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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:

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descriptive statistics for spatial distributions

Descriptive Statistics for Spatial Distributions

Chapter 3 of the textbook

Pages 76-115

overview
Overview
  • Types of spatial data
  • Conversions between types
  • Descriptive spatial statistics
applications of descriptive spatial statistics accessibility nearness
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).
slide4

Applications of Descriptive spatial statistics: dispersion

  • How dispersed are the data?
  • Do the data cluster around a number of ‘centers’?
types of geographic data
Types of Geographic Data
  • Areal
  • Point
  • Network
  • Directional
  • How does this concept fit with the scale of measurement?
switching between data types
Switching Between Data Types
  • Point to area
    • Thiessen Polygons
    • Interpolation
  • Area to point
    • Centroids
thiessen polygons
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
slide9

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
Interpolation Example
  • Calculate the interpolated Z value for point A using B1 B2 B3 B4
interpolation example11
Interpolation Example

point i

known value zi

distance di

weight wi

unknown value (to be interpolated) at

location x

descriptive statistics for areal data
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 data13
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 data14
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
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
Areal Descriptive Statistics Example
  • Apply areal descriptive statistics to the example livestock distribution
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