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Point Patterns

Point Patterns. 10/11/00. Patterns (scattered, random, or clustered). Nearest-neighbor analysis - a technique developed by plant ecologists (Clark and Evans, 1954) measuring pattern in terms of the arrangement. point pattern. d ran =1/2. A. = expected mean nearest neighbor

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Point Patterns

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  1. Point Patterns 10/11/00

  2. Patterns (scattered, random, or clustered) • Nearest-neighbor analysis - a technique developed by plant ecologists (Clark and Evans, 1954) • measuring pattern in terms of the arrangement

  3. point pattern dran=1/2 A = expected mean nearest neighbor distance for a random arrangement of points dran B p=density of the points =number of points divided by the area =8/144=0.056 C D E F G H assume area is 144 km2

  4. Random points dran=1/2 = 1/2x0.237 = 2.11 which means that if the point pattern is arranged randomly the mean nearest-neighbor distance will be 2.11 km

  5. Dispersed Point Pattern- uniform, or regular maximum possible distance separating them dran=21/2/ 31/4 =1.07453/ for the previous case dran = 4.534

  6. d = d /n = 33/8 = 4.125 Nearest Neighbor B A D F C D F G point A B C D E F G H n=8 d 5 5 4 3 4 3 3 6 d=33

  7. Clustered pattern • make a guess, what value will be for the dran?

  8. Nearest-neighbor Index • R = dobs/dran • ranges from 0 to 2.15 (clustered to totally dispersed) • Random R will be 1 • The present case R = 4.125/2.11 = 1.955 (very dispersed)

  9. statistic test c = (dobs - dran)/SEd where SEd is the standard error of the mean nearest-neighbor distance = 0.26136 / where n = number of points and p is the density of points per unit area for the current case, S = 0.26136/ =0.391 so, c=(4.125-2.11)/0.391 = 5.15

  10. Significant or not? • 1.645 - significance level of 0.05

  11. Spatial autocorrelation • Autocorrelation - the relationship between successive values of residuals along a regression line. • Strong spatial autocorrelation means that adjacent values or ones which are near to each other are strongly related. • Joint count statistics

  12. joints counting • binary applications - electoral geography, arable/non-arable farms, poverty/non-poverty and others • Black/white joins counting

  13. Black/white join

  14. Exercise: Create a new project • Projection - UTM, Zone 16 • Map units - meters • Measurement - meters • Create a polygon theme - with area around 200 m2 (fix your scale to 1:1000) • copy files from GISLAB01 to your machine (today’s folder)

  15. Procedure • Add a new field (Area) to your polygon theme using Area_cacu.avx (an extension) • generate a random point patterns using “randompt2.avx” (an extension) • Calculate the R for the point pattern within the polygon using Nearest18 (a script)

  16. Calculate the point pattern from your study county • Make sure you have county boundary file ready • Use the matched student profile as the point pattern • Run “Nearest18” script • Make sure you have your projection system set up.

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