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Summary_A - 6 Knox Statistic for Space-Time Clustering The...

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6. Knox Statistic for Space-Time Clustering The Knox approach is used to test whether there is a significant cluster during a defined distance and time period. First it counts the number of point pairs as either close or distant in space and /or time, then calculates the P-value. Formula For a certain distance d and time period t , the Knox statistic calculates the following number: d(i, j) is the distance of point i and j, t(i, j) is the time interval of point i and j, : the number of point pairs (i, j) with d(i, j) d , and t(i, j) t , : the number of point pairs (i, j) with d(i, j) d , and t(i, j) > t , : the number of point pairs (i, j) with d(i, j) > d , and t(i, j) t , : the number of point pairs (i, j) with d(i, j) > d , and t(i, j) > t , N is the total number of point pairs ( ) The P-value is: where , Input 1. Input data file, which should record X, Y coordinates of points and T the times attached to each points (time elapsed in days, or years or minutes, etc). 2. The time interval.

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3. The distance interval. 4. Output file. Output 1. The input data file name, 2. The total number of points, 3. The minimum and maximum of X, and Y coordinates, and time. 4. The time and distance intervals. 5. The number of point pairs tabulated as t(i, j) <= t t(i, j) > t Space only d(i, j) <= d d(i, j) > d Time only N 6. EN11 is the expected value of . 6. The P-value. Low P-values (e.g., 0.01) represent significant time-space clustering.
7. Join-Count Statistics for Spatial Autocorrelation (Free sampling model) Join-Count statistics are the simplest measure of spatial autocorrelation. They are used for a binary variable ( 1 or 0 ). The two values of the variable are referred to as "black" ( B ) and "white" ( W ). A join links two neighboring areas. So the possible types of joins are black-black ( BB ), black-white ( BW ), and white-white ( WW ). Join counts are counts of the numbers of BB , BW , and WW joins in the study area, and these numbers are compared to the expected numbers of BB, BW and WW joins under the null hypothesis of no spatial autocorrelation. Formulas The observed number of BB, BW and WW joins are given by [1] [2] [3] Where is the binary value, 1 for black, 0 for white, w(i, j) is the binary weight, 1 if two areas are contiguous, 0 otherwise. For different assumptions about the data, the theoretical expressions for E(BB), E(BW) and E ( WW ) will vary. Under the free sampling model, the expected BB, BW and WW are:

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is the number of areas with B values. The variances are Where Input 1. Input data file, which records the binary value for each area. 2. Input weight matrix file, which is an N by N weight matrix with 1 for contiguous areas, 0 otherwise. 3. Output file.
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This note was uploaded on 02/15/2012 for the course GEO 6938 taught by Professor Staff during the Summer '08 term at University of Florida.

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Summary_A - 6 Knox Statistic for Space-Time Clustering The...

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