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### Nearest_neighbor_by_6

Course: GEOG 500, Fall 2009
School: UWO
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Word Count: 659

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neighbor a Nearest form of point pattern analysis computational process involves the measurement of distances between points a coordinate system is created and the horizontal (X) coordinate and the vertical (Y) coordinates for the points are recorded for each point the nearest neighbor is determined distances can be derived as straight line Pythagoran form or measured directly regular once the observed distances...

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neighbor a Nearest form of point pattern analysis computational process involves the measurement of distances between points a coordinate system is created and the horizontal (X) coordinate and the vertical (Y) coordinates for the points are recorded for each point the nearest neighbor is determined distances can be derived as straight line Pythagoran form or measured directly regular once the observed distances are found we can compare the mean observed distance to a hypothesized distance clustered - the theoretical distance dE is zero since the distance between each point and its nearest neighbour would be zero the general formula is: 1 dE = 1 n A dE = where 1 is available from a table to follow n A Where n/A is the density random hexagonal lattice dE = 0.5 n A dE = 10746 . n A 1 the test is similar in form to a t test the test statistic is do - dE c= SEd c is a normal standard deviate like Z In this case 2=.26136 (see table) so SEd = 2 n2 A d o is mean of observed nearest neighbour distances d E is expected mean of nearest neighbour distances for an arrangement SEd is the standard error of the mean nearest neighbour distances SEd = 0.26136 n2 A the standard error is exactly analogous to the ordinary standard error of the mean, which is x = s n c is a standard normal deviate, like Z, so significance is determined by reference to the cumulative normal frequency table, so if =.05, cc=1.96 direct comparison of results from different problems or different regions is difficult to overcome this there is a standardized nearest neighbor index R Where d E is calculated for random situation R= do dE 2 problems the procedure as it stands suffers from serious drawbacks 1) measuring distance only to the closest nearest neighbor can result in observed mean distance values dE that are not logically consistent to get around this problem the approach can be modified to take the average distance from k closest points k is called the order for test statistics for randomness this table can be used order 1 2 1 0.5000 0.2613 2 0.7500 0.2722 3 0.9375 0.2757 4 1.0937 0.2775 5 1.2305 0.2784 6 1.3535 0.2789 2) values of test statistic are affected by the size of the area used in the calculations this is called the boundary problem details of the solutions to this problem is beyond the context this of course but there are 4 solutions a) if the surface is a rectangle or square make it into a torus (donut shaped) and then measure distances b) a disregard strategy - only use distances that are less than between point i and the boundary of the study area c) buffer zone - delimit the study area as a portion of a much larger area, measurements are only made to points within the study area d) use of Donnelly's correction factors in formulas - cannot be used for irregularly shaped areas 3 example four community services for Baltimore are shown in map many public services should be dispersed relatively equally to ensure equal access by the populace One could ask: are the existing sites of the service providing such equal access? Lets look at police service provision First we need to find the nearest neighbors for the police stations Lets look at police service provision First we need to find the nearest neighbors for the police stations The mean nearest neighbor distance is: 1.63 do = calculate the random nearest neighbor distance: area is given as 80.86, 0.26136 is from the table for the randomness test dE = .50 11 80.86 0.26136 = 0.21 121 80.06 SEd = dist = 17.97 = 163 . n 11 Example p=.1038 c= . . d o - d E 163 - 136 . = = 126 .21 SE d Determine if milk production in Puerto Rico is randomly distributed. Use the following map and table as your input. 4 Municipio Aguada Aguadilla Anasco Cabo Rojo Guanica Hormigueros Isabela Lajas Las Marias Maricao Mayaguez Moca Rincon Sabana Grande San German San Sebastian Area 30.21 35.57 40.05 72.35 36.52 11.16 55.47 60.23 47.03 36.85 56.95 50.43 14.14 35.24 53.9 70.8 X 20.0314 23.1881 23.8571 22.6322 36.6477 24.7229 29.103 29.4894 32.1001 34.9884 24.8361 25.8709 17.0815 35.0721 29.2389 32.6112 Y 54.6399 61.1065 50.1807 34.4176 30.8942 40.4245 60.8053 32.815 47.2462 43.1383 45.0923 56.0336 52.8758 37.4654 39.0352 53.1334 neighbour Rincon Moca Mayaguez Hormigueros Sabana Grande Mayaguez Moca San German Maricao Las Marias Hormigueros Aguadilla Aguada Maricao Hormigueros Las Marias distance 3.44 5.74 5.18 6.36 6.76 4.67 6.38 6.23 5.02 5.02 4.67 5.74 3.43 5.67 4.72 5.91 706.9 84.94 Test for randomness Is it random? .50 dE = = 3.3234 16 / 706.9 SE d = .26136 =.4343 162 / 706.9 84.94 do = = 5.3088 16 c= 5.3088 - 3.3234 = 4.5715 0.4343 5
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