Lecture 4. Spatial Statistics

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1 Lecture 4 Spatial Statistics

2 Lecture 4 Outline Statistics in GIS Spatial Metrics Cell Statistics Neighborhood Functions Neighborhood and Zonal Statistics Mapping Density (Density surfaces) Hot Spot Analysis

3 Statistics in GIS Describe certain tendencies in your data. Create new raster datasets Statistical Functions are divided in 3 basic groups: Cell Statistics Neighborhood Statistics Zonal Statistics Methods include: Max, min, standard deviation, sum, mean, etc.

4 Statistics in GIS Spatial Metrics Mean Center: Identifies the geographic center (or the center of concentration) for a set of features. Central Feature: Identifies the most centrally located feature in a point, line, or polygon feature class.

5 Statistics in GIS Spatial Metrics Standard Distance: Measures the degree (compactness) to which features are concentrated or dispersed around the points (or feature centroids) in an input feature class. The value is a distance which is represented by a circle. Directional Distribution: Measures whether a distribution of features exhibits a directional trend (whether features are farther from a specified point in one direction than in another direction).

6 Cell Statistics Allows you to compare two or more raster datasets on a cell by cell basis. Find trends or detect change. Ex. To analyze time series data such as change in landuse. In this example, the middle layer was developed three years before the top layer. In the resulting raster, the gray cells indicate where more than one land use value has occurred. The Cell Statistics function is like sinking an elevator shaft through the matching cells of each raster dataset.

7 Neighborhood Functions Offer exceptional analytical power and flexibility. Operation applied to a raster and stored in an output raster. Depends on the concept of a moving window. The window can be any size or shape. Square, rectangle, circle, etc. Operations can be simple or complex. Ex. Sum, max, min, slope, aspect, etc.

8 Neighborhood Functions The Neighborhoods Statistics function considers the values of cells within a specified neighborhood around the processing cell. With a 3-cell by 3-cell neighborhood, the evaluation cell is located in the center of the neighborhood.

9 Neighborhood Functions Kernels The moving window may be defined by a kernel. A kernal is a set of constants for each cell in a given window. Represents a mean function.

10 Zonal Statistics The Zonal Statistics function considers the values of cells based on groups of like cells, or zones from another dataset. Any two or more cells with the same value belong to the same zone. Zones are composed of regions. A region is a group of connected cells in a zone. In this graphic, there are six zones, but only one is delineated.

11 Produces a table of statistics and a graph. Zonal Statistics

12 Mapping Density Core Area Mapping Core Area: A primary area of influence or activity for an organism, object or resource of interest. Ex. Clustering or patterns in crime. Ex. Home range of endangered animals Usually involves identifying area features from a set of points or lines.

13 Mapping Density The simplest and most obvious measures of central location: Mean Center: Average X, Y coordinates of the sample points. Mean Circle: Defined by the radius measured from the mean center.

14 Mapping Density Kernel Mapping Uses a set of sample locations to estimate a continuous density surface. Calculates the density of features in a neighborhood around those features. The values associated with each point are spread from the point location to the specified radius. Can be calculated for both point and line features.

15 Mapping Density Hot Spot Analysis The tool calculates the Getis-Ord Gi statistic. The G-statistic tells you whether features with high values or features with low values tend to cluster in a study area. Output of G-statistic is the Z score. High Z score = More Clustering Low Z score = Less clustering

16 Mapping Density Hot Spot Analysis Applications: crime analysis, epidemiology, voting patterns, economic geography and demographics. Raw Crime Data Hot Spot Analysis - Location of clusters of tracts in which vandalism represents a larger than expected proportion of all crime events. - Normalized with data from all crime incidents for Lincoln, Nebraska. Y:\courses_dbram\Geog_406\Lectures\E911_SpatialStatisticsAnalysisMap.pdf

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