# Point Patterns - PowerPoint PPT Presentation

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Point Patterns. 10/11/00. Patterns (scattered, random, or clustered). Nearest-neighbor analysis - a technique developed by plant ecologists (Clark and Evans, 1954) measuring pattern in terms of the arrangement. point pattern. d ran =1/2. A. = expected mean nearest neighbor

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Point Patterns

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## Point Patterns

10/11/00

### Patterns (scattered, random, or clustered)

• Nearest-neighbor analysis - a technique developed by plant ecologists (Clark and Evans, 1954)

• measuring pattern in terms of the arrangement

### point pattern

dran=1/2

A

= expected mean nearest neighbor

distance for a random arrangement

of points

dran

B

p=density of the points

=number of points divided by the area

=8/144=0.056

C

D

E

F

G

H

assume area is 144 km2

### Random points

dran=1/2

= 1/2x0.237

= 2.11

which means that if the point pattern is arranged randomly

the mean nearest-neighbor distance will be 2.11 km

### Dispersed Point Pattern- uniform, or regular

maximum possible distance separating them

dran=21/2/ 31/4

=1.07453/

for the previous case

dran = 4.534

Nearest

Neighbor

B

A

D

F

C

D

F

G

point

A

B

C

D

E

F

G

H

n=8

d

5

5

4

3

4

3

3

6

d=33

### Clustered pattern

• make a guess, what value will be for the dran?

### Nearest-neighbor Index

• R = dobs/dran

• ranges from 0 to 2.15 (clustered to totally dispersed)

• Random R will be 1

• The present case R = 4.125/2.11 = 1.955 (very dispersed)

### statistic test

c = (dobs - dran)/SEd

where SEd is the standard error of the mean nearest-neighbor distance =

0.26136 /

where n = number of points and p is the density of points per unit area

for the current case,

S = 0.26136/

=0.391

so, c=(4.125-2.11)/0.391 = 5.15

### Significant or not?

• 1.645 - significance level of 0.05

### Spatial autocorrelation

• Autocorrelation - the relationship between successive values of residuals along a regression line.

• Strong spatial autocorrelation means that adjacent values or ones which are near to each other are strongly related.

• Joint count statistics

### joints counting

• binary applications - electoral geography, arable/non-arable farms, poverty/non-poverty and others

• Black/white joins counting

### Exercise: Create a new project

• Projection - UTM, Zone 16

• Map units - meters

• Measurement - meters

• Create a polygon theme - with area around 200 m2 (fix your scale to 1:1000)

• copy files from GISLAB01 to your machine (today’s folder)

### Procedure

• Add a new field (Area) to your polygon theme using Area_cacu.avx (an extension)

• generate a random point patterns using “randompt2.avx” (an extension)

• Calculate the R for the point pattern within the polygon using Nearest18 (a script)

### Calculate the point pattern from your study county

• Make sure you have county boundary file ready

• Use the matched student profile as the point pattern

• Run “Nearest18” script

• Make sure you have your projection system set up.