Descriptive Statistics for Spatial Distributions

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# Descriptive Statistics for Spatial Distributions - PowerPoint PPT Presentation

Descriptive Statistics for Spatial Distributions. Chapter 3 of the textbook Pages 76-115. Overview. Types of spatial data Conversions between types Descriptive spatial statistics. Applications of descriptive spatial statistics: accessibility/nearness. What types exist? Examples:

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### Descriptive Statistics for Spatial Distributions

Chapter 3 of the textbook

Pages 76-115

Overview
• Types of spatial data
• Conversions between types
• Descriptive spatial statistics
Applications of descriptive spatial statistics: accessibility/nearness
• What types exist?
• Examples:
• What is the nearest ambulance station for a home?
• A point that minimizes overall travel times from a set of homes (where to locate a new hospital).
• A point that minimizes travel times from a majority of homes (where to locate a new store).

Applications of Descriptive spatial statistics: dispersion

• How dispersed are the data?
• Do the data cluster around a number of ‘centers’?
Types of Geographic Data
• Areal
• Point
• Network
• Directional
• How does this concept fit with the scale of measurement?
Switching Between Data Types
• Point to area
• Thiessen Polygons
• Interpolation
• Area to point
• Centroids
Thiessen Polygons
• According to the book…
• 1) Join (draw lines) between all “neighboring” points
• 2) Bisect these lines
• 3) Draw the polygons
• Making Thiessen polygons is all about making triangles
• Draw connecting lines between points and their 2 closest neighbors to make a triangle (some points may be connected to more than 2 points)
• Bisect the 3 connecting lines and extend them until they intersect
• For acute triangles: the intersection point will be inside the triangles and all bisecting lines will actually cross the original connecting lines
• For obtuse triangles: the intersection point will be outside the triangles and the bisecting line opposite the obtuse angle won’t cross the connecting line
• The bisecting lines are the edges of the Thiessen polygons

Spatial Interpolation:Inverse Distance Weighting (IDW)

point i

known value zi

distance di

weight wi

unknown value (to be interpolated) at

location x

The estimate of the unknown value is a weighted average

Sample weighting function

Interpolation Example
• Calculate the interpolated Z value for point A using B1 B2 B3 B4
Interpolation Example

point i

known value zi

distance di

weight wi

unknown value (to be interpolated) at

location x

Descriptive Statistics for Areal Data
• Location Quotient
• Basically the % of a single local population / % of the single population for the entire area
• The textbook refers to these groups as the activity (A) and base (B)
• Example: % of people employed locally in manufacturing / % of manufacturing workers in the region
• Each polygon will have a calculated value for each category of worker
Descriptive Statistics for Areal Data
• Location Coefficient
• A measure of concentration for a single population (or group, activity, etc.) over an entire region
• Calculated by figuring out the percentage difference between % activity and the % base for each areal unit
• Sum either the positive or negative differences
• Divide the sum by the total population
• How is this different from the localization quotient?
Descriptive Statistics for Areal Data
• Lorenz Curve
• A method for showing the results of the location quotient (LQ) graphically
• Calculated by first ranking the areas by LQ
• Then calculate the cumulative percentages for both the activity and the base
• Graph the data with the activity cumulative percentage value acting as the X and the base cumulative percentage value acting as the Y
• Compare the shape of the curve to an unconcentrated line (i.e., a line with a slope of 1)
Gini Coefficient
• Also called the index of dissimilarity
• The maximum distance between the Lorenz curve and the unconcentrated line
• Equivalent to the largest difference between the activity and base percentages
• The Gini coefficient (and the Lorenz curve) are also useful for comparing 2 activities (i.e., testing similarity rather than just concentration)
Areal Descriptive Statistics Example
• Apply areal descriptive statistics to the example livestock distribution