Spatial statistics Lecture 3 2/4/2008 What are spatial statistics • • • • Not like traditional, a-spatial or non-spatial statistics But specific methods that use distance, space, and spatial relationships as part of the math for their computations It is a spatial distribution and pattern analysis tool – Identifying characteristics of a distribution; tools used to answer questions like where is the center, or how are feature distributed around the center? (Measuring Geographic Distributions) – Quantifying or describing spatial pattern; are our features random, clustered, or evenly dispersed across our study area? (Analyzing Patterns) – Mainly deal with point, line, polygon (vector) Why use spatial statistics? – To help assess patterns, trends, and relationships • Better understanding of geographic phenomena • Pinpoint causes of specific geographic patterns • Make decision with high level of confidence • Summarize the distribution in a single number Global Local 1. Measuring geographic (spatial) distribution – Not only crime analysts but also GIS practitioners in many research areas, such as epidemiology, archaeology, wildlife biology, and retail analysis, will benefit from the spatial statistics tools in ArcGIS 9. These tools can be easily modified or extended because most were written using the Python scripting language. The source code for the statistical tools can be accessed from ArcToolbox and serve as samples and templates for further customization Mean center of population distribution and pattern, Track changes in the distribution Average of x, y coordinates Mean center and central feature tools tell about the center of a distribution But do not tell the overall distribution. Standard distance tool tells how dispersed our features are around that center Analyzing spatial patterns • Give us ways to measure the degree to which our features are clustered, dispersed, or randomly distributed across the study area • Analyzing Patterns – Global calculations – Identifies the patterns/overall trends of data • Are features clustered and what is the overall pattern? – Spatial Autocorrelation tool • Mapping Cluster – Local calculations – Identifies the extent and location of clustering or dispersion • Where are the clusters (or where are the hot spots)? – Hot Spot Analysis tool Meaning the clustering in 2003 is more intense than it was in 1994 • Z score is a measure of standard deviation. If you have σ is (-1.96, 1.96), z score is falling between them, you are seeing a pattern of random pattern. If z score falls outside, like -2.5 or 5.4, then you have a pattern that’s too unusual to be a pattern of random chance If there is any place in the USA where people either dying earlier, or living longer, than the average American? Blue living longer than normal, red living shorter than normal • In the global analysis previously, we ask: is there clustering? • In the local analysis, we ask: where are the clusters, or where do features with similar attribute values cluster spatially together? – Hot spots tool reference • “understanding Spatial Statistics in ArcGIS 9” by Sandi Schaefer and Lauren Scott.