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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

• 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