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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 l.jpg

Descriptive Statistics for Spatial Distributions

Chapter 3 of the textbook

Pages 76-115


Overview l.jpg
Overview

  • Types of spatial data

  • Conversions between types

  • Descriptive spatial statistics


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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).


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Applications of Descriptive spatial statistics: dispersion accessibility/nearness

  • How dispersed are the data?

  • Do the data cluster around a number of ‘centers’?


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Types of Geographic Data accessibility/nearness

  • Areal

  • Point

  • Network

  • Directional

  • How does this concept fit with the scale of measurement?


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Switching Between Data Types accessibility/nearness

  • Point to area

    • Thiessen Polygons

    • Interpolation

  • Area to point

    • Centroids


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Thiessen Polygons accessibility/nearness

  • 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


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Thiessen Polygons Example accessibility/nearness


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Spatial Interpolation: accessibility/nearnessInverse 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


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Interpolation Example accessibility/nearness

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


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Interpolation Example accessibility/nearness

point i

known value zi

distance di

weight wi

unknown value (to be interpolated) at

location x


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Descriptive Statistics for Areal Data accessibility/nearness

  • 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


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Descriptive Statistics for Areal Data accessibility/nearness

  • 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?


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Descriptive Statistics for Areal Data accessibility/nearness

  • 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)


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Gini Coefficient accessibility/nearness

  • 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)


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Areal Descriptive Statistics Example accessibility/nearness

  • Apply areal descriptive statistics to the example livestock distribution


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