1. Summary of Prev. Lecture
Parametric Test Continue
Significance of Pearson’s C using t-Statistic
Correlation is not different from 0
Significance of Regression Parameters
Validity: t-statistic
Meaning: F-test
Nonparametric Test
Chi-Square Statistic
Meaning of the correlation between two nominal or categorical data
H0: the observed statistic is not significantly different from zero
Spearman’s Rank Correlation Coefficient using t-statistic
Correlation between two strong ordered data
Kolmogorov-Smirnov Test using K-S D-statistic
Correlation between two weak ordered data
GIS and Spatial Analysis

2. Point Pattern Descriptor
Geography KHU Jinmu Choi
Overview (2)
Points and point pattern
Central Tendency (7)
Mean center, weighted mean center, median center
Dispersion (4)
Standard distance, Standard deviational ellipses
Summary and Next…
GIS and Spatial Analysis

3. GIS and Spatial Analysis
Point Feature
Statistics vs. Spatial Statistics
Location and attribute
Spatial data: point, line, polygon
Points
Little or no spatial extent
A house on a city map
The location of events or incidences
Representative points or the geometric centroids of a polygon
GIS and Spatial Analysis

4. GIS and Spatial Analysis
Point Pattern
Point pattern statistics
To summarize the distribution of a set of points
Descriptors
Centrographic measures: the description of any spatial relationship between individual points
The magnitude of spatial dispersion of a given set of points
The direction bias of a set of points
GIS and Spatial Analysis

5. GIS and Spatial Analysis
Central Tendency
A representative value of a given set of values
Median house value: quick impression on house price
Most common style of houses: general idea about house style in the area
Mean house income: socioeconomic condition in the area
Spatial central tendency
Mean center, weighted mean center, median center
GIS and Spatial Analysis

6. GIS and Spatial Analysis
Mean Center
Spatial mean
Average location of a set of points
Selecting coordinate system
Orienting a proper direction for the project
Situating a proper origin
Using suitable measurement unit
GIS and Spatial Analysis

7. GIS and Spatial Analysis
Mean Center of Shelter
GIS and Spatial Analysis

8. GIS and Spatial Analysis
Weighted Mean Center
Consider weight (attribute)
Women only, relatively large capacity !!!
The calculation of the mean center needs to consider more than just the location of points: when different frequencies or occurrences
Weight variable depends on the issue being studied
School locations, the number of students
GIS and Spatial Analysis

9. GIS and Spatial Analysis
Shelter Capacity
Weight: Concerned with shelter capacity
GIS and Spatial Analysis

10. GIS and Spatial Analysis
Median Center
Minimum distance location from all points
Median center
Median center with weight
Weight can be + or -
GIS and Spatial Analysis

11. Deriving Median Center
Algorithm for Mean Center
Step1. Use mean center as initial median center
Step2. Iteration
Step3. Repeat Step2
until the distance is less than a threshold
GIS and Spatial Analysis

12. GIS and Spatial Analysis
Standard Distance
Relationship between two sets of points
Forest fire locations vs. camping cabin locations
Dispersion: forest fire
Orientation: camping cabin along routes
Standard distance
The average deviation from the spatial mean
Weighted standard distance
GIS and Spatial Analysis

13. Standard Distance of Shelter
Comparing the results from the men-only and women-only shelters offers some insights
Location and spatial dispersion size
GIS and Spatial Analysis

14. Different Reference Frame
Weighted standard distance
Standard distance of Japan’s largest cities with population
Standard distance of Brazil’s largest cities with population
-> Brazil much more dispersed interurban structure
Scaled weighted standard distance
by the average distance between cities in each country
Japan’s case:
Brazil’s case:
GIS and Spatial Analysis

15. Standard Deviational Ellipses
Directional bias
Accidents along a section of a highway, not a circle
Components of S.D. Ellipses
An angle of rotation
Angle btw. North and the y-axis
Deviation along the major axis
Maximum bias direction of points
Deviation along the minor axis
Perpendicular to the major axis
+ angle value: x = minor, y = major
- angle value: x = major, y = minor
GIS and Spatial Analysis

16. GIS and Spatial Analysis
Deriving Ellipsoid
Choose mean center as Origin of new reference
Transform coordinate of each points with new origin
Calculate rotation angle
X and y deviation
GIS and Spatial Analysis

17. S.D Ellipses for Shelters
Y axis: Northeast ~ southwest dir.
X axis: northwest ~ southeast dir.
Men
angle: =62.55
X dev.:
Y dev.:
Car Theft in Cleveland, Ohio
GIS and Spatial Analysis

18. GIS and Spatial Analysis
Summary
Points and point pattern
Locations and distribution of locations
Mean center: spatial mean
Weighted mean center
Spatial mean considering attributes
Median center
Min. distance center from all points
Standard distance
Average distribution of points from the mean center
Standard deviational ellipses
Spatial distribution of points considering directional bias
GIS and Spatial Analysis

19. GIS and Spatial Analysis
Next …
Lab: Point Pattern Descriptors
Lec: Point Pattern Analyzers
Read
-. Chapter 6, pp
GIS and Spatial Analysis