Descriptive Statistics for Spatial DistributionsOverviewApplications of descriptive spatial statistics: accessibility/nearnessSlide 4Types of Geographic DataSwitching Between Data TypesThiessen PolygonsThiessen Polygons ExampleSlide 9Interpolation ExampleSlide 11Descriptive Statistics for Areal DataSlide 13Slide 14Gini CoefficientAreal Descriptive Statistics ExampleDescriptive Statistics for Spatial DistributionsChapter 3 of the textbookPages 76-115OverviewTypes of spatial dataConversions between typesDescriptive spatial statisticsApplications of descriptive spatial statistics: accessibility/nearnessWhat types exist?Examples:–What is the nearest ambulance station for a home?–A point that minimizes overall travel times from a set of homes (where to locate a new hospital).–A point that minimizes travel times from a majority of homes (where to locate a new store).How dispersed are the data?Do the data cluster around a number of ‘centers’?Applications of Descriptive spatial statistics: dispersionTypes of Geographic DataArealPointNetworkDirectionalHow does this concept fit with the scale of measurement?Switching Between Data TypesPoint to area–Thiessen Polygons–InterpolationArea to point–CentroidsThiessen PolygonsAccording to the book…–1) Join (draw lines) between all “neighboring” points–2) Bisect these lines–3) Draw the polygonsMaking Thiessen polygons is all about making triangles–Draw connecting lines between points and their 2 closest neighbors to make a triangle (some points may be connected to more than 2 points)–Bisect the 3 connecting lines and extend them until they intersect –For acute triangles: the intersection point will be inside the triangles and all bisecting lines will actually cross the original connecting lines–For obtuse triangles: the intersection point will be outside the triangles and the bisecting line opposite the obtuse angle won’t cross the connecting line–The bisecting lines are the edges of the Thiessen polygonsThiessen Polygons Examplepoint iknown value zidistance diweight wiunknown value (to be interpolated) atlocation xiiiiixwzwz21iidw The estimate of the unknown value is a weighted averageSample weighting functionSpatial Interpolation:Inverse Distance Weighting (IDW)Interpolation ExampleCalculate the interpolated Z value for point A using B1 B2 B3 B4Interpolation Examplepoint iknown value zidistance diweight wiunknown value (to be interpolated) atlocation xiiiiixwzwz21iidw Descriptive Statistics for Areal DataLocation Quotient–Basically the % of a single local population / % of the single population for the entire area–The textbook refers to these groups as the activity (A) and base (B)–Example: % of people employed locally in manufacturing / % of manufacturing workers in the region–Each polygon will have a calculated value for each category of workerBiBAiALQiii//Descriptive Statistics for Areal DataLocation Coefficient–A measure of concentration for a single population (or group, activity, etc.) over an entire region–Calculated by figuring out the percentage difference between % activity and the % base for each areal unit–Sum either the positive or negative differences–Divide the sum by the total populationHow is this different from the localization quotient?Descriptive Statistics for Areal DataLorenz Curve–A method for showing the results of the location quotient (LQ) graphically–Calculated by first ranking the areas by LQ–Then calculate the cumulative percentages for both the activity and the base–Graph the data with the activity cumulative percentage value acting as the X and the base cumulative percentage value acting as the Y –Compare the shape of the curve to an unconcentrated line (i.e., a line with a slope of 1)Gini CoefficientAlso called the index of dissimilarityThe maximum distance between the Lorenz curve and the unconcentrated line Equivalent to the largest difference between the activity and base percentagesThe Gini coefficient (and the Lorenz curve) are also useful for comparing 2 activities (i.e., testing similarity rather than just concentration)Areal Descriptive Statistics ExampleApply areal descriptive statistics to the example livestock