distance of each
point from the mean center
21 July 2015
From 'An Introduction to Statistical Problem Solving in Geography'
by McGrew & Monroe
Spatial measures of dispersion
Standard Distance
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Like Standard Deviation, strongly influenced by
extreme locations
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Weighted standard distance can be used for
problems that use the weighted mean center
21 July 2015
From 'An Introduction to Statistical Problem Solving in Geography'
by McGrew & Monroe
Manhattan Distance & Median
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Not all analysis would benefit
from the use of straight line
distances
Manhattan distance is
represented by a grid like city
blocks in Manhanttan
Manhattan Median is the center
point in Manhattan space
Manhattan Median cannot be
found for a spatial pattern
having an even number of
points
21 July 2015
From 'An Introduction to Statistical Problem Solving in Geography'
by McGrew & Monroe
Spatial measures of dispersion
Coefficient of Variation
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Calculated by dividing the standard deviation by
the mean
Measures the relative dispersion of values
No analogous methods exists for measuring spatial
dispersion
Dividing the standard distance by the mean center
does not provide meaningful results
21 July 2015
From 'An Introduction to Statistical Problem Solving in Geography'
by McGrew & Monroe
Spatial measures of dispersion
Relative Distance
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To obtain a measure of relative
dispersion, the standard
distance must be divided by
some measure of regional
magnitude
Region magnitude cannot be
mean center
Radius of a circle the same size
that is being evaluated can be
appropriate
21 July 2015
From 'An Introduction to Statistical Problem Solving in Geography'
by McGrew & Monroe
Spatial measures of dispersion
Relative Distance
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Using a circle may not always
be valid. For instance, if the
region is wider than tall, it will
have a strong influence on the
dispersion
A measure of relative
dispersion is influenced by the
boundary of the region being
studied
21 July 2015
Region is not always a Circle
Radius may not be the right choice
From 'An Introduction to Statistical Problem Solving in Geography'
by McGrew & Monroe
Descriptive spatial statistics
Limitations and Locational issues
Geographers should look at geostatistics very carefully
 Interpretation can be difficult
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The mean center for a high income area could be in a low income area
Should view geostatistics as general indicators of location
instead of precise measurements
Point pattern analysis an benefit from consideration of other
possible pattern characteristics
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Using the knowledge of descriptive statistics like skewness and kurtosis
can offer insights about the symmetry of the pattern that geographers
could find useful when comparing point patterns
Value in comparing degrees of clustering and dispersal in different point
patterns thought measuring spatial kurtosis levels
21 July 2015
From 'An Introduction to Statistical Problem Solving in Geography'
by McGrew & Monroe
More Resources
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Wikipedia - http://en.wikipedia.org/wiki/Spatial_descriptive_statistics
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Arthur J. Lembo at
http://www.css.cornell.edu/courses/620/css620.html
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CrimeStat III Application – Stats in Action http://www.icpsr.umich.edu/icpsrweb/CRIMESTAT/about.jsp
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ESRI Spatial Statistics toolbox (ArcGIS 9.2) http://webhelp.esri.com/arcgisdesktop/9.2/index.cfm?TopicName=An_
overview_of_the_Spatial_Statistics_toolbox
21 July 2015
From 'An Introduction to Statistical Problem Solving in Geography'
by McGrew & Monroe
Summary
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Descriptive Spatial Statistics have many similarities with the
descriptive statics – mean, median, standard deviation,
weighted mean, measures of dispersion
Care needs to be taken when evaluating geostatistics because
results sometimes will not be meaningful – methods must be
understood
Methods applied with a GIS can be very powerful in their
application to determine where industries, business, public and
private facilities are located so they provide the greatest values
to the owners and public
21 July 2015
From 'An Introduction to Statistical Problem Solving in Geography'
by McGrew & Monroe