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Descriptive Statistics for Spatial DistributionsPowerPoint Presentation

Descriptive Statistics for Spatial Distributions

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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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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 accessibility/nearness

- How dispersed are the data?
- Do the data cluster around a number of ‘centers’?

Types of Geographic Data accessibility/nearness

- Areal
- Point
- Network
- Directional
- How does this concept fit with the scale of measurement?

Switching Between Data Types accessibility/nearness

- Point to area
- Thiessen Polygons
- Interpolation

- Area to point
- Centroids

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

Thiessen Polygons Example accessibility/nearness

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

Interpolation Example accessibility/nearness

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

Interpolation Example accessibility/nearness

point i

known value zi

distance di

weight wi

unknown value (to be interpolated) at

location x

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

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?

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)

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)

Areal Descriptive Statistics Example accessibility/nearness

- Apply areal descriptive statistics to the example livestock distribution

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