Descriptive Statistics for Spatial Distributions

1. Descriptive Statistics for Spatial Distributions Chapter 3 of the textbook Pages 76-115

2. Overview • Types of spatial data • Conversions between types • Descriptive spatial statistics

3. Applications of descriptive spatial statistics: accessibility/nearness • What 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).

4. Applications of Descriptive spatial statistics: dispersion • How dispersed are the data? • Do the data cluster around a number of ‘centers’?

5. Types of Geographic Data • Areal • Point • Network • Directional • How does this concept fit with the scale of measurement?

6. Switching Between Data Types • Point to area • Thiessen Polygons • Interpolation • Area to point • Centroids

7. Thiessen Polygons • According to the book… • 1) Join (draw lines) between all “neighboring” points • 2) Bisect these lines • 3) Draw the polygons • Making 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 polygons

8. Thiessen Polygons Example

9. Spatial Interpolation:Inverse Distance Weighting (IDW) point i known value zi distance di weight wi unknown value (to be interpolated) at location x The estimate of the unknown value is a weighted average Sample weighting function

10. Interpolation Example • Calculate the interpolated Z value for point A using B1 B2 B3 B4

11. Interpolation Example point i known value zi distance di weight wi unknown value (to be interpolated) at location x

12. Descriptive Statistics for Areal Data • Location 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

13. Descriptive Statistics for Areal Data • Location 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 population • How is this different from the localization quotient?

14. Descriptive Statistics for Areal Data • Lorenz 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)

15. Gini Coefficient • Also called the index of dissimilarity • The maximum distance between the Lorenz curve and the unconcentrated line • Equivalent to the largest difference between the activity and base percentages • The Gini coefficient (and the Lorenz curve) are also useful for comparing 2 activities (i.e., testing similarity rather than just concentration)

16. Areal Descriptive Statistics Example • Apply areal descriptive statistics to the example livestock distribution