05 descriptive spatial stats part1

8/13/2019 05 Descriptive Spatial Stats Part1

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Descriptive Statistics for

Spatial Distributions

Chapter 3 of the textbook

Pages 76-115


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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 ahome?

A point that minimizes overall travel timesfrom 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 newstore).


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How dispersed are the data?

Do the data cluster around a number of

centers?

Applications of Descriptive spatial statistics:

dispersion


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Types of Geographic Data

Areal

Point

NetworkDirectional

How does this concept fit with the scale of

measurement?


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Switching Between Data Types

Point to area

Thiessen Polygons

Interpolation

Area to point

Centroids


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Thiessen PolygonsAccording 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 linesbetween points and their 2 closest neighborsto make a triangle (some points may be connected to more than 2points)

Bisect the 3 connecting linesand extend them until they intersect

For acute triangles: the intersection pointwill be inside thetrianglesand allbisecting lineswill actually cross the original

connecting lines For obtuse triangles: the intersection pointwill be outside the

trianglesand thebisecting lineopposite the obtuse angle wontcross the connecting line

Thebisecting linesare the edges of the Thiessen polygons


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Thiessen Polygons Example


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point iknown value zidistance diweight wi

unknown value (to beinterpolated) atlocationx

i

i

i

iix wzwz

21 ii dw

The estimate of theunknown value is aweighted average

Sample weighting function

Spatial Interpolation:Inverse Distance Weighting (IDW)


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Interpolation Example

Calculate the interpolated Z value for point

A using B1B2B3B4


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Interpolation Example

point iknown value zidistance diweight wi

unknown value(to beinterpolated) atlocationx

i

i

i

iix wzwz

21 ii dw


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Descriptive Statistics for Areal Data

Location Quotient

Basically the % of a single localpopulation / % of the singlepopulation for the entire area

The textbook refers to these groupsas the activity (A) and base (B)

Example: % of people employedlocally in manufacturing / % ofmanufacturing workers in the region

Each polygon will have a calculatedvalue for each category of worker

BiBAiALQ

i

ii

/

/


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Location Coefficient

A measure of concentration for a single population (orgroup, activity, etc.) over an entire region

Calculated by figuring out the percentage differencebetween % 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 localizationquotient?


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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 theactivity and the base

Graph the data with the activity cumulative percentagevalue acting as the X and the base cumulative

percentage value acting as the Y

Compare the shape of the curve to an unconcentratedline (i.e., a line with a slope of 1)


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Gini Coefficient

Also called the index of dissimilarity

The maximum distance between the Lorenz curve and theunconcentrated line

Equivalent to the largest difference between the activityand base percentages

The Gini coefficient (and the Lorenz curve) are also usefulfor comparing 2 activities (i.e., testing similarityratherthan just concentration)


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Areal Descriptive Statistics Example

Apply arealdescriptive

statistics to the

example

livestock

distribution

05 descriptive spatial stats part1

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