Post on 04-Jan-2016
Chapter 4 – Descriptive Spatial Statistics
Scott Kilker Geog 3000- Advanced Geographic Statistics
April 20, 2023From 'An Introduction to Statistical Problem Solving in Geography'
by McGrew & Monroe
Learning Objectives
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
April 20, 2023From '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.
April 20, 2023From 'An Introduction to Statistical Problem Solving in Geography'
by McGrew & Monroe
Central Tendency in a Spatial Context
Mean CenterMean 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.
April 20, 2023From 'An Introduction to Statistical Problem Solving in Geography'
by McGrew & Monroe
Central Tendency in a Spatial Context
Mean Center 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
April 20, 2023From 'An Introduction to Statistical Problem Solving in Geography'
by McGrew & Monroe
Central Tendency in a Spatial Context
Mean Center in Action
April 20, 2023From 'An Introduction to Statistical Problem Solving in Geography'
by McGrew & Monroe
Central Tendency in a Spatial Context
Weighted Mean Center 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
April 20, 2023From 'An Introduction to Statistical Problem Solving in Geography'
by McGrew & Monroe
Central Tendency in a Spatial Context
Least Squares Property
Analogous to the least squares for a mean
– 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– Calculated as the Euclidean
distance
April 20, 2023From 'An Introduction to Statistical Problem Solving in Geography'
by McGrew & Monroe
Central Tendency in a Spatial Context
Euclidean Median
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
April 20, 2023From 'An Introduction to Statistical Problem Solving in Geography'
by McGrew & Monroe
Central Tendency in a Spatial Context
Euclidean Median
Used in economic geography to solve the “Weber” problem which searches for the “best” location for an industry.
The best location will result in– Minimized transportation costs of raw material to factory– Minimized transportation costs of finished products to the market
April 20, 2023From 'An Introduction to Statistical Problem Solving in Geography'
by McGrew & Monroe
Central Tendency in a Spatial Context
Euclidean Median
Heavily used in public and private facility location
Used to minimize the average distance a person must travel to reach a destination.
– 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
April 20, 2023From 'An Introduction to Statistical Problem Solving in Geography'
by McGrew & Monroe
Spatial measures of dispersion
Standard Distance
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
April 20, 2023From 'An Introduction to Statistical Problem Solving in Geography'
by McGrew & Monroe
Spatial measures of dispersion
Standard Distance
Like Standard Deviation, strongly influenced by extreme locations
Weighted standard distance can be used for problems that use the weighted mean center
April 20, 2023From 'An Introduction to Statistical Problem Solving in Geography'
by McGrew & Monroe
Manhattan Distance & Median
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
April 20, 2023From 'An Introduction to Statistical Problem Solving in Geography'
by McGrew & Monroe
Spatial measures of dispersion
Coefficient of Variation
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
April 20, 2023From 'An Introduction to Statistical Problem Solving in Geography'
by McGrew & Monroe
Spatial measures of dispersion
Relative Distance
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
April 20, 2023From 'An Introduction to Statistical Problem Solving in Geography'
by McGrew & Monroe
Spatial measures of dispersion
Relative Distance
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
Region is not always a CircleRadius may not be the right choice
April 20, 2023From '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
– 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
– 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
April 20, 2023From 'An Introduction to Statistical Problem Solving in Geography'
by McGrew & Monroe
More Resources
Wikipedia - http://en.wikipedia.org/wiki/Spatial_descriptive_statistics
Arthur J. Lembo at http://www.css.cornell.edu/courses/620/css620.html
CrimeStat III Application – Stats in Action - http://www.icpsr.umich.edu/icpsrweb/CRIMESTAT/about.jsp
ESRI Spatial Statistics toolbox (ArcGIS 9.2) - http://webhelp.esri.com/arcgisdesktop/9.2/index.cfm?TopicName=An_overview_of_the_Spatial_Statistics_toolbox
April 20, 2023From 'An Introduction to Statistical Problem Solving in Geography'
by McGrew & Monroe
Summary
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