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

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

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

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

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

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

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

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

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

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

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

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

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

Different Reference Frame Weighted standard distance Standard distance of Japan’s largest cities with population 3.27746 Standard distance of Brazil’s largest cities with population 8.84955 -> Brazil much more dispersed interurban structure Scaled weighted standard distance by the average distance between cities in each country Japan’s case: 0.2379 Brazil’s case: 0.0272 GIS and Spatial Analysis

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

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

S.D Ellipses for Shelters Y axis: Northeast ~ southwest dir. X axis: northwest ~ southeast dir. Men angle: 90-27.45=62.55 X dev.: 0.02238 Y dev.: 0.006476 Car Theft in Cleveland, Ohio GIS and Spatial Analysis

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

GIS and Spatial Analysis Next … Lab: Point Pattern Descriptors Lec: Point Pattern Analyzers Read -. Chapter 6, pp. 218-279 GIS and Spatial Analysis